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SSAT Upper Level Math : How to find out an improper fraction from a mixed fraction

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

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Example Questions

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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Example Question #222 : Fractions

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

$5\frac{7}{11}$

Possible Answers:

$\frac{55}{11}$

$\frac{64}{11}$

$\frac{62}{11}$

$\frac{69}{11}$

Correct answer:

$\frac{62}{11}$

Explanation:

To change a mixed number into an improper fraction, keep the denominator. Multiply the whole number part of the mixed number by the denominator and add your result to the given numerator to find the numerator of the improper fraction.

$5\frac{7}{11}=\frac{5\times11+7}{11}=\frac{62}{11}$

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

Write $12\frac{1}{12}$ as an improper fraction.

Possible Answers:

$\frac{145}{144}$

$\frac{144}{12}$

$\frac{145}{2}$

$\frac{145}{12}$

Correct answer:

$\frac{145}{12}$

Explanation:

To change a mixed number to an improper fraction, keep the denominator.

Then, multiply the whole number by the denominator and add that to the given numerator.

$12\frac{1}{12}=\frac{12\times12+1}{12}=\frac{145}{12}$

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Example Question #4 : How To Find Out An Improper Fraction From A Mixed Fraction

Write $7\frac{8}{9}$ as an improper fraction.

Possible Answers:

$\frac{71}{9}$

$\frac{64}{9}$

$\frac{56}{9}$

$\frac{82}{9}$

Correct answer:

$\frac{71}{9}$

Explanation:

To change a mixed number to an improper fraction, keep the denominator.

Then, multiply the whole number by the denominator and add that to the given numerator.

$7\frac{8}{9}=\frac{7\times9+8}{9}=\frac{71}{9}$

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Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

Write $10\frac{4}{7}$ as an improper fraction.

Possible Answers:

$\frac{79}{14}$

$\frac{74}{7}$

$\frac{7}{74}$

$\frac{17}{7}$

Correct answer:

$\frac{74}{7}$

Explanation:

To change a mixed number to an improper fraction, keep the denominator.

Then, multiply the whole number by the denominator and add that to the given numerator.

$10\frac{4}{7}=\frac{10\times7+4}{7}=\frac{74}{7}$

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Example Question #6 : How To Find Out An Improper Fraction From A Mixed Fraction

Write $10\frac{3}{8}$ as an improper fraction.

Possible Answers:

$\frac{8}{83}$

$\frac{38}{8}$

$\frac{83}{8}$

$\frac{21}{8}$

Correct answer:

$\frac{83}{8}$

Explanation:

To change a mixed number to an improper fraction, keep the denominator.

Then, multiply the whole number by the denominator and add that to the given numerator.

$10\frac{3}{8}=\frac{10\times8+3}{8}=\frac{83}{8}$

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SSAT Upper Level Math : How to find out an improper fraction from a mixed fraction

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

All SSAT Upper Level Math Resources

Example Questions

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

Example Question #222 : Fractions

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

Example Question #4 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #6 : How To Find Out An Improper Fraction From A Mixed Fraction

All SSAT Upper Level Math Resources

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