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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #2 : Mixed / Improper Fractions

Which of the following is 80% of $\frac{55}{3}$ ?

Possible Answers:

$12\frac{2}{3}$

$14 \frac{2}{3}$

$13\frac{1}{3}$

Correct answer:

$14 \frac{2}{3}$

Explanation:

80% of a number is equal to $\frac{4}{5}$ multiplied by that number, so 80% of $\frac{55}{3}$ is

$\frac{4}{5} \times \frac{55}{3} = \frac{4}{1} \times \frac{11}{3} = \frac{44}{3}$

Since $44 \div 3 = 14 \textup{ R }2$ ,

$\frac{44}{3} = 14 \frac{2}{3}$ .

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Example Question #1341 : Ssat Upper Level Quantitative (Math)

Which of the following is $\frac{32}{9}$ increased by 25%?

Possible Answers:

$4 \frac{4}{9}$

$5 \frac{5}{9}$

The correct answer is not among the other responses.

$3\frac{1}{3}$

$6\frac{2}{3}$

Correct answer:

$4 \frac{4}{9}$

Explanation:

A number increased by 25% is 125%, or $\frac{5}{4}$ , multiplied by the number. $\frac{32}{9}$ increased by 25% is therefore

$\frac{5}{4} \times \frac{32}{9} = \frac{5}{1} \times \frac{8}{9} = \frac{40} {9}$

$40 \div 9 = 4 \textup{ R }4$ , so

$\frac{40} {9} = 4 \frac{4}{9}$

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Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

Decrease $\frac{88}{21}$ by 12.5%. What is the result?

Possible Answers:

$3\frac{1}{3}$

$2\frac{2}{3}$

$3\frac{2}{3}$

Correct answer:

$3\frac{2}{3}$

Explanation:

Decreasing a number by 12.5% is the same as taking 87.5% of a number, or multiplying it by

$\frac{87.5}{100} = \frac{87.5 \div 12.5 }{100\div 12.5} = \frac{7}{8}$ .

$\frac{7}{8} \times \frac{88}{21} = \frac{11}{3}$

$11 \div 3 = 3\textup{ R }2$ , so

$\frac{11}{3} = 3\frac{2}{3}$

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Example Question #273 : Number Concepts And Operations

$\frac{34}{5}$

Change to a mixed number

Possible Answers:

$34\frac{1}{5}$

$3\frac{4}{5}$

$6\frac{4}{5}$

$4 \frac{6}{5}$

$4 \frac{5}{6}$

Correct answer:

$6\frac{4}{5}$

Explanation:

To convert from a fraction to a mixed number we must find out how many times the denominator goes into the numerator using division and the remainder becomes the new fraction.

$\frac{34}{5} = 6\ r 4 \ so \6\frac{4}{5}$

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Example Question #274 : Number Concepts And Operations

Write $\frac{91}{4}$ as a mixed fraction.

Possible Answers:

$20\frac{1}{4}$

$22\frac{3}{4}$

$22\frac{1}{2}$

$21\frac{1}{2}$

Correct answer:

$22\frac{3}{4}$

Explanation:

Divide the numerator by the denominator.

$91\div4=22 R 3$

Now, the whole number part will be . Write the remainder on top of the denominator to get the fraction.

$\frac{91}{4}=22\frac{3}{4}$

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Example Question #5 : Mixed / Improper Fractions

If $5\frac{4}{7}$ is rewritten as an improper fraction, what will its numerator be?

Possible Answers:

Correct answer:

Explanation:

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator:

$5 \times 7 + 4 = 35 + 4 = 39$

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Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Rewrite $5\frac{9}{12}$ as an improper fraction in lowest terms, and call the sum of its numerator and its denominator. Which of the following is a true statement?

Possible Answers:

$30 < N \le 35$

$20 < N \le 25$

$15 < N \le 20$

$25 < N \le 30$

$10 < N \le 15$

Correct answer:

$25 < N \le 30$

Explanation:

$\frac{9}{12}$ , in lowest terms, is $\frac{9}{12} = \frac{9 \div 3}{12\div 3} = \frac{3}{4}$ , so $5\frac{9}{12}$ is rewritten as $5\frac{3}{4}$ .

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator. The new denominator is the same as the old one. Therefore,

$5\frac{3}{4} = \frac{5 \times 4+ 3}{4} = \frac{23}{4}$ ,

Add the numerator and the denominator: 23+4 = 27 .

The correct response is $25 < N \le 30$ .

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Example Question #2 : Mixed / Improper Fractions

Rewrite $8\frac{16}{20}$ as an improper fraction in lowest terms. If we assign to the numerator of this fraction, which of the following will be a true statement?

Possible Answers:

$70 < N \le 80$

$50 < N \le 60$

$30 < N \le 40$

$60 < N \le 70$

$40 < N \le 50$

Correct answer:

$40 < N \le 50$

Explanation:

$\frac{16}{20}$ in lowest terms is $\frac{16 \div 4}{20 \div 4} = \frac{4}{5}$ , so first, rewrite $8\frac{16}{20}$ as $8\frac{4}{5}$ .

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator:

$8 \times 5 + 4 = 40 + 4 = 44$

The correct response is $40 < N \le 50$ .

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Example Question #3 : How To Find Out An Improper Fraction From A Mixed Fraction

Rewrite $7\frac{3}{8}$ as an improper fraction in lowest terms. What will the sum of its numerator and its denominator be?

Possible Answers:

$\textup{None of the other responses are correct}$

Correct answer:

Explanation:

$7\frac{3}{8} = \frac{7 \times 8 + 3}{8} = \frac{56+3}{8}= \frac{59}{8}$

Add the numerator and the denominator: 59+8 = 67

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Example Question #221 : Fractions

Change the following mixed number into an improper fraction in simplest form:

$6\frac{4}{7}$

Possible Answers:

$\frac{46}{7}$

$\frac{7}{48}$

$\frac{48}{7}$

$\frac{49}{8}$

Correct answer:

$\frac{46}{7}$

Explanation:

To change a mixed fraction into an improper fraction, keep the denominator the same.

To find the numerator, multiply the whole number part of the mixed fraction by the denominator, then add that value to the numerator.

$6\frac{4}{7}=\frac{6\times7+4}{7}=\frac{46}{7}$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #2 : Mixed / Improper Fractions

Example Question #1341 : Ssat Upper Level Quantitative (Math)

Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

Example Question #273 : Number Concepts And Operations

Example Question #274 : Number Concepts And Operations

Example Question #5 : Mixed / Improper Fractions

Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #2 : Mixed / Improper Fractions

Example Question #3 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #221 : Fractions

All SSAT Upper Level Math Resources

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