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SSAT Upper Level Math : Rational Numbers

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Mixed / Improper Fractions

Which of the following is one more than $\frac{34}{7}$ ?

Possible Answers:

$5\frac{6}{7}$

$6\frac{1}{7}$

$5\frac{2}{7}$

$5\frac{4}{7}$

Correct answer:

$5\frac{6}{7}$

Explanation:

Rewrite $\frac{34}{7}$ as follows:

$34 \div 7 = 4 \textup{ R }6$ , so $\frac{34}{7} = 4\frac{6}{7}$ .

Add one: $4\frac{6}{7} + 1 = 5\frac{6}{7}$

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

Which of the following is three times $\frac{15}{8}$ ?

Possible Answers:

$5 \frac{ 5}{8}$

$4\frac{1}{2}$

$5\frac{1}{4}$

$4\frac{7}{8}$

Correct answer:

$5 \frac{ 5}{8}$

Explanation:

$3 \times \frac{15}{8} = \frac{3}{1} \times \frac{15}{8} = \frac{45}{8}$

Since $45 \div 8 = 5 \textup{ R }5$ ,

$\frac{45}{8} = 5 \frac{ 5}{8}$

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Example Question #2 : Mixed / Improper Fractions

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

Possible Answers:

$13\frac{1}{3}$

$14 \frac{2}{3}$

$12\frac{2}{3}$

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 #1342 : Ssat Upper Level Quantitative (Math)

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

Possible Answers:

$4 \frac{4}{9}$

The correct answer is not among the other responses.

$5 \frac{5}{9}$

$6\frac{2}{3}$

$3\frac{1}{3}$

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 #1343 : Ssat Upper Level Quantitative (Math)

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

Possible Answers:

$2\frac{2}{3}$

$3\frac{1}{3}$

$3\frac{2}{3}$

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 #3 : Algebraic Fractions

$\frac{34}{5}$

Change to a mixed number

Possible Answers:

$3\frac{4}{5}$

$6\frac{4}{5}$

$34\frac{1}{5}$

$4 \frac{5}{6}$

$4 \frac{6}{5}$

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 #3 : Mixed / Improper Fractions

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

Possible Answers:

$22\frac{1}{2}$

$21\frac{1}{2}$

$20\frac{1}{4}$

$22\frac{3}{4}$

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

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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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Rational Numbers

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : Mixed / Improper Fractions

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

Example Question #2 : Mixed / Improper Fractions

Example Question #1342 : Ssat Upper Level Quantitative (Math)

Example Question #1343 : Ssat Upper Level Quantitative (Math)

Example Question #3 : Algebraic Fractions

Example Question #3 : Mixed / Improper Fractions

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

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

Example Question #2 : Mixed / Improper Fractions

All SSAT Upper Level Math Resources

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