explain 16 1/9 + 13 9/10 + 16 2/9 — step-by-step solution

⚠ 16 1/9 is read as the mixed number 16 + 1/9

⚠ 13 9/10 is read as the mixed number 13 + 9/10

Let's evaluate:

16

+ \frac{1}{9}

+ 13

+ \frac{9}{10}

+ 16

+ \frac{2}{9}

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

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

\frac{1 + 2}{9}

ℹ

16 + 13

29

29

+ \frac{1 + 2}{9}

+ \frac{9}{10}

+ 16

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

1 + 2

3

ℹ

29 + 16

45

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

ℹ

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

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

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

ⓘMultiplications are done before additions and subtractions:

3 \times 10

30

ℹ

9 \times 9

81

‖

9 \times 10

90

45 + \frac{30 + 81}{90}

ℹ

30 + 81

111

45 + \frac{111}{90}

ⓘWe simplify the fraction by dividing the numerator and the denominator by the number

3

\frac{111}{90}

\frac{37 \times 3}{30 \times 3}

\frac{37}{30}

45 + \frac{37}{30}

ⓘThe fraction

\frac{37}{30}

is greater than 1: add its integer part

1

to the whole part:

\frac{37}{30} + 45

46 + \frac{7}{30}

▶Result:

46

\frac{7}{30}

The approximate value of:

46 + \frac{7}{30}

is:

46 + \approx 0.2333

▷

\approx 46.2333