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

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Question

$\frac{34}{5}$

Change to a mixed number

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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 $\frac{34}{7}$ ?

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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 $\frac{15}{8}$ ?

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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 $\frac{55}{3}$ ?

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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%?

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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?

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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.

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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

$\frac{34}{5}$

Change to a mixed number

Tap to reveal answer

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 $\frac{34}{7}$ ?

Tap to reveal answer

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 $\frac{15}{8}$ ?

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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 $\frac{55}{3}$ ?

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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%?

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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?

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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.

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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

$\frac{34}{5}$

Change to a mixed number

Tap to reveal answer

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 $\frac{34}{7}$ ?

Tap to reveal answer

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 $\frac{15}{8}$ ?

Tap to reveal answer

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 $\frac{55}{3}$ ?

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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%?

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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?

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

Change to a mixed number

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.

Which of the following is one more than ?

Rewrite as follows: , so . Add one:

Which of the following is three times ?

Since ,

Which of the following is 80% of ?

80% of a number is equal to multiplied by that number, so 80% of is Since , .

Which of the following is increased by 25%?

A number increased by 25% is 125%, or , multiplied by the number. increased by 25% is therefore , so

Decrease by 12.5%. What is the result?

Decreasing a number by 12.5% is the same as taking 87.5% of a number, or multiplying it by . , so

Write as a mixed fraction.

Divide the numerator by the denominator. Now, the whole number part will be . Write the remainder on top of the denominator to get the fraction.

Change to a mixed number

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.

Which of the following is one more than ?

Rewrite as follows: , so . Add one:

Which of the following is three times ?

Since ,

Which of the following is 80% of ?

80% of a number is equal to multiplied by that number, so 80% of is Since , .

Which of the following is increased by 25%?

A number increased by 25% is 125%, or , multiplied by the number. increased by 25% is therefore , so

Decrease by 12.5%. What is the result?

Decreasing a number by 12.5% is the same as taking 87.5% of a number, or multiplying it by . , so

Write as a mixed fraction.

Divide the numerator by the denominator. Now, the whole number part will be . Write the remainder on top of the denominator to get the fraction.

Change to a mixed number

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.

Which of the following is one more than ?

Rewrite as follows: , so . Add one:

Which of the following is three times ?

Since ,

Which of the following is 80% of ?

80% of a number is equal to multiplied by that number, so 80% of is Since , .

Which of the following is increased by 25%?

A number increased by 25% is 125%, or , multiplied by the number. increased by 25% is therefore , so

Decrease by 12.5%. What is the result?

Decreasing a number by 12.5% is the same as taking 87.5% of a number, or multiplying it by . , so

$\frac{34}{5}$

Change to a mixed number

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 $\frac{34}{7}$ ?

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 $\frac{15}{8}$ ?

$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 $\frac{55}{3}$ ?

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%?

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?

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.

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

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 $\frac{34}{7}$ ?

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 $\frac{15}{8}$ ?

$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 $\frac{55}{3}$ ?

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%?

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?

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.

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

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 $\frac{34}{7}$ ?

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 $\frac{15}{8}$ ?

$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 $\frac{55}{3}$ ?

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%?

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?

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$\frac{2}{3}$