Question

1. in the following exercises, convert the mixed number to an improper fraction.

a) $1\frac{2}{3}$
b) $1\frac{2}{5}$
c) $2\frac{1}{4}$
d) $2\frac{5}{6}$
e) $2\frac{7}{9}$
f) $2\frac{5}{7}$
g) $3\frac{4}{7}$
h) $3\frac{5}{9}$
i) $5\frac{3}{8}$
source: \prealgebra\ by lynn marecek & mary anne anthony-smith is licensed under cc by 4.0 / a derivative from the original work

Explanation:

Step1: Multiply whole + denominator

For a mixed number $a\frac{b}{c}$, calculate $a \times c + b$

Step2: Place over original denominator

Form improper fraction $\frac{a \times c + b}{c}$

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Part a) $1\frac{2}{3}$

Step1: Compute numerator value

$1 \times 3 + 2 = 5$

Step2: Write final fraction

$\frac{5}{3}$

Part b) $1\frac{2}{5}$

Step1: Compute numerator value

$1 \times 5 + 2 = 7$

Step2: Write final fraction

$\frac{7}{5}$

Part c) $2\frac{1}{4}$

Step1: Compute numerator value

$2 \times 4 + 1 = 9$

Step2: Write final fraction

$\frac{9}{4}$

Part d) $2\frac{5}{6}$

Step1: Compute numerator value

$2 \times 6 + 5 = 17$

Step2: Write final fraction

$\frac{17}{6}$

Part e) $2\frac{7}{9}$

Step1: Compute numerator value

$2 \times 9 + 7 = 25$

Step2: Write final fraction

$\frac{25}{9}$

Part f) $2\frac{5}{7}$

Step1: Compute numerator value

$2 \times 7 + 5 = 19$

Step2: Write final fraction

$\frac{19}{7}$

Part g) $3\frac{4}{7}$

Step1: Compute numerator value

$3 \times 7 + 4 = 25$

Step2: Write final fraction

$\frac{25}{7}$

Part h) $3\frac{5}{9}$

Step1: Compute numerator value

$3 \times 9 + 5 = 32$

Step2: Write final fraction

$\frac{32}{9}$

Part i) $5\frac{3}{8}$

Step1: Compute numerator value

$5 \times 8 + 3 = 43$

Step2: Write final fraction

$\frac{43}{8}$

Answer:

a) $\frac{5}{3}$
b) $\frac{7}{5}$
c) $\frac{9}{4}$
d) $\frac{17}{6}$
e) $\frac{25}{9}$
f) $\frac{19}{7}$
g) $\frac{25}{7}$
h) $\frac{32}{9}$
i) $\frac{43}{8}$