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SSAT Upper Level Math : Operations with Fractions

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Example Questions

Example Question #1252 : Ssat Upper Level Quantitative (Math)

Janice had $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a cup of milk. If she used $\frac{1}{12}$ $\displaystyle \frac{1}{12}$ cup to make some scrambled eggs, how much of a cup of milk does she have left?

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Correct answer:

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Explanation:

Subtract the two fractions. To subtract them, they must have a common denominator. Multiply the numerator and denominator of $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ by $\displaystyle 3$ to create a common denominator of $\displaystyle 12$ , then subtract the numerators and reduce the resulting fraction.

$\frac{3}{4}-\frac{1}{12}=\frac{9}{12}-\frac{1}{12}=\frac{8}{12}=\frac{2}{3}$ $\displaystyle \frac{3}{4}-\frac{1}{12}=\frac{9}{12}-\frac{1}{12}=\frac{8}{12}=\frac{2}{3}$

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Example Question #1 : Operations With Fractions

What is the result of this operation?

$\frac{3}{4}-\frac{1}{4}=?$ $\displaystyle \frac{3}{4}-\frac{1}{4}=?$

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle 1$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{2}{7}$ $\displaystyle \frac{2}{7}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Explanation:

Since the denominators are exactly the same, we can just subtract the tops.

$\frac{3}{4}-\frac{1}{4}=\frac{2}{4}$ $\displaystyle \frac{3}{4}-\frac{1}{4}=\frac{2}{4}$

By reducing we get

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

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Example Question #2 : Operations With Fractions

What is the result of this operation?

$\frac{2}{7}-\frac{1}{7}=?$ $\displaystyle \frac{2}{7}-\frac{1}{7}=?$

Possible Answers:

$\displaystyle 0$

$\frac{2}{7}$ $\displaystyle \frac{2}{7}$

$\frac{4}{7}$ $\displaystyle \frac{4}{7}$

$\frac{1}{7}$ $\displaystyle \frac{1}{7}$

$\frac{3}{7}$ $\displaystyle \frac{3}{7}$

Correct answer:

$\frac{1}{7}$ $\displaystyle \frac{1}{7}$

Explanation:

Since the denominators are the same, we can just subtract the numerators.

$\frac{2}{7}-\frac{1}{7}=\frac{1}{7}$ $\displaystyle \frac{2}{7}-\frac{1}{7}=\frac{1}{7}$

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Example Question #3 : Operations With Fractions

What is the result of this operation?

$\frac{4}{9}-\frac{1}{9}=?$ $\displaystyle \frac{4}{9}-\frac{1}{9}=?$

Possible Answers:

$\displaystyle 3$

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

$\frac{1}{9}$ $\displaystyle \frac{1}{9}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{2}{9}$ $\displaystyle \frac{2}{9}$

Correct answer:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Explanation:

Since the denominators are the same, we can just subtract the numerators.

$\frac{4}{9}-\frac{1}{9}=\frac{3}{9}$ $\displaystyle \frac{4}{9}-\frac{1}{9}=\frac{3}{9}$

By reducing our result, we get

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

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Example Question #4 : Operations With Fractions

What is the result of this operation?

$\frac{2}{9}-\frac{2}{9}=?$ $\displaystyle \frac{2}{9}-\frac{2}{9}=?$

Possible Answers:

$\displaystyle 4$

$\displaystyle 9$

$\displaystyle 0$

$\displaystyle 1$

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

Correct answer:

$\displaystyle 0$

Explanation:

Since the denominators are the same, we can just subtract the numerators.

$\frac{2}{9}-\frac{2}{9}=\frac{0}{9}$ $\displaystyle \frac{2}{9}-\frac{2}{9}=\frac{0}{9}$

The result can just be reduced to

$\displaystyle 0$

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Example Question #5 : Operations With Fractions

What is the result of the operation

$\frac{4}{5}-\frac{3}{5}=?$ $\displaystyle \frac{4}{5}-\frac{3}{5}=?$

Possible Answers:

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\displaystyle 0$

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Correct answer:

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

Explanation:

Since the denominators are the exact same, we can just subtract the numerators.

$\frac{4}{5}-\frac{3}{5}=\frac{1}{5}$ $\displaystyle \frac{4}{5}-\frac{3}{5}=\frac{1}{5}$

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Example Question #1261 : Ssat Upper Level Quantitative (Math)

What is the result of this operation

$\frac{4}{13}-\frac{2}{13}=?$ $\displaystyle \frac{4}{13}-\frac{2}{13}=?$

Possible Answers:

$\frac{4}{13}$ $\displaystyle \frac{4}{13}$

$\frac{1}{13}$ $\displaystyle \frac{1}{13}$

$\frac{2}{13}$ $\displaystyle \frac{2}{13}$

$\frac{3}{13}$ $\displaystyle \frac{3}{13}$

$\frac{5}{13}$ $\displaystyle \frac{5}{13}$

Correct answer:

$\frac{2}{13}$ $\displaystyle \frac{2}{13}$

Explanation:

Since the denominators are the exact same, we can just subtract the numerators.

$\frac{4}{13}-\frac{2}{13}=\frac{2}{13}$ $\displaystyle \frac{4}{13}-\frac{2}{13}=\frac{2}{13}$

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Example Question #1262 : Ssat Upper Level Quantitative (Math)

What is the result of this operation

$\frac{6}{6}-\frac{3}{6}=?$ $\displaystyle \frac{6}{6}-\frac{3}{6}=?$

Possible Answers:

$\frac{9}{6}$ $\displaystyle \frac{9}{6}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Explanation:

Since the denominators are the same, we can just subtract the numerators.

$\frac{6}{6}-\frac{3}{6}=\frac{3}{6}$ $\displaystyle \frac{6}{6}-\frac{3}{6}=\frac{3}{6}$

which we can reduce to

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

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Example Question #192 : Number Concepts And Operations

What is the result of this operation?

$\frac{1}{6}-\frac{1}{3}=?$ $\displaystyle \frac{1}{6}-\frac{1}{3}=?$

Possible Answers:

$\frac{1}{12}$ $\displaystyle \frac{1}{12}$

$-\frac{1}{6}$ $\displaystyle -\frac{1}{6}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$-\frac{1}{3}$ $\displaystyle -\frac{1}{3}$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

Correct answer:

$-\frac{1}{6}$ $\displaystyle -\frac{1}{6}$

Explanation:

Since the denominators are different, we need to transform them into the same denominator.

$\frac{1}{6}-\frac{1}{3}=?$ $\displaystyle \frac{1}{6}-\frac{1}{3}=?$

becomes

$\frac{1}{6}-\frac{1*2}{3*2}=?$ $\displaystyle \frac{1}{6}-\frac{1*2}{3*2}=?$

$\frac{1}{6}-\frac{2}{6}=?$ $\displaystyle \frac{1}{6}-\frac{2}{6}=?$

Now subtract the numerators

$\frac{1}{6}-\frac{2}{6}=\frac{-1}{6}$ $\displaystyle \frac{1}{6}-\frac{2}{6}=\frac{-1}{6}$

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Example Question #6 : Operations With Fractions

What is the result of this operation

$\frac{2}{7}-\frac{3}{7}=?$ $\displaystyle \frac{2}{7}-\frac{3}{7}=?$

Possible Answers:

$\displaystyle 7$

$\frac{2}{7}$ $\displaystyle \frac{2}{7}$

$-\frac{1}{7}$ $\displaystyle -\frac{1}{7}$

$\frac{1}{7}$ $\displaystyle \frac{1}{7}$

$-\frac{2}{7}$ $\displaystyle -\frac{2}{7}$

Correct answer:

$-\frac{1}{7}$ $\displaystyle -\frac{1}{7}$

Explanation:

Since the denominators are the same, we can just subtract the numerators.

$\frac{2}{7}-\frac{3}{7}=\frac{-1}{7}$ $\displaystyle \frac{2}{7}-\frac{3}{7}=\frac{-1}{7}$

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SSAT Upper Level Math : Operations with Fractions

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1252 : Ssat Upper Level Quantitative (Math)

Example Question #1 : Operations With Fractions

Example Question #2 : Operations With Fractions

Example Question #3 : Operations With Fractions

Example Question #4 : Operations With Fractions

Example Question #5 : Operations With Fractions

Example Question #1261 : Ssat Upper Level Quantitative (Math)

Example Question #1262 : Ssat Upper Level Quantitative (Math)

Example Question #192 : Number Concepts And Operations

Example Question #6 : Operations With Fractions

All SSAT Upper Level Math Resources

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