explain 5 4/9 + 3 1/8 + 2 7/16 — step-by-step solution

⚠ 5 4/9 is read as the mixed number 5 + 4/9

⚠ 3 1/8 is read as the mixed number 3 + 1/8

Let's evaluate:

5

+ \frac{4}{9}

+ 3

+ \frac{1}{8}

+ 2

+ \frac{7}{16}

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

\frac{1}{8} + \frac{7}{16}

\frac{2 + 7}{16}

ℹ

5 + 3

8

8

+ \frac{4}{9}

+ \frac{2 + 7}{16}

+ 2

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

2 + 7

9

ℹ

8 + 2

10

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

ℹ

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

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

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

ⓘMultiplications are done before additions and subtractions:

4 \times 16

(10 + 6) \times 4

10 \times 4 + 6 \times 4

40 + 24

64

‖

9 \times 16

(10 + 6) \times 9

10 \times 9 + 6 \times 9

90 + 54

144

ℹ

9 \times 9

81

10 + \frac{64 + 81}{144}

ℹ

64 + 81

145

10 + \frac{145}{144}

ⓘThe fraction

\frac{145}{144}

is greater than 1: add its integer part

1

to the whole part:

\frac{145}{144} + 10

11 + \frac{1}{144}

▶Result:

11

\frac{1}{144}

The numeric value of:

11 + \frac{1}{144}

equals:

11 + \approx 6.9444 \times 10^{- 3}

▷

\approx 11.0069