How to find out a mixed fraction from an improper fraction - SSAT Upper Level Quantitative

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$\frac{34}{5}$

Change to a mixed number

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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$\frac{4}{5}$

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

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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}$$

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

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$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 $\frac{ 5}{8}$

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

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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 $\frac{2}{3}$ .

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

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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 $\frac{4}{9}$

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

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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$\frac{2}{3}$

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

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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$\frac{3}{4}$

$\frac{34}{5}$

Change to a mixed number

Tap to see back →

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$\frac{4}{5}$

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

Tap to see back →

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}$$

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

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$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 $\frac{ 5}{8}$

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

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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 $\frac{2}{3}$ .

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

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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 $\frac{4}{9}$

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

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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$\frac{2}{3}$

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

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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$\frac{3}{4}$

$\frac{34}{5}$

Change to a mixed number

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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$\frac{4}{5}$

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

Tap to see back →

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}$$

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

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$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 $\frac{ 5}{8}$

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

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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 $\frac{2}{3}$ .

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

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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 $\frac{4}{9}$

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

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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$\frac{2}{3}$