explain 4 9/10 + 16 11/12 + 18 8/9 — step-by-step solution

⚠ 4 9/10 is read as the mixed number 4 + 9/10

⚠ 16 11/12 is read as the mixed number 16 + 11/12

Let's evaluate:

4

+ \frac{9}{10}

+ 16

+ \frac{11}{12}

+ 18

+ \frac{8}{9}

ℹ

4 + 16

20

20

+ \frac{9}{10}

+ \frac{11}{12}

+ 18

+ \frac{8}{9}

ℹ

20 + 18

38

38

+ \frac{9}{10}

+ \frac{11}{12}

+ \frac{8}{9}

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

\frac{9}{10} + \frac{11}{12}

\frac{9 \times 6 + 11 \times 5}{10 \times 6}

38 + \frac{9 \times 6 + 11 \times 5}{10 \times 6} + \frac{8}{9}

ⓘMultiplications are done before additions and subtractions:

9 \times 6

54

‖

11 \times 5

(10 + 1) \times 5

10 \times 5 + 5

50 + 5

55

ℹ

10 \times 6

60

38 + \frac{54 + 55}{60} + \frac{8}{9}

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

54 + 55

109

38 + \frac{109}{60} + \frac{8}{9}

ℹ

\frac{109}{60} + \frac{8}{9}

\frac{109 \times 3 + 8 \times 20}{60 \times 3}

38 + \frac{109 \times 3 + 8 \times 20}{60 \times 3}

ⓘ

109 \times 3

(100 + 9) \times 3

100 \times 3 + 9 \times 3

300 + 27

327

ℹ

8 \times 20

160

‖

60 \times 3

180

38 + \frac{327 + 160}{180}

ℹ

327 + 160

487

38 + \frac{487}{180}

ⓘThe fraction

\frac{487}{180}

is greater than 1: add its integer part

2

to the whole part:

\frac{487}{180} + 38

40 + \frac{127}{180}

▶Result:

40

\frac{127}{180}

The numeric value of:

40 + \frac{127}{180}

is:

40 + \approx 0.7056

▷

\approx 40.7056