explain 3 4/9 + 1 15/16 + 11 6/7 — step-by-step solution

⚠ 3 4/9 is read as the mixed number 3 + 4/9

⚠ 1 15/16 is read as the mixed number 1 + 15/16

Let's evaluate:

3

+ \frac{4}{9}

+ 1

+ \frac{15}{16}

+ 11

+ \frac{6}{7}

ℹ

3 + 1

4

4

+ \frac{4}{9}

+ \frac{15}{16}

+ 11

+ \frac{6}{7}

ℹ

4 + 11

15

15

+ \frac{4}{9}

+ \frac{15}{16}

+ \frac{6}{7}

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

\frac{4}{9} + \frac{15}{16}

\frac{4 \times 16 + 15 \times 9}{9 \times 16}

15 + \frac{4 \times 16 + 15 \times 9}{9 \times 16} + \frac{6}{7}

ⓘMultiplications are done before additions and subtractions:

4 \times 16

(10 + 6) \times 4

10 \times 4 + 6 \times 4

40 + 24

64

‖

15 \times 9

(10 + 5) \times 9

10 \times 9 + 5 \times 9

90 + 45

135

‖

9 \times 16

(10 + 6) \times 9

10 \times 9 + 6 \times 9

90 + 54

144

15 + \frac{64 + 135}{144} + \frac{6}{7}

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

64 + 135

199

15 + \frac{199}{144} + \frac{6}{7}

ℹ

\frac{199}{144} + \frac{6}{7}

\frac{199 \times 7 + 6 \times 144}{144 \times 7}

15 + \frac{199 \times 7 + 6 \times 144}{144 \times 7}

ⓘ

199 \times 7

(100 + 90 + 9) \times 7

100 \times 7 + 90 \times 7 + 9 \times 7

700 + 630 + 63

1393

‖

6 \times 144

(100 + 40 + 4) \times 6

100 \times 6 + 40 \times 6 + 4 \times 6

600 + 240 + 24

864

‖

144 \times 7

(100 + 40 + 4) \times 7

100 \times 7 + 40 \times 7 + 4 \times 7

700 + 280 + 28

1008

15 + \frac{1393 + 864}{1008}

ℹ

1393 + 864

2257

15 + \frac{2257}{1008}

ⓘThe fraction

\frac{2257}{1008}

is greater than 1: add its integer part

2

to the whole part:

\frac{2257}{1008} + 15

17 + \frac{241}{1008}

▶Result:

17

\frac{241}{1008}

The numeric value of:

17 + \frac{241}{1008}

equals:

17 + \approx 0.2391

▷

\approx 17.2391