17 7/20 + 22 9/10 + 20 11/12

⚠ 17 7/20 is read as the mixed number 17 + 7/20■22 9/10 is read as the mixed number 22 + 9/10■20 11/12 is read as the mixed number 20 + 11/12

1) Let's evaluate:

17

+ \frac{7}{20}

+ 22

+ \frac{9}{10}

+ 20

+ \frac{11}{12}

ⓘ Start from

17

and move forward

22

on the number line:

17 + 22

39

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

\frac{7}{20} + \frac{9}{10}

\frac{7 + 2 \times 9}{20}

39

+ \frac{7 + 2 \times 9}{20}

+ 20

+ \frac{11}{12}

ⓘ Perform multiplications before additions and subtractions:

2 \times 9

18

■Start from

39

and move forward

20

on the number line:

39 + 20

59

59 + \frac{7 + 18}{20} + \frac{11}{12}

ⓘ Calculate the numerator and denominator before dividing:

7 + 18

25

59 + \frac{25}{20} + \frac{11}{12}

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

60

, the least common multiple of

20

and

12

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

\frac{25}{20} + \frac{11}{12}

\frac{25 \times 3}{20 \times 3} + \frac{11 \times 5}{12 \times 5}

\frac{25 \times 3 + 11 \times 5}{20 \times 3}

59 + \frac{25 \times 3 + 11 \times 5}{20 \times 3}

ⓘ Perform multiplications before additions and subtractions:

25 \times 3

(20 + 5) \times 3

20 \times 3 + 5 \times 3

60 + 15

75

11 \times 5

(10 + 1) \times 5

10 \times 5 + 5

50 + 5

55

ⅰ

20 \times 3

60

59 + \frac{75 + 55}{60}

ⓘ Calculate the numerator and denominator before dividing:

75 + 55

130

59 + \frac{130}{60}

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

10

, their greatest common divisor:

\frac{130}{60}

\frac{13 \times 10}{6 \times 10}

\frac{13}{6}

59 + \frac{13}{6}

▶Result:

61

\frac{1}{6}

ⓘ Since the fraction

\frac{13}{6}

exceeds 1, take

2

out of it and add it to the whole part:

59 + \frac{13}{6}

59 + \frac{12 + 1}{6}

59 + \frac{12}{6} + \frac{1}{6}

59 + 2 + \frac{1}{6}

61 + \frac{1}{6}

2) The numeric value of:

61 + \frac{1}{6}

equals:

61 + \approx 0.1667

▷

\approx 61.1667

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