13 3/4 + 21 11/15 + 1 5/7

⚠ 13 3/4 is read as the mixed number 13 + 3/4■21 11/15 is read as the mixed number 21 + 11/15■1 5/7 is read as the mixed number 1 + 5/7

1) Let's calculate:

13

+ \frac{3}{4}

+ 21

+ \frac{11}{15}

+ 1

+ \frac{5}{7}

ⓘ Start from

13

and move forward

21

on the number line:

13 + 21

34

34

+ \frac{3}{4}

+ \frac{11}{15}

+ 1

+ \frac{5}{7}

ⓘ Start from

34

and move forward

1

on the number line:

34 + 1

35

35

+ \frac{3}{4}

+ \frac{11}{15}

+ \frac{5}{7}

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

60

, the least common multiple of

4

and

15

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

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

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

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

35 + \frac{3 \times 15 + 11 \times 4}{4 \times 15} + \frac{5}{7}

ⓘ Multiplications are done before additions and subtractions:

3 \times 15

3 \times (10 + 5)

3 \times 10 + 3 \times 5

30 + 15

45

11 \times 4

(10 + 1) \times 4

10 \times 4 + 4

40 + 4

44

ⅰ

4 \times 15

4 \times (10 + 5)

4 \times 10 + 4 \times 5

40 + 20

60

35 + \frac{45 + 44}{60} + \frac{5}{7}

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

45 + 44

89

35 + \frac{89}{60} + \frac{5}{7}

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

420

, the least common multiple of

60

and

7

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

\frac{89}{60} + \frac{5}{7}

\frac{89 \times 7}{60 \times 7} + \frac{5 \times 60}{7 \times 60}

\frac{89 \times 7 + 5 \times 60}{60 \times 7}

35 + \frac{89 \times 7 + 5 \times 60}{60 \times 7}

ⓘ Multiplications are done before additions and subtractions:

89 \times 7

(80 + 9) \times 7

80 \times 7 + 9 \times 7

560 + 63

623

5 \times 60

300

ⅰ

60 \times 7

420

35 + \frac{623 + 300}{420}

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

623 + 300

923

35 + \frac{923}{420}

▶Result:

37

\frac{83}{420}

ⓘ Since the fraction

\frac{923}{420}

exceeds 1, take

2

out of it and add it to the whole part:

35 + \frac{923}{420}

35 + \frac{840 + 83}{420}

35 + \frac{840}{420} + \frac{83}{420}

35 + 2 + \frac{83}{420}

37 + \frac{83}{420}

2) The numeric value of:

37 + \frac{83}{420}

equals:

37 + \approx 0.1976

▷

\approx 37.1976

100% free