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ACT Math : Fractions

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Example Questions

Example Question #161 : Fractions

Simplify the following expression:

$\frac{2}{3}\div\frac{5}{6}$

Possible Answers:

$\frac{4}{5}$

$\frac{5}{9}$

$\frac{7}{9}$

$\frac{1}{5}$

Correct answer:

$\frac{4}{5}$

Explanation:

$\frac{2}{3}\div\frac{5}{6}=\frac{2}{3}\times\frac{6}{5}=\frac{12}{15}=\frac{4}{5}$

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Example Question #162 : Fractions

Evaluate the following:

$7\frac{1}{3}\div6\frac{2}{3}$

Possible Answers:

$6\frac{1}{10}$

$1\frac{1}{10}$

$1\frac{1}{3}$

$\frac{65}{60}$

$1\frac{6}{10}$

Correct answer:

$1\frac{1}{10}$

Explanation:

Start by converting 7¹/₃to 22/3, and 6 ²/₃to 20/3. We then multiply 22/3 by the reciprocal of 20/3, 3/20, and you get 66/60. This simplifies to 1¹/₁₀.

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Example Question #1 : Operations And Fractions

Solve.

$\small \frac{2}{5}\div \frac{1}{25}=$

Possible Answers:

$\small \frac{2}{5}$

$\small \frac{1}{2}$

$\small \frac{27}{5}$

$\small \frac{1}{15}$

Correct answer:

Explanation:

Remember, to divide a number by a fraction, multiply the number by the reciprocal of the fraction. In this case, $\small \small \frac{2}{5}\div \frac{1}{25}=\frac{2}{5}\times \frac{25}{1}=\frac{50}{5}=10$

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Example Question #482 : Arithmetic

Solve for x where

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

Possible Answers:

$3\frac{5}{6}$

$2\frac{5}{6}$

$3\frac{1}{5}$

$5\frac{2}{3}$

$5\frac{2}{5}$

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 #481 : Arithmetic

Solve for :

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

Possible Answers:

$\frac{5}{16}$

$\frac{1}{4}$

$-\frac{3}{16}$

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 #3 : How To Subtract Fractions

Simplify:

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

Possible Answers:

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

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

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

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

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

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 #1553 : Act Math

Choose the answer which best solves the equation below:

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

Possible Answers:

$\frac{1}{6}$

$\frac{1}{12}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{4}$

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 #2 : How To Subtract 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:

$\frac{7}{18}$

$\frac{9}{18}$

$\frac{17}{36}$

$\frac{17}{24}$

$\frac{15}{24}$

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 #2 : How To Subtract 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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Example Question #1 : How To Add Fractions

Add the following fractions

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

Possible Answers:

$\frac{321}{240}$

$\frac{79}{60}$

$\frac{37}{30}$

$\frac{22}{60}$

$\frac{6}{240}$

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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ACT Math : Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #161 : Fractions

Example Question #162 : Fractions

Example Question #1 : Operations And Fractions

Example Question #482 : Arithmetic

Example Question #481 : Arithmetic

Example Question #3 : How To Subtract Fractions

Example Question #1553 : Act Math

Example Question #2 : How To Subtract Fractions

Example Question #2 : How To Subtract Fractions

Example Question #1 : How To Add Fractions

All ACT Math Resources

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