Question

mye review
find the quotient of the fractions. simplify your answer when possible. (hint: k.c.f. = keep - change - flip)
50.)
$\frac{4}{6} div \frac{3}{4}$
=
51.)
$\frac{6}{7} div \frac{2}{5}$
=
52.)
$\frac{3}{9} div \frac{1}{11}$
=
53.)
$\frac{1}{2} div \frac{1}{9}$

Explanation:

50. $\boldsymbol{\frac{4}{6} \div \frac{3}{4}}$

Step1: Apply K.C.F. (Keep, Change, Flip)

Keep the first fraction, change division to multiplication, flip the second fraction. So, $\frac{4}{6} \div \frac{3}{4} = \frac{4}{6} \times \frac{4}{3}$

Step2: Multiply the numerators and denominators

Multiply numerators: $4 \times 4 = 16$; Multiply denominators: $6 \times 3 = 18$. So we get $\frac{16}{18}$

Step3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor, which is 2. $\frac{16 \div 2}{18 \div 2} = \frac{8}{9}$

Step1: Apply K.C.F.

$\frac{6}{7} \div \frac{2}{5} = \frac{6}{7} \times \frac{5}{2}$

Step2: Multiply and simplify (if possible)

Multiply numerators: $6 \times 5 = 30$; Multiply denominators: $7 \times 2 = 14$. Then simplify $\frac{30}{14}$ by dividing numerator and denominator by 2: $\frac{30 \div 2}{14 \div 2} = \frac{15}{7}$ (or as a mixed number $2\frac{1}{7}$, but improper fraction is also acceptable)

Step1: Apply K.C.F.

$\frac{3}{9} \div \frac{1}{11} = \frac{3}{9} \times \frac{11}{1}$

Step2: Simplify the first fraction and multiply

Simplify $\frac{3}{9}$ to $\frac{1}{3}$ (dividing numerator and denominator by 3). Then multiply: $\frac{1}{3} \times \frac{11}{1} = \frac{11}{3}$ (or $3\frac{2}{3}$)

Answer:

$\frac{8}{9}$

51. $\boldsymbol{\frac{6}{7} \div \frac{2}{5}}$