explain 17 11/16 + 21 1/5 + 5 2/15 — step-by-step solution

⚠ 17 11/16 is read as the mixed number 17 + 11/16

⚠ 21 1/5 is read as the mixed number 21 + 1/5

Let's calculate:

17

+ \frac{11}{16}

+ 21

+ \frac{1}{5}

+ 5

+ \frac{2}{15}

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

\frac{1}{5} + \frac{2}{15}

\frac{3 + 2}{15}

ℹ

17 + 21

38

38

+ \frac{11}{16}

+ \frac{3 + 2}{15}

+ 5

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

3 + 2

5

ℹ

38 + 5

43

43 + \frac{11}{16} + \frac{5}{15}

ℹ

\frac{11}{16} + \frac{5}{15}

\frac{11 \times 15 + 5 \times 16}{16 \times 15}

43 + \frac{11 \times 15 + 5 \times 16}{16 \times 15}

ⓘMultiplications are done before additions and subtractions:

11 \times 15

15 \times (10 + 1)

15 \times 10 + 15

150 + 15

165

‖

5 \times 16

(10 + 6) \times 5

10 \times 5 + 6 \times 5

50 + 30

80

‖

16 \times 15

16 \times (10 + 5)

16 \times 10 + 16 \times 5

160 + 80

240

43 + \frac{165 + 80}{240}

ℹ

165 + 80

245

43 + \frac{245}{240}

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

5

\frac{245}{240}

\frac{49 \times 5}{48 \times 5}

\frac{49}{48}

43 + \frac{49}{48}

ⓘThe fraction

\frac{49}{48}

is greater than 1: add its integer part

1

to the whole part:

\frac{49}{48} + 43

44 + \frac{1}{48}

▶Result:

44

\frac{1}{48}

The numeric value of:

44 + \frac{1}{48}

is:

44 + \approx 2.0833 \times 10^{- 2}

▷

\approx 44.0208