3 7/10 + 14 11/12 + 20 1/2

⚠ 3 7/10 is read as the mixed number 3 + 7/10■14 11/12 is read as the mixed number 14 + 11/12■20 1/2 is read as the mixed number 20 + 1/2

Let's evaluate:

3

+ \frac{7}{10}

+ 14

+ \frac{11}{12}

+ 20

+ \frac{1}{2}

ⓘ Start from

3

and move forward

14

on the number line:

3 + 14

17

■Add fractions by using a common denominator and then adding their numerators:

\frac{7}{10} + \frac{1}{2}

\frac{7 + 5}{10}

17

+ \frac{7 + 5}{10}

+ \frac{11}{12}

+ 20

ⓘ Calculate the numerator and denominator before dividing:

7 + 5

12

17

+ \frac{12}{10}

+ \frac{11}{12}

+ 20

ⓘ Start from

17

and move forward

20

on the number line:

17 + 20

37

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

2

, their greatest common divisor:

\frac{12}{10}

\frac{6 \times 2}{5 \times 2}

\frac{6}{5}

37 + \frac{6}{5} + \frac{11}{12}

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

60

, the least common multiple of

5

and

12

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

\frac{6}{5} + \frac{11}{12}

\frac{6 \times 12}{5 \times 12} + \frac{11 \times 5}{12 \times 5}

\frac{6 \times 12 + 11 \times 5}{5 \times 12}

37 + \frac{6 \times 12 + 11 \times 5}{5 \times 12}

ⓘ Multiplications are done before additions and subtractions:

6 \times 12

6 \times (10 + 2)

6 \times 10 + 6 \times 2

60 + 12

72

11 \times 5

(10 + 1) \times 5

10 \times 5 + 5

50 + 5

55

ⅰ

5 \times 12

5 \times (10 + 2)

5 \times 10 + 5 \times 2

50 + 10

60

37 + \frac{72 + 55}{60}

ⓘ Calculate the numerator and denominator before dividing:

72 + 55

127

37 + \frac{127}{60}

▶Result:

39

\frac{7}{60}

ⓘ Since the fraction

\frac{127}{60}

exceeds 1, take

2

out of it and add it to the whole part:

37 + \frac{127}{60}

37 + \frac{120 + 7}{60}

37 + \frac{120}{60} + \frac{7}{60}

37 + 2 + \frac{7}{60}

39 + \frac{7}{60}

The numeric value of:

39 + \frac{7}{60}

equals:

39 + \approx 0.1167

▷

\approx 39.1167

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