Mixed / Improper Fractions - SSAT Upper Level Quantitative

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

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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}$$

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

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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}$$

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

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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}$$

$\frac{34}{5}$

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 $\frac{2}{3}$ .

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

$5$\frac{7}{11}$$

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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}$$

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$\frac{3}{4}$

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

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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:

$5 \times 7 + 4 = 35 + 4 = 39$

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

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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}$$

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?

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$\frac{9}{12}$ , 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 $25 < N \le 30$ .

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?

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$\frac{16}{20}$ 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 $40 < N \le 50$ .

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

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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:

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

$6$\frac{4}{7}$$

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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}$$

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

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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}$$

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

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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}$$

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

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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}$$