18 8/15 + 13 11/20 + 21 1/9

⚠ 18 8/15 is read as the mixed number 18 + 8/15■13 11/20 is read as the mixed number 13 + 11/20■21 1/9 is read as the mixed number 21 + 1/9

1) Let's calculate:

18

+ \frac{8}{15}

+ 13

+ \frac{11}{20}

+ 21

+ \frac{1}{9}

ⓘ Start from

18

and move forward

13

on the number line:

18 + 13

31

31

+ \frac{8}{15}

+ \frac{11}{20}

+ 21

+ \frac{1}{9}

ⓘ Start from

31

and move forward

21

on the number line:

31 + 21

52

52

+ \frac{8}{15}

+ \frac{11}{20}

+ \frac{1}{9}

ⓘ Add fractions by using a common denominator and then adding their numerators. We choose

60

, the least common multiple of

15

and

20

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

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

\frac{8 \times 4}{15 \times 4} + \frac{11 \times 3}{20 \times 3}

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

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

ⓘ Perform multiplications before additions and subtractions:

8 \times 4

32

11 \times 3

(10 + 1) \times 3

10 \times 3 + 3

30 + 3

33

ⅰ

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}

ⓘ Add fractions by using a common denominator and then adding their numerators. We choose

180

, the least common multiple of

60

and

9

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

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

\frac{65 \times 3}{60 \times 3} + \frac{1 \times 20}{9 \times 20}

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

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

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

ⓘ Perform multiplications before additions and subtractions:

65 \times 3

(60 + 5) \times 3

60 \times 3 + 5 \times 3

180 + 15

195

ⅰ

60 \times 3

180

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

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

195 + 20

215

52 + \frac{215}{180}

ⓘ Simplify the fraction by dividing the numerator and the denominator by

5

, their greatest common divisor:

\frac{215}{180}

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

\frac{43}{36}

52 + \frac{43}{36}

▶Result:

53

\frac{7}{36}

ⓘ The fraction

\frac{43}{36}

is greater than 1: extract

1

from it and add it to the whole part:

52 + \frac{43}{36}

52 + \frac{36 + 7}{36}

52 + \frac{36}{36} + \frac{7}{36}

52 + 1 + \frac{7}{36}

53 + \frac{7}{36}

2) The numeric value of:

53 + \frac{7}{36}

is:

53 + \approx 0.1944

▷

\approx 53.1944

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