Question

1. $\frac{6}{8} div \frac{4}{11} =$ 19. $\frac{4}{5} div \frac{2}{7} =$ 20. $\frac{8}{9} div \frac{5}{6} =$ 23. $\frac{8}{9} div \frac{3}{7} =$ 24. $\frac{8}{9} div \frac{2}{4} =$ 25. $\frac{4}{6} div \frac{2}{9} =$

Explanation:

Let's solve these fraction division problems one by one. Remember that dividing by a fraction is the same as multiplying by its reciprocal.

Problem 18: $\boldsymbol{\frac{6}{8} \div \frac{4}{11}}$

Step 1: Find the reciprocal of the divisor

The reciprocal of $\frac{4}{11}$ is $\frac{11}{4}$.

Step 2: Multiply the dividend by the reciprocal

$\frac{6}{8} \times \frac{11}{4} = \frac{6 \times 11}{8 \times 4} = \frac{66}{32}$

Step 3: Simplify the fraction

Divide numerator and denominator by 2: $\frac{66 \div 2}{32 \div 2} = \frac{33}{16}$

Problem 19: $\boldsymbol{\frac{4}{5} \div \frac{2}{7}}$

Step 1: Find the reciprocal of the divisor

The reciprocal of $\frac{2}{7}$ is $\frac{7}{2}$.

Step 2: Multiply the dividend by the reciprocal

$\frac{4}{5} \times \frac{7}{2} = \frac{4 \times 7}{5 \times 2} = \frac{28}{10}$

Step 3: Simplify the fraction

Divide numerator and denominator by 2: $\frac{28 \div 2}{10 \div 2} = \frac{14}{5}$

Problem 20: $\boldsymbol{\frac{8}{9} \div \frac{5}{6}}$

Step 1: Find the reciprocal of the divisor

The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$.

Step 2: Multiply the dividend by the reciprocal

$\frac{8}{9} \times \frac{6}{5} = \frac{8 \times 6}{9 \times 5} = \frac{48}{45}$

Step 3: Simplify the fraction

Divide numerator and denominator by 3: $\frac{48 \div 3}{45 \div 3} = \frac{16}{15}$

Problem 23: $\boldsymbol{\frac{8}{9} \div \frac{3}{7}}$

Step 1: Find the reciprocal of the divisor

The reciprocal of $\frac{3}{7}$ is $\frac{7}{3}$.

Step 2: Multiply the dividend by the reciprocal

$\frac{8}{9} \times \frac{7}{3} = \frac{8 \times 7}{9 \times 3} = \frac{56}{27}$

Problem 24: $\boldsymbol{\frac{8}{9} \div \frac{2}{4}}$ (simplify $\frac{2}{4}$ to $\frac{1}{2}$ first)

Step 1: Simplify the divisor

$\frac{2}{4} = \frac{1}{2}$

Step 2: Find the reciprocal of the divisor

The reciprocal of $\frac{1}{2}$ is $2$.

Step 3: Multiply the dividend by the reciprocal

$\frac{8}{9} \times 2 = \frac{16}{9}$

Problem 25: $\boldsymbol{\frac{4}{6} \div \frac{2}{9}}$ (simplify $\frac{4}{6}$ to $\frac{2}{3}$ first)

Step 1: Simplify the dividend

$\frac{4}{6} = \frac{2}{3}$

Step 2: Find the reciprocal of the divisor

The reciprocal of $\frac{2}{9}$ is $\frac{9}{2}$.

Step 3: Multiply the dividend by the reciprocal

$\frac{2}{3} \times \frac{9}{2} = \frac{18}{6} = 3$

Final Answers:

1. $\boldsymbol{\frac{33}{16}}$
2. $\boldsymbol{\frac{14}{5}}$
3. $\boldsymbol{\frac{16}{15}}$
4. $\boldsymbol{\frac{56}{27}}$
5. $\boldsymbol{\frac{16}{9}}$
6. $\boldsymbol{3}$

Answer:

Let's solve these fraction division problems one by one. Remember that dividing by a fraction is the same as multiplying by its reciprocal.

Problem 18: $\boldsymbol{\frac{6}{8} \div \frac{4}{11}}$

Step 1: Find the reciprocal of the divisor

The reciprocal of $\frac{4}{11}$ is $\frac{11}{4}$.

Step 2: Multiply the dividend by the reciprocal

$\frac{6}{8} \times \frac{11}{4} = \frac{6 \times 11}{8 \times 4} = \frac{66}{32}$

Step 3: Simplify the fraction

Divide numerator and denominator by 2: $\frac{66 \div 2}{32 \div 2} = \frac{33}{16}$

Problem 19: $\boldsymbol{\frac{4}{5} \div \frac{2}{7}}$

Step 1: Find the reciprocal of the divisor

The reciprocal of $\frac{2}{7}$ is $\frac{7}{2}$.

Step 2: Multiply the dividend by the reciprocal

$\frac{4}{5} \times \frac{7}{2} = \frac{4 \times 7}{5 \times 2} = \frac{28}{10}$

Step 3: Simplify the fraction

Divide numerator and denominator by 2: $\frac{28 \div 2}{10 \div 2} = \frac{14}{5}$

Problem 20: $\boldsymbol{\frac{8}{9} \div \frac{5}{6}}$

Step 1: Find the reciprocal of the divisor

The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$.

Step 2: Multiply the dividend by the reciprocal

$\frac{8}{9} \times \frac{6}{5} = \frac{8 \times 6}{9 \times 5} = \frac{48}{45}$

Step 3: Simplify the fraction

Divide numerator and denominator by 3: $\frac{48 \div 3}{45 \div 3} = \frac{16}{15}$

Problem 23: $\boldsymbol{\frac{8}{9} \div \frac{3}{7}}$

Step 1: Find the reciprocal of the divisor

The reciprocal of $\frac{3}{7}$ is $\frac{7}{3}$.

Step 2: Multiply the dividend by the reciprocal

$\frac{8}{9} \times \frac{7}{3} = \frac{8 \times 7}{9 \times 3} = \frac{56}{27}$

Problem 24: $\boldsymbol{\frac{8}{9} \div \frac{2}{4}}$ (simplify $\frac{2}{4}$ to $\frac{1}{2}$ first)

Step 1: Simplify the divisor

$\frac{2}{4} = \frac{1}{2}$

Step 2: Find the reciprocal of the divisor

The reciprocal of $\frac{1}{2}$ is $2$.

Step 3: Multiply the dividend by the reciprocal

$\frac{8}{9} \times 2 = \frac{16}{9}$

Problem 25: $\boldsymbol{\frac{4}{6} \div \frac{2}{9}}$ (simplify $\frac{4}{6}$ to $\frac{2}{3}$ first)

Step 1: Simplify the dividend

$\frac{4}{6} = \frac{2}{3}$

Step 2: Find the reciprocal of the divisor

The reciprocal of $\frac{2}{9}$ is $\frac{9}{2}$.

Step 3: Multiply the dividend by the reciprocal

$\frac{2}{3} \times \frac{9}{2} = \frac{18}{6} = 3$

Final Answers:

1. $\boldsymbol{\frac{33}{16}}$
2. $\boldsymbol{\frac{14}{5}}$
3. $\boldsymbol{\frac{16}{15}}$
4. $\boldsymbol{\frac{56}{27}}$
5. $\boldsymbol{\frac{16}{9}}$
6. $\boldsymbol{3}$