How to find out a mixed fraction from an improper fraction - 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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