Q&A for How to Add and Subtract Fractions

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Why do I have to multiply and find a common denominator?

Donagan

Top Answerer

Think of adding or subtracting fractions as a bit like adding or subtracting apples and oranges. You can't add 1 apple to 2 oranges unless you call each of them "pieces of fruit." Then if you added them, you'd have 3 pieces of fruit. Similarly you can't add 1/4 to 1/3 unless you re-name each fraction such that they have the same denominator: 1/4 becomes 3/12, and 1/3 becomes 4/12. Adding them together simply involves adding the numerators to get 7/12. Subtracting is similar, except you subtract one numerator from the other.

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Question

I'm trying to work this out. I know the answer because I used my calculator, but whats the formula for 7/9 - 1/6 + 8/12?

Donagan

Top Answerer

First reduce fractions. The only one that will reduce is 8/12, reducing to 2/3. Next find the lowest (or least) common denominator: the LCD is 9 x 6 = 54. Then 7/9 = 42/54, 1/6 = 9/54, and 2/3 = 36/54. So 42/54 - 9/54 + 36/54 = 69/54 = 1 15/54.

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Question

What about 5 1/2 - 2 2/3?

Donagan

Top Answerer

Convert 5½ to 11/2 and then to 33/6. Convert 2 2/3 to 8/3 and then to 16/6. 33/6 - 16/6 = 17/6 = 2 5/6.

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Question

How do I find the sum of 21/6 + 12/3?

Donagan

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Change 12/3 to 24/6. 21/6 + 24/6 = 45/6 = 7 3/6 = 7½.

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Question

2 + (-3/4) is too much hard for me. I know how to do it, but the answer is not coming. I tried several times but failed. Can you please help?

Donagan

Top Answerer

2 + (-¾) = 2 - ¾. 2 is the same as 8/4. 8/4 - 3/4 = 5/4 = 1¼.

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Question

In the first question above 21/6 + 12/3, how did you get 24/6? I need clarity.

Magajes, Amilla

Community Answer

First, get the LCD. The LCD of 3 and 6 is 6 why? Because 6 is a multiple of 3 and 6 is a multiple of 6. Next, To get its numerator. Whatever you multiplied with 6 to get the LCD, you also multiply it with the numerator. So it is like this, we multiplied 6 with 1 so, we multiply 1 with the number 21. 21 x 1 is 21 and for 3, we multiplied it with 2 because 2 x 3 is 6 so it is like this, 12 x 2 is 24. So, our answer is 24/6 and we should also convert that into a Mixed Number. Then, simplify if needed.

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Question

How do I subtract 7/2 - 5/4?

GB742

Top Answerer

First, convert both fractions so that they have the same denominator (bottom number): 7/2 = 14/4. Then, subtract the second numerator (top number) from the first numerator: 14 - 5 = 9. This gives the solution of 9/4.

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Question

How can I solve this 2 4/18 + 6/18?

GB742

Top Answerer

First, convert 2 4/18 to an improper fraction: 2 4/18 = ((2*18)+4)/18 = 40/18. Then add 6 to 40, giving an answer of 46. Therefore, 2 4/18 + 6/18 = 46/18. This can be simplified further 46/18 -> 23/9 or converted back into a mixed number 2 10/18, which simplifies to 2 5/9.

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In the question above 7/9 - 1/6 + 8/12, why is the common denominator 36 and not 18?

GB742

Top Answerer

Whilst 9 and 6 are both factors of 18, 12 is not a factor of 18, therefore the common denominator cannot be 18. To find the common denominator, you need to find the smallest integer which all of the denominators given in the question multiply to (known as the Lowest Common Multiple [LCM] or Lowest Common Denominator [LCD]), in this case 9*4 = 36, 6*6 = 36, 12*3=36, therefore the LCD is 36.

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Question

Simplify 5 1/2 + 1 3/7 - 2 5/7.

Community Answer

First change the mixed numbers to improper fractions: 11/2 + 10/7 - 19/7. Now find the common denominator: (2)(7) = 14. Now change the expression so that all of the denominators are 14: 77/14 + 20/14 - 38/14. Now add and subtract: 59/14 = 4 3/14.

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Question

Multiply the following: 8 × 2 ÷ 3.

Community Answer

(8)(2) / 3 = 16/3 = 5 1/3.

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In the sum of 21/6 + 12/3, how did you get 73/6?

Community Answer

That is a mistake. 21/6 + 12/3 = 21/6 + 24/6 = 45/6 = 7 3/6 = 7 1/2.

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