explain 18 8/15 + 13 11/20 + 21 1/9 — step-by-step solution

⚠ 18 8/15 is read as the mixed number 18 + 8/15

⚠ 13 11/20 is read as the mixed number 13 + 11/20

Let's calculate:

18

+ \frac{8}{15}

+ 13

+ \frac{11}{20}

+ 21

+ \frac{1}{9}

ℹ

18 + 13

31

31

+ \frac{8}{15}

+ \frac{11}{20}

+ 21

+ \frac{1}{9}

ℹ

31 + 21

52

52

+ \frac{8}{15}

+ \frac{11}{20}

+ \frac{1}{9}

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

\frac{8}{15} + \frac{11}{20}

\frac{8 \times 4 + 11 \times 3}{15 \times 4}

52 + \frac{8 \times 4 + 11 \times 3}{15 \times 4} + \frac{1}{9}

ⓘMultiplications are done before additions and subtractions:

8 \times 4

32

‖

11 \times 3

(10 + 1) \times 3

10 \times 3 + 3

30 + 3

33

‖

15 \times 4

(10 + 5) \times 4

10 \times 4 + 5 \times 4

40 + 20

60

52 + \frac{32 + 33}{60} + \frac{1}{9}

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

32 + 33

65

52 + \frac{65}{60} + \frac{1}{9}

ℹ

\frac{65}{60} + \frac{1}{9}

\frac{65 \times 3 + 1 \times 20}{60 \times 3}

52 + \frac{65 \times 3 + 1 \times 20}{60 \times 3}

ⓘ

65 \times 3

(60 + 5) \times 3

60 \times 3 + 5 \times 3

180 + 15

195

ℹ

1 \times 20

20

‖

60 \times 3

180

52 + \frac{195 + 20}{180}

ℹ

195 + 20

215

52 + \frac{215}{180}

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

5

\frac{215}{180}

\frac{43 \times 5}{36 \times 5}

\frac{43}{36}

52 + \frac{43}{36}

ⓘThe fraction

\frac{43}{36}

is greater than 1: add its integer part

1

to the whole part:

\frac{43}{36} + 52

53 + \frac{7}{36}

▶Result:

53

\frac{7}{36}

The numeric value of:

53 + \frac{7}{36}

is:

53 + \approx 0.1944

▷

\approx 53.1944