6 3/7 + 6 13/16 + 6 5/9

⚠ 6 3/7 is read as the mixed number 6 + 3/7■6 13/16 is read as the mixed number 6 + 13/16■6 5/9 is read as the mixed number 6 + 5/9

1) Let's calculate:

6

+ \frac{3}{7}

+ 6

+ \frac{13}{16}

+ 6

+ \frac{5}{9}

ⓘ Start from

6

and move forward

6

on the number line:

6 + 6

12

12

+ \frac{3}{7}

+ \frac{13}{16}

+ 6

+ \frac{5}{9}

ⓘ Start from

12

and move forward

6

on the number line:

12 + 6

18

18

+ \frac{3}{7}

+ \frac{13}{16}

+ \frac{5}{9}

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

112

, the least common multiple of

7

and

16

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

\frac{3}{7} + \frac{13}{16}

\frac{3 \times 16}{7 \times 16} + \frac{13 \times 7}{16 \times 7}

\frac{3 \times 16 + 13 \times 7}{7 \times 16}

18 + \frac{3 \times 16 + 13 \times 7}{7 \times 16} + \frac{5}{9}

ⓘ Perform multiplications before additions and subtractions:

3 \times 16

3 \times (10 + 6)

3 \times 10 + 3 \times 6

30 + 18

48

13 \times 7

(10 + 3) \times 7

10 \times 7 + 3 \times 7

70 + 21

91

ⅰ

7 \times 16

7 \times (10 + 6)

7 \times 10 + 7 \times 6

70 + 42

112

18 + \frac{48 + 91}{112} + \frac{5}{9}

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

48 + 91

139

18 + \frac{139}{112} + \frac{5}{9}

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

1008

, the least common multiple of

112

and

9

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

\frac{139}{112} + \frac{5}{9}

\frac{139 \times 9}{112 \times 9} + \frac{5 \times 112}{9 \times 112}

\frac{139 \times 9 + 5 \times 112}{112 \times 9}

18 + \frac{139 \times 9 + 5 \times 112}{112 \times 9}

ⓘ Perform multiplications before additions and subtractions:

139 \times 9

(100 + 30 + 9) \times 9

100 \times 9 + 30 \times 9 + 9 \times 9

900 + 270 + 81

1251

5 \times 112

5 \times (100 + 10 + 2)

5 \times 100 + 5 \times 10 + 5 \times 2

500 + 50 + 10

560

ⅰ

112 \times 9

(100 + 10 + 2) \times 9

100 \times 9 + 10 \times 9 + 2 \times 9

900 + 90 + 18

1008

18 + \frac{1251 + 560}{1008}

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

1251 + 560

1811

18 + \frac{1811}{1008}

▶Result:

19

\frac{803}{1008}

ⓘ Since the fraction

\frac{1811}{1008}

exceeds 1, take

1

out of it and add it to the whole part:

18 + \frac{1811}{1008}

18 + \frac{1008 + 803}{1008}

18 + \frac{1008}{1008} + \frac{803}{1008}

18 + 1 + \frac{803}{1008}

19 + \frac{803}{1008}

2) The numeric value of:

19 + \frac{803}{1008}

is:

19 + \approx 0.7966

▷

\approx 19.7966

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