3 4/9 + 1 15/16 + 11 6/7

⚠ 3 4/9 is read as the mixed number 3 + 4/9■1 15/16 is read as the mixed number 1 + 15/16■11 6/7 is read as the mixed number 11 + 6/7

1) Let's calculate:

3

+ \frac{4}{9}

+ 1

+ \frac{15}{16}

+ 11

+ \frac{6}{7}

ⓘ Start from

3

and move forward

1

on the number line:

3 + 1

4

4

+ \frac{4}{9}

+ \frac{15}{16}

+ 11

+ \frac{6}{7}

ⓘ Start from

4

and move forward

11

on the number line:

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. 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{15}{16}

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

\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

4 \times (10 + 6)

4 \times 10 + 4 \times 6

40 + 24

64

15 \times 9

(10 + 5) \times 9

10 \times 9 + 5 \times 9

90 + 45

135

ⅰ

9 \times 16

9 \times (10 + 6)

9 \times 10 + 9 \times 6

90 + 54

144

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

ⓘ Calculate the numerator and denominator before dividing:

64 + 135

199

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

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

1008

, the least common multiple of

144

and

7

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

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

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

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

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

ⓘ Multiplications are done before additions and subtractions:

199 \times 7

(100 + 90 + 9) \times 7

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

700 + 630 + 63

1393

6 \times 144

6 \times (100 + 40 + 4)

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

600 + 240 + 24

864

ⅰ

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}

ⓘ Calculate the numerator and denominator before dividing:

1393 + 864

2257

15 + \frac{2257}{1008}

▶Result:

17

\frac{241}{1008}

ⓘ The fraction

\frac{2257}{1008}

is greater than 1: extract

2

from it and add it to the whole part:

15 + \frac{2257}{1008}

15 + \frac{2016 + 241}{1008}

15 + \frac{2016}{1008} + \frac{241}{1008}

15 + 2 + \frac{241}{1008}

17 + \frac{241}{1008}

2) The numeric value of:

17 + \frac{241}{1008}

equals:

17 + \approx 0.2391

▷

\approx 17.2391

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