SSAT Upper Level Quantitative - Mixed / Improper Fractions

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

$\frac{25}{7}$

$\frac{12}{7}$

$\frac{7}{25}$

$\frac{7}{7}$

Explanation

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.

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

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

$\frac{25}{7}$

$\frac{12}{7}$

$\frac{7}{25}$

$\frac{7}{7}$

Explanation

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.

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

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

$\frac{71}{9}$

$\frac{56}{9}$

$\frac{82}{9}$

$\frac{64}{9}$

Explanation

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

$\frac{71}{9}$

$\frac{56}{9}$

$\frac{82}{9}$

$\frac{64}{9}$

Explanation

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.

$7\frac{8}{9}=\frac{7\times9+8}{9}=\frac{71}{9}$

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?

$40 < N \le 50$

$60 < N \le 70$

$50 < N \le 60$

$30 < N \le 40$

$70 < N \le 80$

Explanation

$\frac{16}{20}$ 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 $5\frac{9}{12}$ 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?

$25 < N \le 30$

$30 < N \le 35$

$20 < N \le 25$

$10 < N \le 15$

$15 < N \le 20$

Explanation

$\frac{9}{12}$ , 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 $7\frac{3}{8}$ as an improper fraction in lowest terms. What will the sum of its numerator and its denominator be?

$\textup{None of the other responses are correct}$

Explanation

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

Add the numerator and the denominator:

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?

$40 < N \le 50$

$60 < N \le 70$

$50 < N \le 60$

$30 < N \le 40$

$70 < N \le 80$

Explanation

$\frac{16}{20}$ 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 $5\frac{9}{12}$ 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?

$25 < N \le 30$

$30 < N \le 35$

$20 < N \le 25$

$10 < N \le 15$

$15 < N \le 20$