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ACT Math : How to add fractions

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Example Questions

Example Question #15 : Operations And Fractions

Add the following fractions

$\frac{2}{5}+\frac{3}{4}+\frac{1}{12}$

Possible Answers:

$\frac{37}{30}$

$\frac{79}{60}$

$\frac{22}{60}$

$\frac{6}{240}$

$\frac{321}{240}$

Correct answer:

$\frac{37}{30}$

Explanation:

To add fractions you first must find the lowest common denominator. For these fractions it is 60. Then you must multiply the numerator and denominator by the number such that the denominator is equal to the LCD. For example $\frac{2}{5}$ gets multiplied by 12 (on both the numerator and denominator) because 5 times 12 is 60. When you do that you get the expression

$\frac{24}{60}+\frac{45}{60}+\frac{5}{60}$

then you just add the numerators and get

$\frac{74}{60}$

2 goes into both of those numbers so you get

$\frac{37}{30}$

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Example Question #16 : Operations And Fractions

Simplify the expression:

$\frac{1}{2}-\frac{2}{9}+\frac{5}{6}$

Possible Answers:

$\frac{10}{9}$

$\frac{3}{2}$

$\frac{1}{18}$

$\frac{2}{3}$

$\frac{14}{9}$

Correct answer:

$\frac{10}{9}$

Explanation:

First you want to find the least common denominator (in this case it's 18):

$\frac{9*1}{9*2}-\frac{2*2}{2*9}+\frac{1*15}{1*18}$

$\frac{9}{18}-\frac{4}{18}+\frac{15}{18}$

$\frac{9-4+15}{18}$

$\frac{20}{18}=\frac{10}{9}$

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Example Question #1 : Operations

What is the result of adding $20\%$ of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Possible Answers:

$\frac{23}{11}$

$\frac{43}{140}$

$\frac{47}{140}$

$\frac{3}{28}$

$\frac{3}{39}$

Correct answer:

$\frac{43}{140}$

Explanation:

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

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Example Question #18 : Operations And Fractions

Which of the following is equal to $\frac{1}{y(y+1)}$ ?

Possible Answers:

$\frac{1}{y}-\frac{1}{y+1}$

$\frac{y}{y-1}$

$\frac{1}{y}+\frac{1}{y+1}$

$\frac{y}{y+1}$

$\frac{1}{y+1}-\frac{1}{y}$

Correct answer:

$\frac{1}{y}-\frac{1}{y+1}$

Explanation:

We have two options here. We can manipulate the answers to work backwards and find a common denominator. This involves simply subtracting or adding two fractions. We can also try to rewrite the numerator by adding and subtracting the value . This serves the purpose of creating a sum in the numerator than can be split into y+1 and . This gives us one of the factors in the denominator in each numerator. When we separate or decompose the fraction, we can divide out by the common factor to re-express this as the difference of two rational expressions.

$\frac{1}{y(y+1)}=\frac{1+y-y}{y(y+1)}=\frac{y+1}{y(y+1)}-\frac{y}{y(y+1)}=\frac{1}{y}-\frac{1}{y+1}$

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ACT Math : How to add fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #15 : Operations And Fractions

Example Question #16 : Operations And Fractions

Example Question #1 : Operations

Example Question #18 : Operations And Fractions

All ACT Math Resources

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