16 1/9 + 13 9/10 + 16 2/9

⚠ 16 1/9 is read as the mixed number 16 + 1/9■13 9/10 is read as the mixed number 13 + 9/10■16 2/9 is read as the mixed number 16 + 2/9

Let's calculate:

16

+ \frac{1}{9}

+ 13

+ \frac{9}{10}

+ 16

+ \frac{2}{9}

ⓘ Start from

16

and move forward

13

on the number line:

16 + 13

29

■Add fractions by using a common denominator and then adding their numerators:

\frac{1}{9} + \frac{2}{9}

\frac{1 + 2}{9}

29

+ \frac{1 + 2}{9}

+ \frac{9}{10}

+ 16

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

1 + 2

3

29

+ \frac{3}{9}

+ \frac{9}{10}

+ 16

ⓘ Start from

29

and move forward

16

on the number line:

29 + 16

45

■We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{3}{9}

\frac{1 \times 3}{3 \times 3}

\frac{1}{3}

45 + \frac{1}{3} + \frac{9}{10}

ⓘ Add fractions by using a common denominator and then adding their numerators. We choose

30

, the least common multiple of

3

and

10

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

\frac{1}{3} + \frac{9}{10}

\frac{1 \times 10}{3 \times 10} + \frac{9 \times 3}{10 \times 3}

\frac{1 \times 10 + 9 \times 3}{3 \times 10}

\frac{10 + 9 \times 3}{3 \times 10}

45 + \frac{10 + 9 \times 3}{3 \times 10}

ⓘ Perform multiplications before additions and subtractions:

9 \times 3

27

ⅰ

3 \times 10

30

45 + \frac{10 + 27}{30}

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

10 + 27

37

45 + \frac{37}{30}

▶Result:

46

\frac{7}{30}

ⓘ The fraction

\frac{37}{30}

is greater than 1: extract

1

from it and add it to the whole part:

45 + \frac{37}{30}

45 + \frac{30 + 7}{30}

45 + \frac{30}{30} + \frac{7}{30}

45 + 1 + \frac{7}{30}

46 + \frac{7}{30}

The numeric value of:

46 + \frac{7}{30}

equals:

46 + \approx 0.2333

▷

\approx 46.2333

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