Mixed / Improper Fractions - SSAT Upper Level Quantitative (Math)

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Question

$\frac{34}{5}$

Change to a mixed number

Answer

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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Question

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

Answer

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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Question

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

Answer

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

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

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

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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?

Answer

$\frac{9}{12}$ , 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: .

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

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Question

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?

Answer

$\frac{16}{20}$ 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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Question

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

Answer

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,

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

Add the numerator and the denominator:

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Question

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

$6\frac{4}{7}$

Answer

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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Question

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

$5\frac{7}{11}$

Answer

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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Question

Express $3\frac{4}{7}$ as an improper fraction.

Answer

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.

$3\frac{4}{7}=\frac{3\times7+4}{7}=\frac{25}{7}$

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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