explain 22 3/20 + 23 11/12 — step-by-step solution

⚠ 22 3/20 is read as the mixed number 22 + 3/20

⚠ 23 11/12 is read as the mixed number 23 + 11/12

Let's evaluate:

22

+ \frac{3}{20}

+ 23

+ \frac{11}{12}

ℹ

22 + 23

45

45 + \frac{3}{20} + \frac{11}{12}

ⓘTo add fractions, put them over the same denominator, then add the numerators:

\frac{3}{20} + \frac{11}{12}

\frac{3 \times 3 + 11 \times 5}{20 \times 3}

45 + \frac{3 \times 3 + 11 \times 5}{20 \times 3}

ⓘMultiplications are done before additions and subtractions:

3 \times 3

9

‖

11 \times 5

(10 + 1) \times 5

10 \times 5 + 5

50 + 5

55

ℹ

20 \times 3

60

45 + \frac{9 + 55}{60}

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

9 + 55

64

45 + \frac{64}{60}

ⓘWe simplify the fraction by dividing the numerator and the denominator by the number

4

\frac{64}{60}

\frac{16 \times 4}{15 \times 4}

\frac{16}{15}

45 + \frac{16}{15}

ⓘThe fraction

\frac{16}{15}

is greater than 1: add its integer part

1

to the whole part:

\frac{16}{15} + 45

46 + \frac{1}{15}

▶Result:

46

\frac{1}{15}

The approximate value of:

46 + \frac{1}{15}

equals:

46 + \approx 6.6667 \times 10^{- 2}

▷

\approx 46.0667