explain 10 5/9 + 2 7/16 + 17 9/20 — step-by-step solution

⚠ 10 5/9 is read as the mixed number 10 + 5/9

⚠ 2 7/16 is read as the mixed number 2 + 7/16

Let's evaluate:

10

+ \frac{5}{9}

+ 2

+ \frac{7}{16}

+ 17

+ \frac{9}{20}

ℹ

10 + 2

12

12

+ \frac{5}{9}

+ \frac{7}{16}

+ 17

+ \frac{9}{20}

ℹ

12 + 17

29

29

+ \frac{5}{9}

+ \frac{7}{16}

+ \frac{9}{20}

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

\frac{5}{9} + \frac{7}{16}

\frac{5 \times 16 + 7 \times 9}{9 \times 16}

29 + \frac{5 \times 16 + 7 \times 9}{9 \times 16} + \frac{9}{20}

ⓘMultiplications are done before additions and subtractions:

5 \times 16

(10 + 6) \times 5

10 \times 5 + 6 \times 5

50 + 30

80

‖

9 \times 16

(10 + 6) \times 9

10 \times 9 + 6 \times 9

90 + 54

144

ℹ

7 \times 9

63

29 + \frac{80 + 63}{144} + \frac{9}{20}

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

80 + 63

143

29 + \frac{143}{144} + \frac{9}{20}

ℹ

\frac{143}{144} + \frac{9}{20}

\frac{143 \times 5 + 9 \times 36}{144 \times 5}

29 + \frac{143 \times 5 + 9 \times 36}{144 \times 5}

ⓘ

143 \times 5

(100 + 40 + 3) \times 5

100 \times 5 + 40 \times 5 + 3 \times 5

500 + 200 + 15

715

‖

9 \times 36

(30 + 6) \times 9

30 \times 9 + 6 \times 9

270 + 54

324

‖

144 \times 5

(100 + 40 + 4) \times 5

100 \times 5 + 40 \times 5 + 4 \times 5

500 + 200 + 20

720

29 + \frac{715 + 324}{720}

ℹ

715 + 324

1039

29 + \frac{1039}{720}

ⓘThe fraction

\frac{1039}{720}

is greater than 1: add its integer part

1

to the whole part:

\frac{1039}{720} + 29

30 + \frac{319}{720}

▶Result:

30

\frac{319}{720}

The approximate value of:

30 + \frac{319}{720}

is:

30 + \approx 0.4431

▷

\approx 30.4431