explain 13 3/4 + 21 11/15 + 1 5/7 — step-by-step solution

⚠ 13 3/4 is read as the mixed number 13 + 3/4

⚠ 21 11/15 is read as the mixed number 21 + 11/15

Let's calculate:

13

+ \frac{3}{4}

+ 21

+ \frac{11}{15}

+ 1

+ \frac{5}{7}

ℹ

13 + 21

34

34

+ \frac{3}{4}

+ \frac{11}{15}

+ 1

+ \frac{5}{7}

ℹ

34 + 1

35

35

+ \frac{3}{4}

+ \frac{11}{15}

+ \frac{5}{7}

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

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

\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

(10 + 5) \times 3

10 \times 3 + 5 \times 3

30 + 15

45

‖

11 \times 4

(10 + 1) \times 4

10 \times 4 + 4

40 + 4

44

‖

4 \times 15

(10 + 5) \times 4

10 \times 4 + 5 \times 4

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}

ℹ

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

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

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

ⓘ

89 \times 7

(80 + 9) \times 7

80 \times 7 + 9 \times 7

560 + 63

623

ℹ

5 \times 60

300

‖

60 \times 7

420

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

ℹ

623 + 300

923

35 + \frac{923}{420}

ⓘThe fraction

\frac{923}{420}

is greater than 1: add its integer part

2

to the whole part:

\frac{923}{420} + 35

37 + \frac{83}{420}

▶Result:

37

\frac{83}{420}

The approximate value of:

37 + \frac{83}{420}

equals:

37 + \approx 0.1976

▷

\approx 37.1976