5 4/9 + 3 1/8 + 2 7/16

⚠ 5 4/9 is read as the mixed number 5 + 4/9■3 1/8 is read as the mixed number 3 + 1/8■2 7/16 is read as the mixed number 2 + 7/16

Let's calculate:

5

+ \frac{4}{9}

+ 3

+ \frac{1}{8}

+ 2

+ \frac{7}{16}

ⓘ Start from

5

and move forward

3

on the number line:

5 + 3

8

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

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

\frac{2 + 7}{16}

8

+ \frac{4}{9}

+ \frac{2 + 7}{16}

+ 2

ⓘ Calculate the numerator and denominator before dividing:

2 + 7

9

8

+ \frac{4}{9}

+ \frac{9}{16}

+ 2

ⓘ Start from

8

and move forward

2

on the number line:

8 + 2

10

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

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

144

, the least common multiple of

9

and

16

. Multiplying the numerator and the denominator by the same number does not change the fraction:

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

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

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

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

ⓘ Perform multiplications before additions and subtractions:

4 \times 16

4 \times (10 + 6)

4 \times 10 + 4 \times 6

40 + 24

64

9 \times 9

81

ⅰ

9 \times 16

9 \times (10 + 6)

9 \times 10 + 9 \times 6

90 + 54

144

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

ⓘ Calculate the numerator and denominator before dividing:

64 + 81

145

10 + \frac{145}{144}

▶Result:

11

\frac{1}{144}

ⓘ The fraction

\frac{145}{144}

is greater than 1: extract

1

from it and add it to the whole part:

10 + \frac{145}{144}

10 + \frac{144 + 1}{144}

10 + \frac{144}{144} + \frac{1}{144}

10 + 1 + \frac{1}{144}

11 + \frac{1}{144}

The numeric value of:

11 + \frac{1}{144}

equals:

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

▷

\approx 11.0069

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