simplify 7/12+3/8-1/20 — step-by-step solution

Let's reduce:

\frac{7}{12} + \frac{3}{8} - \frac{1}{20}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

24

, the least common multiple of

12

and

8

. Multiplying the numerator and the denominator by the same number does not change the fraction:

\frac{7}{12} + \frac{3}{8}

\frac{7 \times 2}{12 \times 2} + \frac{3 \times 3}{8 \times 3}

\frac{7 \times 2 + 3 \times 3}{12 \times 2}

\frac{7 \times 2 + 3 \times 3}{12 \times 2} - \frac{1}{20}

ⓘ Multiplications are done before additions and subtractions:

7 \times 2

14

3 \times 3

9

ⅰ

12 \times 2

(10 + 2) \times 2

10 \times 2 + 2 \times 2

20 + 4

24

\frac{14 + 9}{24} - \frac{1}{20}

ⓘ The numerator and the denominator are computed before the division:

14 + 9

23

\frac{23}{24} - \frac{1}{20}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

120

, the least common multiple of

24

and

20

. Multiplying the numerator and the denominator by the same number does not change the fraction:

\frac{23}{24} - \frac{1}{20}

\frac{23 \times 5}{24 \times 5} + \frac{-1 \times 6}{20 \times 6}

\frac{23 \times 5 - 1 \times 6}{24 \times 5}

\frac{23 \times 5 - 1 \times 6}{24 \times 5}

ⓘ Multiplications are done before additions and subtractions:

23 \times 5

(20 + 3) \times 5

20 \times 5 + 3 \times 5

100 + 15

115

1 \times 6

6

ⅰ

24 \times 5

(20 + 4) \times 5

20 \times 5 + 4 \times 5

100 + 20

120

\frac{115 - 6}{120}

ⓘ The numerator and the denominator are computed before the division:

115 - 6

109

▶Simplified form:

\frac{109}{120}

The numeric value of:

\frac{109}{120}

equals:

▷

\approx 0.9083