If We Give You Two Fractions, Can You Tell Us Their Sum?

EDUCATION

By: Daniel Yetman

6 Min Quiz

What do these numbers with the same denominator add to: 3/8+1/8?

Summing these two fractions should be pretty straightforward. 1/8 and 3/8 share a common base so you can add the (numerators together). This gives you 4/8, which can reduce further to 1/2.

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Here's another fraction that uses big numbers: 13/100 + 11/10. Do you think you know the answer?

Are you starting to get the drill? Multiply the second fraction by ten to make its base 100 and then add the numerators together. You can right the answer as either 123/100 or 1 23/100 as a mixed fraction.

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Your friend cuts a pie into 10 pieces. You eat one piece (1/10) and your friends eat eight pieces (8/10). How pieces were eaten in total?

Do you have trouble with word problems? This problem is pretty straight forward (1/10+8/10). However, it can often be trickier having to read through a question and pick out the important information than solving the question by itself.

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Can you add these two mixed fractions: 1 1/3 + 2 1/3?

When you add mixed numbers together, you can add the full numbers together and then add the fractions separately. You can also convert the numbers back into improper fractions and add them together that way.

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You're feeding a group of 74 pigeons at the park. You throw a handful of breadcrumbs and 45 pigeons flock toward you. You throw another handful of breadcrumbs and 17 more pigeons flock toward you. What fraction of pigeons have flocked toward you?

Originally 45/74 pigeons flock toward you. After the second handful of breadcrumbs, 17/74 pigeons flock toward you, which sums to 62/74 pigeons in total. This can be reduced to 31/37.

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What's the sum of these two mixed numbers: 6 3/8 + 1 4/7?

Remember, when we add mixed numbers, you can either convert each fraction back into an improper fraction or add the whole numbers together and add the fractions separately.

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Do you remember how to add negative fractions? How about this one: -2/3 + 1/3?

When you add negative fractions, you're essentially subtracting them from each other instead of adding. However, it's a little harder to conceptualize negative fractions with real-world examples. For example, if you have one-third of a cookie, it would be impossible for somebody to take two-thirds.

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You might use these numbers when baking: What's the sum of 1/3 + 1/2?

In order to get a common base for this question, you need to multiply 1/3 by two and 1/2 by three. That gives us the equation 3/6+2/6, which is much easier to solve now that we have a common base.

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What do you think the answer is to this question: 89/100 + 11/10?

If you want to solve this problem, you'll have to multiply our second fraction by ten to make its base 100. From there, you can add the numerators to get 199/100 or 1 99/100.

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Can you think back to middle school and give us the sum of 8/10 + 3/5?

Remember, when you're adding fractions with different denominators (the bottom number), you have to make them the same before adding the two numbers. In this case, doubling 3/5 to make 6/10 gives us a common base.

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You drop an entire pack of 52 cards on the floor. You pick up seven cards in one hand and then 33 cards in the other hand. What fraction of the cards are you holding?

The key to this question is to be able to pick up the vital information in the question and to be able to reduce the fraction. Since you picked up 7/52 and 33/52 cards, you picked up 40/52 cards in total, which can be reduced to 10/52.

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14/13 + 7/8 = what?

Unfortunately, the lowest common denominator of these two numbers is 104, which means you'll have to o a lot of multiplication before adding these two fractions together. These fractions add to 203/104 or 1 99/104.

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Here's a tricker question for you. What's the sum of 6/10+1/7?

You can use the same steps to solve this problem as our first few questions. Since our numbers have different bases, you need to find a base they have in common. In this case, that base is 70, which can be reduced to 35 after the addition.

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Are you smart enough to figure this one out: 3/2 + 9/7?

What's the lowest common denominator of these two fractions? Once we turn them in 21/14 and 18/14, we can add them together to get 39/14. What else can this be written as? You'd be correct if you said 2 11/14.

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Solve this! 2/15 + 15 /2 = what mixed number?

Wouldn't it be nice if you could add these two fractions together to make 17/17? That would solve a lot of trouble, but unfortunately, you have to find a common denominator and go through our usual steps.

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We're going to challenge you with this one. What's the sum of 97/12 and 13/3?

To find a common base for these two fractions, we don't have to look too hard. Since three is a multiple of four, we can multiply our section fraction by four to get 52/12. Then we can add our two fractions directly.

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1543/2000 +1 1/2 = what mixed number?

There are several ways to solve this question, but perhaps the easiest is to convert the second number into a mixed number and multiply by 1000 to get 1543/2000 + 3000/2000 = 4543 /2000

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Can you answer this question for us: 8/19 + 4/24?

The hardest part of this question is dealing with the large numbers that come from finding a common denominator. If you multiply 19 by 24 to get a common base, you end up with 192/456 + 76/456.

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Want a challenge? Here's a harder one. What's the sum of 375/376 + 375/376?

Actually, this question isn't much harder than the others even though we used higher numbers! Since the bases are already the same, you can add the numerators together normally.

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Can you add this improper fraction with a mixed number: 5 2/10 + 64/6?

The way we recommend solving this question is by converting the first fraction to an improper fraction and finding a common denominator. The lowest common denominator in this question would be 30, which reduces to 15.

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There's a trick to solving this question. What's the sum of 312/21 + (-312/21)?

Remember, adding a negative fraction is the same as subtraction. When you subtract 312 from 312, you get 0. So 0/21 can be simplified to 0. Make sure you always check for negatives and double negatives!

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Let's go back to negative numbers. What's the sum of these fractions: 10/7 + (-29/2)?

Our first fraction is positive while the second fraction is negative, which means we're going to end up with a negative number. Once we find the lowest common denominator, the question becomes 20/14 - 203/14.

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Are you enough of a fraction genius to solve this final question: 8/19 + 4/24?

Have you learned the pattern by now? You can multiply 19 by 24 to find a common denominator and add the numerators together. After reducing the fractions to a base of 114, you get 67/114.

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7/3 + 19/4 = what fraction?

Hopefully, you understand how we came to this answer. When you multiply the two fractions to find a common denominator, you get 28/12 + 57/12, which gives a sum of 85/12.

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Can you give us the answer to this question: -7/11 + (-4/11)?

When you add -4/11, you're actually subtracting 4/11 from -7/11, giving a total of -11/11. You can reduce this to simply -1. Fractions with negatives aren't more difficult than regular fractions, but it can be tricky to keep track of the negative signs.

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Can you add these two big fractions for us: 199/200 + 99/100?

This summation requires one extra step from our last question. You need to double the second fraction to get a common base and then you can add 199/200 + 198/200 to get 397/200.

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Any idea what the sum of these two fractions is: 1 3/4 + 3 1/3?

When solving this question, you can convert these fractions to 7/4 and 10/3. What's the lowest common denominator of four and three? Using base 12, we can convert these fractions to 21/12 and 40/12.

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Give this one a go. What's the sum of 3/10 + 5/2?

Since two is a multiple of 10, you can multiply our second fraction by five to get a common denominator. This turns our question in a summation of 3/10 + 25/10, which we can add together as 28/10 or 2 4/5.

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Okay, we're going to make one of the numbers even higher. Can you solve this question: 1999/2000 + 1/2?

Even though it looks like there's a lot of work involved at a glance, you can just multiply the second fraction by 1000. 1999/2000 + 1000/2000 = 2999/2000. You could also write it as 1 999/2000.

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Any idea what the sum of 3/6+4/5 is?

These two numbers share the common base of 30. When you add them together with a base of 30, you get 39/30. However, we can also turn this into the mixed number 1 9/30. Do you see a way to reduce this further? Since 9 and 30 are multiples of 30, we can condense to 1 3/10

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What the sum of these two fractions: 5/9+1/2?

Can you spot the lowest common denominator that we can find with these two numbers? We can change this equation to 10/18+9/18. When we add them together, we get 19/18, which could also be written as 1 1/18.

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Can you sum these two negative fractions: -4/5 + (-4/5)?

Both fractions are negative, so when you add them, you have to subtract a negative from a negative. You can solve the equation the same as an equation with positive fractions but by switching the sign.

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If you eat 1/5 of a pie and later you eat another 1/4 of the pie, how much of the pie did you eat?

If you eat 1/5 of the pie the first time and 1/4 of the pie the second time, that's the equivalent of setting up the question as 1/4 + 1/5 = ?. Once we find a common base and add them together, we get 9/20.

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6/11 + 17/23 = what mixed number?

This equation follows the same pattern as our other questions, only it uses large numbers in the denominators. Multiply the first fraction by 23 and the second fraction by 11 to add the numerators.

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All right, let's see you solve this one. What's 5/7 + 5/18?

Even though the numerators are the same, you can't add fractions without making sure the denominators are also the same. The lowest common denominator of these two fractions is 126.

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Image: Luis Diaz Devesa/ Moment/ Getty Images

About This Quiz

When you were in school, did you love or hate math class? It seems to be one of those subjects that polarizes people. However, like it or not, you use fractions every day even without thinking about it. From dividing slices cake among friends to calculating your monthly budget, having at least a rudimentary understanding of fractions will make your life easier.

People have been learning about and using fractions for over 6,000 years. There's evidence that the Egyptians used fractions in their calculations around 4000 B.C. However, they had slightly different methods for solving problems and didn't use our current fraction notation. Greek mathematicians also used fractions before the year 0, but it wasn't until around 500 A.D. that fractions began to take their modern form. Mathematicians in India around this time wrote fractions as two numbers stacked on top of each other like modern fractions but without the bar between. The bar didn't come into use until around the year 1200, and the Moroccon mathematician Al-Hassar is credited as the inventor.

Can you remember how to add fractions properly? Does finding the lowest common denominator ring a bell? It's time to take a trip back to your middle school math class so grab your protector, ruler, and compass. Get started to see if you're a fraction genius!

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