Question

16 2/3 divided 5 5/7

Answer 1

$16\frac{2}{3} : 5\frac{5}{7} = \\ \\ = \frac{16 \times 3 + 2}{3} : \frac{5 \times 7 + 5}{7} = \\ \\ = \frac{50}{3} : \frac{40}{7} = \\ \\ = \frac{50}{3} \times \frac{7}{40} = \\ \\ = \frac{350}{120} = 2.91(6)$

Answer 2

Answer: 2 and 11/12

Step-by-step explanation: To divide mixed numbers, first write the mixed numbers as improper fractions.

We can write a mixed number as an improper fraction by multiplying the denominator by the whole number and then adding the numerator. Finally, we put our new number over original denominator.

So here, we can write 16 and 2/3 as the improper fraction 50/3 and we can write 5 and 5/7 as the improper fraction 40/7.

So here we have 50/3 ÷ 40/7.

Dividing by a fraction is the same as multiplying by the reciprocal of that fraction. So here, 50/3 ÷ 40/7 is the same as 50/3 × 7/40.

So now we are simply multiplying fractions.

To multiply fractions, we multiply across the numerators and multiply across the denominators.

$\frac{50}{3} x \frac{7}{40}$ = $\frac{350}{120}$

Notice however that 350/120 is not in lowest terms so we divide the numerator and the denominator by 10 and we get the equivalent fraction 35/12. The fraction 35/12 can be converted into a mixed number by dividing the denominator into the numerator.

35 ÷ 12 = 2 with a remainder of 11 or 2 and 11/12.

Therefore, 16 and 2/3 ÷ 5 and 5/7 = 2 and 11/12.