explain 23 13/15 + 10 9/20 + 8 7/16 — step-by-step solution

⚠ 23 13/15 is read as the mixed number 23 + 13/15

⚠ 10 9/20 is read as the mixed number 10 + 9/20

Let's evaluate:

23

+ \frac{13}{15}

+ 10

+ \frac{9}{20}

+ 8

+ \frac{7}{16}

ℹ

23 + 10

33

33

+ \frac{13}{15}

+ \frac{9}{20}

+ 8

+ \frac{7}{16}

ℹ

33 + 8

41

41

+ \frac{13}{15}

+ \frac{9}{20}

+ \frac{7}{16}

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

\frac{13}{15} + \frac{9}{20}

\frac{13 \times 4 + 9 \times 3}{15 \times 4}

41 + \frac{13 \times 4 + 9 \times 3}{15 \times 4} + \frac{7}{16}

ⓘMultiplications are done before additions and subtractions:

13 \times 4

(10 + 3) \times 4

10 \times 4 + 3 \times 4

40 + 12

52

‖

15 \times 4

(10 + 5) \times 4

10 \times 4 + 5 \times 4

40 + 20

60

ℹ

9 \times 3

27

41 + \frac{52 + 27}{60} + \frac{7}{16}

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

52 + 27

79

41 + \frac{79}{60} + \frac{7}{16}

ℹ

\frac{79}{60} + \frac{7}{16}

\frac{79 \times 4 + 7 \times 15}{60 \times 4}

41 + \frac{79 \times 4 + 7 \times 15}{60 \times 4}

ⓘ

79 \times 4

(70 + 9) \times 4

70 \times 4 + 9 \times 4

280 + 36

316

‖

7 \times 15

(10 + 5) \times 7

10 \times 7 + 5 \times 7

70 + 35

105

ℹ

60 \times 4

240

41 + \frac{316 + 105}{240}

ℹ

316 + 105

421

41 + \frac{421}{240}

ⓘThe fraction

\frac{421}{240}

is greater than 1: add its integer part

1

to the whole part:

\frac{421}{240} + 41

42 + \frac{181}{240}

▶Result:

42

\frac{181}{240}

The numeric value of:

42 + \frac{181}{240}

equals:

42 + \approx 0.7542

▷

\approx 42.7542