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ACT Math : How to subtract fractions

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Example Questions

Example Question #1 : How To Subtract Fractions

Solve for x where

$4\frac{1}{3}=x+1\frac{1}{2}$

Possible Answers:

$3\frac{1}{5}$

$5\frac{2}{3}$

$2\frac{5}{6}$

$3\frac{5}{6}$

$5\frac{2}{5}$

Correct answer:

$2\frac{5}{6}$

Explanation:

To solve this, subtract 1 1/2 from both sides. Convert to common denominators.

4 1/3 – 1 1/2 = 4 2/6 – 1 3/6.

In order to subtract, you'll want to "borrow" from the 4 2/6. Rewrite 4 2/6 as 3 8/6 and then subtract 1 3/6 from this. Your solution is 2 5/6. Most calculators will also do these calculations for you.

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Example Question #3 : Operations And Fractions

Solve for :

$\frac{7}{12}x+\frac{5}{4}=\frac{1}{2}+\frac{4}{3}x$

Possible Answers:

$\frac{1}{4}$

$\frac{5}{16}$

$-\frac{3}{16}$

Correct answer:

Explanation:

$\frac{7}{12}x+\frac{5}{4}=\frac{1}{2}+\frac{4}{3}x$

Begin by isolating your variable:

$\frac{7}{12}x-\frac{4}{3}x=\frac{1}{2}-\frac{5}{4}$

Next, you need to find the common denominator. For the left side of your equation, it is . For the right, it is . This means that you need to rewrite as follows:

$\frac{7}{12}x-\frac{4}{3}*\frac{4}{4}x=\frac{2}{4}-\frac{5}{4}$

Now, simplify and combine terms:

$\frac{7}{12}x-\frac{16}{12}x=-\frac{3}{4}$

$-\frac{9}{12}x=-\frac{3}{4}$

You can further simplify the left side:

$-\frac{3}{4}x=-\frac{3}{4}$

Next, multiply both sides by $-\frac{4}{3}$ . This gives you:

$x=-\frac{3}{4}*-\frac{4}{3}=1$

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Example Question #11 : Operations And Fractions

Simplify:

$\frac{1}{4}-\frac{x-2}{5}-\frac{2x+7}{20}$

Possible Answers:

$\frac{2-3x}{10}$

$\frac{3-3x}{10}$

$\frac{7-12x}{20}$

$\frac{8+3x}{5}$

$\frac{6+5}{21}$

Correct answer:

$\frac{3-3x}{10}$

Explanation:

First, you must convert your fractions to the common denominator of :

$\frac{5}{20}-\frac{4}{4}*\frac{x-2}{5}-\frac{2x+7}{20}$

Next, do your subtraction:

$\frac{5}{20}-\frac{4x-8}{20}-\frac{2x+7}{20}$

Next, you must be very careful. Notice how you must handle your subtractions in order to maintain the correct distribution of signs:

$\frac{5-(4x-8)-(2x+7)}{20}$

Now, carefully distribute for each group:

$\frac{5-4x+8-2x-7}{20}$

Next, simplify:

$\frac{6-6x}{20}$

Factor out the common in the numerator:

$\frac{2(3-3x)}{20}=\frac{3-3x}{10}$

There is still a common , but that does not help you get your fraction into the form found in the answers.

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Example Question #12 : Operations And Fractions

Choose the answer which best solves the equation below:

$\frac{5}{12} - \frac{1}{3} =$

Possible Answers:

$\frac{1}{6}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{12}$

Correct answer:

$\frac{1}{12}$

Explanation:

To solve this equation, you must first make sure that both fractions have a common denominator.

In this case the common denominator will be 12:

$\frac{5}{12} - \left(\frac{1}{3} \cdot \frac{4}{4}\right) =$

Then you perform your operation:

$\frac{5}{12} - \left(\frac{1\cdot 4}{3 \cdot 4}\right)$

$=\frac{5}{12} - \left(\frac{4}{12}\right)$

$=\frac{1}{12}$

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Example Question #13 : Operations And Fractions

If John has slices of an slice pizza left over, and he eats 3.5 of them, what fraction of the pizza does he have left over?

Possible Answers:

$\frac{15}{24}$

$\frac{17}{36}$

$\frac{17}{24}$

$\frac{7}{18}$

$\frac{9}{18}$

Correct answer:

$\frac{17}{36}$

Explanation:

To find this answer, first you need to set up your equation:

$\frac{12}{18} - \frac{3.5}{18} =$

And you need to get rid of the decimal in the numerator. We can do this by multiplying each fraction by 2/2.

$\left(\frac{12}{18}\cdot \frac{2}{2} \right) - \left(\frac{3.5}{18}\cdot \frac{2}{2} \right) =$

$\frac{24}{36} - \frac{7}{36} =$

Then solve for your answer:

$\frac{17}{36}$

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Example Question #14 : Operations And Fractions

What common number can you add to the numerator and denominator of $\frac{7}{19}$ to get $\frac{1}{2}$ ?

Possible Answers:

Correct answer:

Explanation:

Set up an equation where you add the same unknown number (x) to both the numerator and the denominator of the original fraction, and set the equation equal to $\frac{1}{2}$ .

$\newline \frac{7+x}{19+x}=\frac{1}{2}$

Cross-multiply the fractions to simplify.

$(7+x)\cdot (2)=(19+x)\cdot (1)$

14+2x=19+x

Now, solve for x.

14+2x=19+x

14+x-14=19-14

x=5

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ACT Math : How to subtract fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Subtract Fractions

Example Question #3 : Operations And Fractions

Example Question #11 : Operations And Fractions

Example Question #12 : Operations And Fractions

Example Question #13 : Operations And Fractions

Example Question #14 : Operations And Fractions

All ACT Math Resources

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