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Thursday, 30 April 2015

This Guy Captures Delightfully Weird Photos Of Squirrels Weightlifting

Max Ellis poses the squirrels right in his London backyard.

London photographer Max Ellis often photographs body builders.

London photographer Max Ellis often photographs body builders.

Max Ellis / Via maxphotographic.com

But they're no match for the buff squirrels he encounters in his own backyard.

But they're no match for the buff squirrels he encounters in his own backyard.

Max Ellis / Via maxphotographic.com

OK, so Ellis actually does some behind-the-scenes staging to get his Squirrelisimo photos exactly right.

OK, so Ellis actually does some behind-the-scenes staging to get his Squirrelisimo photos exactly right.

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He hangs the props from fishing wire and waits for the right moment, which can take anywhere from a few minutes to a few days.

He hangs the props from fishing wire and waits for the right moment, which can take anywhere from a few minutes to a few days.

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19 Puppies Who Are Here To Encourage You During Finals

You got this!

"You're the greatest!"

"You're the greatest!"

Via s214.photobucket.com

"Chase your dreams!"

"Chase your dreams!"

Via reddit.com

"Gimme a high five!"

"Gimme a high five!"

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"I know you can do it!"

"I know you can do it!"

Via thefrisky.com


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This Elderly Man Punched A Bear In The Face To Save His Dog

“He looked at me like, ‘Go eff yourself.’”

Carl Moore, a 73-year-old man from Sacramento, California, saw a wild bear approaching his dog, so he did what few men would dare to do: HE PUNCHED THE BEAR IN THE FACE.

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First of all, let's get one thing clear: Carl Moore is a boss.

First of all, let's get one thing clear: Carl Moore is a boss.

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But he also has a sensitive side. This is Lacey, his beloved dog who almost got mauled by a bear:

But he also has a sensitive side. This is Lacey, his beloved dog who almost got mauled by a bear:

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After he heard Lacey whimpering, Carl ran outside to see what was happening and immediately confronted the bear.

After he heard Lacey whimpering, Carl ran outside to see what was happening and immediately confronted the bear.

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This Puppy Doesn't Know How Hiccups Work And It's Adorable

Hiccuping has never been so cute.

Puppies are cute, but hiccups can be bothersome. YouTube user Matthew Kennelly recently uploaded a video of his blue heeler puppy Buck, is adorably confused by the whole process.

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Buck initially hiccups and stands still.

Buck initially hiccups and stands still.

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After another, he growls and snaps at it.

After another, he growls and snaps at it.

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After one more, he barks in confusion to make them go away.

After one more, he barks in confusion to make them go away.

Matthew captioned the video,"What are these things inside me!? I will scare them away!"

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How To Draw A Dog That Will Take You Back To Your Childhood

Better known as the story that turns into a dog.

There once was a man with no arms.

There once was a man with no arms.

Elaina Wahl

He was chased by a swarm of bees.

He was chased by a swarm of bees.

Elaina Wahl

So he jumped into a pond to escape them.

So he jumped into a pond to escape them.

Elaina Wahl

But he drowned. So he was buried in a cemetery.

(Those are headstones in case you missed the connection.)

But he drowned. So he was buried in a cemetery.

Elaina Wahl


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A Glance Into The Inner Workings Of The Internet

Because you wanted to know what it really looks like. (H/T LaughingSquid)

Basically, it's complete and totally adorable chaos.

ALL BEDLAM, ALL THE TIME.

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21 Dog Pictures For Anyone Who's Feeling Down

BECAUSE DOGS.

This lil' guy being real brave at the vet.

This lil' guy being real brave at the vet.

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And this insanely happy camper.

And this insanely happy camper.

i.imgur.com

This wrinkly dude with his teddy buddy.

This wrinkly dude with his teddy buddy.

i.imgur.com

And this champion billiards shooter.

And this champion billiards shooter.

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This Hip Cat Knows How To Ring A Bell For Treats

Pavlov’s cat?

Pecan, a very well-dressed kitty, has learned to ring a bell for treats.

Impressive.

watergirlmv / Via youtube.com

Not only does Pecan know how to rock a plaid button-down, he knows what he wants and how to get it!

Not only does Pecan know how to rock a plaid button-down, he knows what he wants and how to get it!

watergirlmv / Via youtube.com

He could just ring that bell all day. And who could say no to that face?

He could just ring that bell all day. And who could say no to that face?

watergirlmv / Via youtube.com

All of the treats, please!

All of the treats, please!

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A Pig's Guide To Being A Dog

Don’t let the cat take advantage of you.

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19 Times Koalas Were Total Badasses

Koala-fied to not give a f**k.

When they demanded first class service.

When they demanded first class service.

"Bow down to me bitches".

Qantas

When they wrestled each other in broad daylight.

When they wrestled each other in broad daylight.

"Smack down".

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When they took a stroll down main street like it was nobody's business.

When they took a stroll down main street like it was nobody's business.

"Coming through peasants".

Facebook: chris.kerrigan.100

When they didn't care for your driving.

When they didn't care for your driving.

"Cop this".

Facebook: MeanwhileInAustralia


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15 Inspiring Stories Of Rescue Animals Who Saved Their Humans

Sometimes it’s hard to tell who rescued who.

We asked members of the BuzzFeed Community to tell us their animal adoption stories. Here are a few of the heartwarming and inspiring responses.

We asked members of the BuzzFeed Community to tell us their animal adoption stories. Here are a few of the heartwarming and inspiring responses.

Creative Commons / Flickr: pictureclara

I adopted an orange tabby, Rowdy, who is a wonderful kitty. The night I brought him home, there was a small fire in the basement of our house. My roommate and I both slept through the alarms and the smoke was really filling the house. I only woke up because Rowdy was prancing over my bed and patting at me until he woke me up. He was the only thing I grabbed when we evacuated the house.

Submitted by Jessica Chi, Facebook

I have schizophrenia that is more intense at night, and my hallucinations make it extremely difficult to sleep, and it affects me daily. When I first met Bam Bam in the shelter, I would have never guessed how dependent on him I would grow to be. He sleeps nestled between my stomach and thighs, and feeling his warm body brings me so much comfort that I can now sleep through the night most of the time. I can't sleep without him anymore!

Submitted by laurenpratt1997

Creative Commons / Flickr: 30800139@N04


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How to Make a Wedding Toast

Whether you want to give a speech at a wedding or you've been asked to, the idea of performing a wedding speech properly can be a nerve-wracking process. It doesn't have to be. Learning to find a good theme for your speech, write it out clearly, and perform your speech well can take the stress out of the equation and ensure that you'll give the best speech you can.

Steps

Finding a Theme

  1. Start brainstorming the toast early. This is your chance to honor the couple, so don't wait until the night before the wedding to think of what you're going to say. Even if you want to be spontaneous in part, it's good to have a toast written out in note form in case your mind goes blank.

    Make a Wedding Toast Step 01.jpg
    • Start by brainstorming different anecdotes, stories, or themes that your speech might take on. What do you think of immediately when you think of your friend or relative who is getting married?
    • What do you want to say about your friend? What do you want to emphasize? Start thinking of the major ideas that you'd like to include in your speech. What's important about this union of two people?
    • Alternatively, don't worry about themes or abstract concepts and just start writing. Put pen to paper and free-write about the person who you're toasting. Aim to write for 10 minutes without stopping. Just keep your pencil moving. See what comes up.
  2. Keep it short, sweet, and personal. The best wedding toasts are sincere stories that come straight from the heart. While some may be funny and others may be sad, all wedding toasts should have one thing in common: paying tribute to the couple, or one member of the couple, and celebrating their union in a personal way.

    Make a Wedding Toast Step 02.jpg
    • You don’t have to be a stand-up comedian. A humorous quote or story can add a nice touch, just keep it tasteful. Anecdotes that involve nakedness, drunkenness, or ex-significant others could make the moment awkward if the story falls flat. Err on the side of sincerity.
  3. Make the toast about the couple. Giving a toast isn’t an opportunity to show off. It isn’t your day and the toast shouldn’t be about you, even if you're a central character in one of those stories you're telling. Whether you’re telling an anecdote or reciting a poem, the toast should connect with the couple, pay tribute to them, and come from the heart.

    Make a Wedding Toast Step 03.jpg
    • To do a double-check, count up all the uses of "I" in your speech and all the uses of the newlyweds' names. If you show up more than them, you might need to revise the speech.
    • Speeches that dwell on how difficult marriage is, however realistic, can make it sound like the couple is doomed to fail. It's usually best to avoid cold or intellectual speeches. Just go for sincere emotion.
    • Treat the bride and groom as a single unit, even if you've known only one of them for a long time. Also, remember, you're not toasting to the "good old days," you're toasting to their future.
  4. Find your “in.” All a toast needs to get going is one little anecdote, moment, or theme to get you up and running. That’s your “in.” Typical wedding toasts will revolve around the first time you heard about your friend’s new partner, or the first time you realized the couple was an important part of your life, and those are perfect ways to open up the toast and make it personal. It’ll be unique because it’s your story. You can also think of creative ways to find your in:

    Make a Wedding Toast Step 04.jpg
    • Start your toast with a story about a challenge the couple faced together, or how one member of the couple used the other for support in a time of need.
    • Start your toast with observations about the way a member of the couple has changed since they started seeing each other.
    • When you’re old and gray, what will you remember most about the couple? What one thing will you think of?
    • Start your toast by celebrating an unheralded character trait in one or both members of the couple. If the groom is an astrophysicist, but you’ve seen him do something no one else has, consider starting there. Keep it clean.

Writing the Speech

  1. Outline the speech. Once you've found some themes, stories, or ideas that you want to cover in your speech, you can go one of two ways: writing out the speech word-for-word, or outlining the major points. Both are equally effective methods of writing a speech for a wedding.

    Make a Wedding Toast Step 05.jpg
    • If you want to be more spontaneous and conversational, jot down the major talking points to jog your memory and keep your speech moving forward in a casual manner. Include short quotes or key phrases like "Talk about meeting bride for first time, mention how comfortable they were with each other." The idea is for the note to jog your memory, but the actual wording should be off the top of your head, provided you follow the next step.
    • If the idea of going freestyle freaks you out, write it out word for word and take special care to bring yourself back to the audience. Script out everything, down to the gestures, pauses, and glances up. Don’t give yourself any chance to mess up. Practice to make sure your speech isn't robotic.[1]
  2. Write your speech on index cards. You might get flashbacks of making presentations in school, but that's a good thing. You want this to be good. Putting notes on index cards is a good way of keeping yourself organized and concise, especially if you're not confident in your public speaking abilities.[2]

    Make a Wedding Toast Step 06.jpg
    • If you're writing out your speech word-for-word, keep the speech big enough so that you'll be able to read it easily. Don't cram everything onto one card. Still, it's important to keep your cards manageable, so aim to have no more than three or four cards. Number your cards to make sure they're in order.
    • If you're writing out your major speech points only, write them clearly and concisely. You should know your own shorthand: make sure that you don't write "Talk about that party" on a card and go blank in the moment.
  3. Include an ending for the toast. Include a formal indication to inform them of the ending of the toast and what to say next. For example: "Let us now toast the happiness of Jill and Jack. To Jill and Jack!" As you say this, wave your glass to all, then tip it towards the person you are toasting to, or clink their glass if you're close enough.[3]

    Make a Wedding Toast Step 07.jpg
  4. Practice. You should aim to trim your speech into about two minutes of solid-gold stuff that comes straight from the heart. There will likely be lots of toasts and lots of talking at most weddings, and people will be ready to eat and dance at some point, so you don't want to be the one who rambles on and stumbles over their words. Whatever the tone, the style, or the content of your wedding speech, practice it until you've smoothed out all the edges and made it short and sweet.

    Make a Wedding Toast Step 08.jpg
    • Do not write a long speech. A whole wedding ceremony is sometimes as short as 15 or 20 minutes. There's no reason you should give a toast that goes for more than five.
    • Modify your index cards as needed. If you find yourself rushing during one part of the speech, write "slow down" somewhere on the card where you'll see it. If you repeatedly stumble over one part, just skip it. If something isn't working, go with something else.
    • If you're very nervous about the speech, try to imagine where the audience is sitting, for example, and pretend to make gestures and eye contact in that direction. If you practice, it'll be automatic in the moment.

Making the Speech

  1. Find out when toasts will be given. If you’re toasting the happy couple, chances are you're not the only one. In formal weddings, the toast is usually given after the meal, between cake-cutting and desert, or after the first dances.[4] Always check with the toastmaster or the emcee of the event to find out the schedule and order of the toasts. One traditional order for toasts is as follows:

    Make a Wedding Toast Step 09.jpg
    • The father of the bride or an old friend of the family will toast the couple.
    • The groom will toast the bridesmaids.
    • The best man will toast the parents of the couple.
  2. Read the room. Before zero-hour, you’ve got a last chance to read the room and determine whether or not your written speech is appropriate. It’s never too late for an audible. If you were expecting college friends and young people and got a room full of over-60, will your toast still be acceptable? Might you cut it short before the Las Vegas story?

    Make a Wedding Toast Step 10 Version 2.jpg
    • If you find yourself in an emergency situation, in which you feel you must throw out your speech, make sure you have something to back it up with. It wouldn't be inappropriate to go super-short but sincere, saying something like, "There's nothing to me more thrilling than seeing these two people commit to each other for the rest of their life. Before I get choked up, I'm going to leave it at that."
  3. Make your first drink the toast itself. Common wedding mistake: calming nerves with a few too many. Don’t risk making your thoughtful toast an awkward scene by slurring your words and stumbling to the microphone. Avoid drinks before you have to give your toast and celebrate with one afterwards. It’ll taste better.

    Make a Wedding Toast Step 11.jpg
  4. Stand up when it’s your turn. Some toasts are signaled by everyone clinking glasses, while in others the room will be totally silent and the emcee will introduce each toaster with a microphone. Whatever the protocol, follow it.

    Make a Wedding Toast Step 12.jpg
    • In some cultures, it’s important to make sure that all glasses are filled before giving the toast. Look around and check that all glasses (including yours) are full before making the toast. There should be wine, champagne, or something that looks like wine or champagne in your glass, as toasting with water is offensive in some cultures.
  5. Announce your relationship to the couple. Some people at the wedding might not know who you are, so making this clear at the beginning will avoid any confusion. Bring your glass down as you start to speak, but continue holding it in one hand.

    Make a Wedding Toast Step 13.jpg
  6. Give the speech as best as you can. Look at the person you're toasting to, but also shift eye contact towards the guests occasionally. Make a conscious effort to look up and engage with everyone. Watching some read coldly and robotically from a note card is hard to get involved with.

    Make a Wedding Toast Step 14.jpg
    • If you find yourself talking quickly, which happens to some people due to nerves, make a conscious effort to slow down. Pause between your sentences and take a breath. Look up, take a sip of your drink, and slow down. Speak clearly and get through it. Then, cheers.


Tips

  • Since weddings are as individual as the couples that have them, feel free to adjust your words and the toasting conventions to suit the occasion.
  • The toast will certainly be colored by the lens you view the couple through, but check to be sure that the star in the toast is the couple (or at least the half of the couple you know) and not the person giving it.
  • Usually, the people in the wedding party are more familiar with one half of the newly married couple than the other. Try to get to know that other person as much as possible, and include something that relates to a unique aspect of both the bride and groom - something about their personality or their interests.
  • It can be tempting to do a short, sweet and generic toast. But the couple would probably like something a little more personal, otherwise it may seem like you didn't care about this duty, or that the couple isn't interesting enough to be the subject of a toast.
  • Bring tissues if you think you may shed a few tears while you're speaking.
  • An audience will be very forgiving as long as your toast is heartfelt, decent, and relatively short. A TV commercial is only 30 seconds long. Only confident speakers should go longer than a minute and a half.

Warnings

  • Avoid inside jokes as well as other references which might be deemed inappropriate for the occasion. For this reason, you should probably avoid any lines about how this is unfortunately the end of your friends "wild" days, even if the two of you were "partners in crime" so to speak.
  • Do not use this event as a way to kick-start your comedy career. If you tell a joke and it bombs, finish up as quickly as possible.
  • Don't drink before you toast. Your speech should be spoken, not slurred.

Related wikiHows


Sources and Citations


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Wednesday, 29 April 2015

10 Signs Your Dog Is Your Best Friend

Two beers before lunch? Fido isn’t counting.

You're on the same page about almost everything.

You look at each other knowingly when a friend asks if you want to kick it in the park and play some disc golf. The two of you also assume the friend will sit in the backseat on the way there.

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PDA is natural and expected.

No uncomfortable hugs between you two. Whether it's lazy naps together on the couch, or completely casual face licks — it's all about the love.

Adventure means being together.

Your family rolls their eyes when you ask if the hotel for the family vacation is "pet friendly." You never consider going on a cruise because your dog gets seasick. And forget about flying an airline that doesn't allow your best pal in the cabin.

You both have the same taste in music.

You both have the same taste in music.

Or at least that's what you tell yourself when you don't hear any complaints from the pooch in the passenger seat. He knows you're still heartsick about Kim Gordon and Thurston Moore splitting up. He doesn't judge.

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17 Times Petunia Tender-Mulaney Was Your Inspiration

Somehow, she makes being awesome look effortless.

When she schooled you in proper airport etiquette.

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When she oyster'd up for bedtime.

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When she took her nap to the next, and lower, level in order to keep things real.

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When she knew EXACTLY what she wanted, and that something was popcorn.

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16 Cats Who Just Really Need All Of The Attention

GIVE IT HERE.

"'Scuse me, I think I'm a little bit more important than your reading."

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"THAT'S ENOUGH WORK FOR TODAY. NOW IT'S ME TIME."

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"I'm gonna sit here until she fully acknowledges my presence."

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"The meowing is going to begin soon if you don't look at me."

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How to Add and Subtract Integers

You might think of integers as just ordinary numbers, like 3, -12, 17, 0, 7000, or -582. Integers are also called whole numbers because they aren't divided into parts of numbers, like fractions and decimals are. Read this article to learn everything you need to know about adding and subtracting integers, or skip to the section you need help with.

Steps

Adding and Subtracting Positive Integers with a Number Line

  1. Understand what a number line is. Number lines turn basic math into something real and physical that you can see in front of you. By just using a few marks and some common sense, we can use them like calculators to add and subtract numbers.

    Add and Subtract Integers Step 1 Version 2.jpg
  2. Draw a basic number line. Imagine or draw a straight, flat line. Make a mark near the middle of your line. Write a 0 or zero next to this mark.

    Add and Subtract Integers Step 2 Version 2.jpg
    • Your math book might call this point the origin, since it's where numbers originate, or start from.
  3. Draw two marks, one on each side of your zero. Write -1 next to the mark on the left and 1 next to the mark on the right. These are the integers closest to zero.

    Add and Subtract Integers Step 3 Version 2.jpg
    • Don't worry about making the spacing perfect - as long as you're close enough that you can tell what it's supposed to mean, the number line will work.
    • The left side is the side at the beginning of a sentence.
  4. Complete your number line by adding more numbers. Make more marks to the left of -1 and to the right of 1. Moving left from -1, label the next marks -2, -3, and -4. Moving right from 1, label the next marks 2, 3, and 4. You can keep going if you have space on your paper.

    Add and Subtract Integers Step 4 Version 2.jpg
    • The example image shows a number line from -6 to 6.
  5. Understand positive and negative integers. A positive integer, also called a natural number, is an integer larger than zero. 1, 2, 3, 25, 99, and 2007 are all positive integers. A negative integer is an integer less than zero (like -2, -4 and -88).

    Add and Subtract Integers Step 5 Version 2.jpg
    • An integer is just another way of saying a "whole number". Fractions like 1/2 (one half) are only part of a number, so they are not integers. Same with a decimal like 0.25 (zero point two five); decimals are not integers.
  6. Start solving 1+2 by putting your finger on the mark labeled 1. We're going to solve the simple addition problem 1+2 using the number line you just made. The first number in this problem is 1, so start by putting your finger on that number.

    Add and Subtract Integers Step 6 Version 2.jpg
    • Do you think this is too easy? If you've done any addition at all, you probably know the answer to 1+2. That's good: if you know the answer it will be easier to understand how number lines work. Then you can use a number line for more difficult addition problems, or to prepare you for more difficult math like algebra.
  7. Add 1+2 by moving your finger 2 marks to the right. Slide your finger to the right, counting the number of marks (other numbers) you pass by. Once you've hit 2 new marks, stop. The number your finger is pointing to, 3, is the answer.

    Add and Subtract Integers Step 7 Version 2.jpg
  8. Add any positive integers by moving right on a number line. Suppose we're figuring out what 3 + 2 is. Start at 3, move to the right or increase by 2. We end up at 5. This is written as 3 + 2 = 5.

    Add and Subtract Integers Step 8 Version 2.jpg
  9. Subtract positive integers by moving left on a number line. For example, if we have 6 - 4, we start at 6, move left four spaces, and end up at 2. This is written as 6 - 4 = 2.

    Add and Subtract Integers Step 9 Version 2.jpg

Adding and Subtracting Negative Numbers with a Number Line

  1. Learn what a number line is. If you don't know how to make a number line, go back to Adding and Subtracting Positive Numbers with a Number Line to learn how.

    Add and Subtract Integers Step 10 Version 2.jpg
  2. Understand negative numbers. Positive numbers are increases, or movements right on the number line. Negative numbers are decreases, or movements left on the number line. Adding a negative number moves the pointer left on the number line.

    Add and Subtract Integers Step 11 Version 2.jpg
    • For example, let's add 1 and -4. In the standard, familiar number writing you're used to, this is just:
      1 + (-4)

      On a number line, we start at 1, move 4 spaces left, and end up at -3.
  3. Use a basic equation to understand adding a negative number. Notice that -3, our answer, is the same thing we'd get if we just did 1 - 4. Adding 1 + (-4) and subtracting 4 from 1 are the same. We can write this as as an equation, a kind of mathematical sentence showing one things equals another:

    1 + (-4) = 1 - 4 = -3


    Add and Subtract Integers Step 12 Version 2.jpg
  4. Instead of adding a negative number, turn it into a subtraction problem using only positive numbers. As we can see from our simple equation above, we can go both ways — changing "add a negative number" to "subtract a positive number" and vice versa. You might have just been taught "change a minus-plus to a minus" without really knowing why — this is why.

    Add and Subtract Integers Step 13 Version 2.jpg
    • For example, consider -4. When we add -4 to 1, it decreases 1 by 4. We can "say this in math" by writing

      1 + (-4) = 1 - 4


      We'd write this on a number line, as starting with our pointer at 1, then adding a move 4 spaces to the left (in other words, adding a -4). Since it's an equation, one thing equals another - so the reverse works too:

      1 - 4 = 1 + (-4)
  5. Understand how subtraction and negative numbers work on a number line. On a number line, subtracting a negative is a decrease in the length of a decrease. Let's start with 5 - 8.

    Add and Subtract Integers Step 14 Version 2.jpg
    • On a number line, we start with our pointer at 5, decrease by 8, and arrive with our pointer at -3.
  6. Decrease the amount you're subtracting and see what happens. Suppose we decrease the amount we're decreasing by one less, or in other words subtract 7 instead of 8. Now we move one less space to the left on the number line. In written terms, we started with

    5 - 8 = -3


    Now we'll only be moving 7 left, so we have

    5 - 7 = -2


    Add and Subtract Integers Step 15 Version 2.jpg
  7. Notice how decreasing a decrease can result in an increase. For our example, we decrease the amount we go left by 1. In equation terms, we could write our shorter move as:
    5 - 7 = -2 = 5 - (8 - 1)


    Add and Subtract Integers Step 16 Version 2.jpg
  8. Change minuses to pluses when adding negative numbers. Using our step of "change all subtraction to addition", we could write our shorter move now as:
    5 - (8 - 1) = 5 - 7 = 5 - 8 + 1

    .

    Add and Subtract Integers Step 17 Version 2.jpg
    • We already know that 5 - 8 = -3, so let's take 5 - 8 out of our equation now and put in -3:
      5 - (8 - 1) = 5 - 7 = -3 + 1
    • We already know what 5 - (8 - 1) is — it's going one space less than 5 - 8. Our equation can show the fact that 5 - 8 gives us -3, and going one space short gives us -2. Our equation can be written like this now:

      -3 - (-1) = -3 + 1
  9. Write subtraction of negative numbers as addition. Notice what's happened at the end of this - we've proved that:

    -3 + 1 = -3 - (-1)


    We can express this as a simple, more general rule for writing math:

    first number plus a second number = first number minus (negative second number)

    Or, in more simple terms like you've probably heard in a math class:

    Change two minuses to a plus
    .

    Add and Subtract Integers Step 18.jpg

Adding Large Positive Integers

  1. Write the addition problem 2,503 + 7,461 with one number over the other. Line up the numbers so the 2 is above the 7, the 5 is above the 4, and so on. In this method, we'll learn how to add integers that are too large to do in your head or on a number line.

    Add and Subtract Integers Step 19.jpg
    • Write a + to the left of the bottom number, and a line underneath it, just as you probably learned to do for smaller addition problems.
  2. Start by adding the two numbers furthest to the right. It might seem a little odd to start from the right, since when reading numbers we start from the left. We have to add in this order to get the right answer, though, as you'll see later on.

    Add and Subtract Integers Step 20.jpg
    • Underneath the two numbers to the right, 3 and 1, write what you get when you add them together: 4.
  3. Add each other number the same way. Moving left, you'll add 0+6, 5+4, and 2+7. Write the answers below each pair of numbers.

    Add and Subtract Integers Step 21.jpg
    • You should end up with the answer to the problem: 9,964. Check your work if you made a mistake.
  4. Now begin adding 857+135. You should notice something different as soon as add the first pair of numbers on the right. 7+5 equals 12, a two digit number, but you can only write one digit beneath that column. Keep reading to find out what to do, and why you always need to start on the right instead of the left.

    Add and Subtract Integers Step 22.jpg
  5. Add 7+5 and learn where to put the answer. 7+5=12, but you shouldn't put both the 1 and the 2 underneath the bottom line. Instead, put the last digit, 2, underneath the line and put the first digit, 1, above the column to the left, 5+3.

    Add and Subtract Integers Step 23.jpg
    • If you're curious about how this works, think about what dividing the 1 and 2 means. You've actually split 12 into 10 and 2. You can write the full 10 above the numbers if you want, and you'll see that the 1 lines up with the 5 and 3, just like before.
  6. Add 1+5+3 to get the next digit of the answer. You now have three digits to add for this number, since you added a 1 to this column. The answer is 9, so your answer so far should be 92.

    Add and Subtract Integers Step 24.jpg
  7. Finish the problem as normal. Keep moving left until you've added all the numbers, in this case just one more column. Your final answer should be 992.

    Add and Subtract Integers Step 25.jpg
    • You can try more complicated problems, like 974+568. Remember, each time you get a two digit number, only write the last digit as the answer, and put the other digit above the column to the left, the one you'll add together next. If the last column ends up with a two digit number, you can just write it as your answer.
    • See the Tips section for an answer to the problem 974+568 after you try to solve it.

Subtracting Large Positive Integers

  1. Write the subtraction problem 4713 - 502 with the first number above the other. Write them so the 3 is directly above the 2, the 1 is above the 0, the 7 is above the 5, and the 4 is above a blank space.

    Add and Subtract Integers Step 26.jpg
    • You can write a 0 underneath the 4 if it helps you keep track of which number is above which other number. You can always add zeros in front of a number without changing it. Make sure to add it in front of the number and not after it.
  2. Subtract each bottom number from the number directly above it, starting from the right. Always start from the right. Solve for 3-2, 1-0, 7-5, and 4-0, putting the answer to each problem directly underneath the two numbers in that subtraction problem.

    Add and Subtract Integers Step 27.jpg
    • You should end up with the answer, 4,211.
  3. Now write down the problem 924 - 518 in the same way. These numbers are the same length, so you can line them up easily. This problem will teach you something new about subtracting integers, if you didn't know it already.

    Add and Subtract Integers Step 28.jpg
  4. Learn how to solve the first problem, on the far right. This is 4 - 8. This is tricky, since 4 is smaller than 8, but don't use negative numbers. Instead, follow these steps:

    Add and Subtract Integers Step 29.jpg
    • On the top line, cross out the 2 and write 1 instead. The 2 should be directly to the left of the 4.
    • Cross out the 4 and write 14. Do this in a small space so it's clear the 14 is entirely above the 8. You can also just write a 1 in front of the 4 to make it 14 if you have the room.
    • What you just did is "borrow" a 1 from the tens place, or second column from the right, and turn it into 10 in the ones place, or furthest column to the right. one 10 is the same as ten 1s, so this is still the same problem.
  5. Now solve the problem 14 - 8 and write the answer under the right column. You should now have a 6 on the far right of the line where your answer will be.

    Add and Subtract Integers Step 30.jpg
  6. Solve the next column to the left using the new number you wrote down. This should now be 1 - 1, which equals 0.

    Add and Subtract Integers Step 31.jpg
    • Your answer so far should be 06.
  7. Finish the problem by solving the last, left column. 9 - 5=4, so your final answer is 406.

    Add and Subtract Integers Step 32.jpg
  8. Now begin a problem where you subtract a larger number from a smaller number. Say you're asked to solve 415,990 - 968,772. You write the second number underneath the first, and then realize the number at the bottom is larger! You can tell this immediately by the first digits on the left: 9 is smaller than 4, so the number beginning with 9 has to be larger.

    Add and Subtract Integers Step 33.jpg
    • Make sure to line the numbers up correctly before comparing them. 912 is not bigger than 5000, which you can tell if you've lined them up correctly, since the 5 is above nothing at all. You can add leading zeros if it helps, for instance writing 912 as 0912 so it lines up well with 5000.
  9. Write the smaller number underneath the larger and add a - sign in front of the answer. Whenever you subtract a number from a smaller number, you'll get a negative number as your answer. It's best to write this sign before solving, so you don't forget to include it.

    Add and Subtract Integers Step 34.jpg
  10. To find the answer, subtract the small number from the larger one and remember to include the - sign. Your answer will be negative, as you showed by writing a - sign. Do not try to subtract the larger number from the smaller and just make it negative; you will not get the wrong answer.

    Add and Subtract Integers Step 35.jpg
    • The new problem to solve is: 968,772 - 415,990 = - ? Look at the Tips for the answer after trying to solve it.

Adding and Subtracting Negative Integers

  1. Learn how to add a negative and a positive number. Adding a negative integer is the same as subtracting a positive one. This is easier to see by testing this out with the number line method described in another section, but you can think about it in words too. A negative number is not a normal quantity; it is less than zero, and can represent an amount being taken away. If you add this "taking away" to a normal number, you'll end up making it smaller.

    Add and Subtract Integers Step 36.jpg
    • Example: 10 + -3 = 10 - 3 = 7
    • Example: -12 + 18 = 18 + -12 = 18 – 12 = 6. Remember that you can always switch the order of numbers in an addition problem, but not in a subtraction problem.
  2. Learn what to do if this turns into a subtraction problem with a smaller number first. Sometimes turning your addition problem into a subtraction problem as described above can end up with odd results like 4 – 7. When this happens, reverse the order of the numbers and make your answer negative.

    Add and Subtract Integers Step 37.jpg
    • Say you begin with 4 + -7.
    • Turn this into a subtraction problem: 4 - 7
    • Reverse the order and make it negative: -(7 – 4) = -(3) = -3.
    • If you aren't used to parentheses in your equations yet, think of it like this: 4 - 7 turns into 7 - 4 with a minus sign added. 7 - 4 = 3 but I should make it -3 for the right answer to the problem 4 - 7.
  3. Learn how to add two negative integers. Two negative numbers added together will always make a number more negative. There is nothing positive being added, so you'll always end up with something further from 0. Finding the answer is simple:

    Add and Subtract Integers Step 38.jpg
    • -3 + -6 = -9
    • -15 + -5 = -20
    • Do you see the pattern? All you need to do is add the numbers as though they were positive and add a negative sign. -4 + -3 = -(4 + 3) = -7
  4. Learn how to subtract a negative integer. Just like the addition problems, you can rewrite these so you only have to deal with positive numbers. If you're subtracting a negative number, you're "taking away" some "stuff taken away", which is the same as adding a positive number.

    Add and Subtract Integers Step 39.jpg
    • Think of the negative number as stolen money. If you "subtract", or take away, some stolen money so you can return it, that's the same as giving that person money, right?
    • Example: 10 – -5 = 10 + 5 = 15
    • Example: -1 – -2 = -1 + 2. You already learned how to solve this problem in an early step, remember? Reread Learn how to add a negative and a positive number if you don't remember.
    • Here's the full solution to the last example: -1 – -2 = -1 + 2 = 2 + -1 = 2 – 1 = 1.


Video

Tips

  • You might be used to writing long numbers like 2,521,301 with a period (.) instead of a comma (,) depending on where you live. Just stick with whatever your teacher tells you so you don't confuse each other with different systems.
  • Make your number lines different scales to represent different numbers. There is no rule that number lines must always be divided by a space that equals 1. Imagine a number line where we make marks every 10 instead of every one. Aside from the fact that each space now represents 10, the basic movements of addition and subtraction are still the same. Try it out if you don't think so.
  • If you tried the extra challenge problems in the Long Numbers section, here are the answers: 974 + 568 = 1,542. The answer to 415,990 - 968,772 is -552,782.

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