13 8/9 + 22 5/6 + 22 11/20

⚠ 13 8/9 is read as the mixed number 13 + 8/9■22 5/6 is read as the mixed number 22 + 5/6■22 11/20 is read as the mixed number 22 + 11/20

1) Let's evaluate:

13

+ \frac{8}{9}

+ 22

+ \frac{5}{6}

+ 22

+ \frac{11}{20}

ⓘ Start from

13

and move forward

22

on the number line:

13 + 22

35

35

+ \frac{8}{9}

+ \frac{5}{6}

+ 22

+ \frac{11}{20}

ⓘ Start from

35

and move forward

22

on the number line:

35 + 22

57

57

+ \frac{8}{9}

+ \frac{5}{6}

+ \frac{11}{20}

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

18

, the least common multiple of

9

and

6

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

\frac{8}{9} + \frac{5}{6}

\frac{8 \times 2}{9 \times 2} + \frac{5 \times 3}{6 \times 3}

\frac{8 \times 2 + 5 \times 3}{9 \times 2}

57 + \frac{8 \times 2 + 5 \times 3}{9 \times 2} + \frac{11}{20}

ⓘ Perform multiplications before additions and subtractions:

8 \times 2

16

5 \times 3

15

ⅰ

9 \times 2

18

57 + \frac{16 + 15}{18} + \frac{11}{20}

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

16 + 15

31

57 + \frac{31}{18} + \frac{11}{20}

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

180

, the least common multiple of

18

and

20

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

\frac{31}{18} + \frac{11}{20}

\frac{31 \times 10}{18 \times 10} + \frac{11 \times 9}{20 \times 9}

\frac{31 \times 10 + 11 \times 9}{18 \times 10}

57 + \frac{31 \times 10 + 11 \times 9}{18 \times 10}

ⓘ Perform multiplications before additions and subtractions:

31 \times 10

(30 + 1) \times 10

30 \times 10 + 10

300 + 10

310

11 \times 9

(10 + 1) \times 9

10 \times 9 + 9

90 + 9

99

ⅰ

18 \times 10

(10 + 8) \times 10

10 \times 10 + 8 \times 10

100 + 80

180

57 + \frac{310 + 99}{180}

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

310 + 99

409

57 + \frac{409}{180}

▶Result:

59

\frac{49}{180}

ⓘ The fraction

\frac{409}{180}

is greater than 1: extract

2

from it and add it to the whole part:

57 + \frac{409}{180}

57 + \frac{360 + 49}{180}

57 + \frac{360}{180} + \frac{49}{180}

57 + 2 + \frac{49}{180}

59 + \frac{49}{180}

2) The numeric value of:

59 + \frac{49}{180}

equals:

59 + \approx 0.2722

▷

\approx 59.2722

100% free