Question

mfm2p
g) $\frac{11}{12} - \frac{3}{4}$
h) $\frac{8}{10} - \frac{2}{5} - \frac{1}{2}$
multiplying and dividing fractions: remember the trick to dividing!!!
express answers in lowest terms.
a) $\frac{5}{9} \times \frac{2}{7} = \frac{10}{63}$
b) $\frac{2}{15} \times \frac{3}{10} = \frac{6}{150}$
c) $\frac{9}{20}$
d) $\frac{2}{5} \times \frac{3}{4} \times \frac{1}{2} = \frac{6}{40}$ (with $\frac{3}{20}$ circled)
e) $\frac{2}{9} \div \frac{5}{6} = \frac{10}{54}$ (and $\frac{2}{9} \times \frac{6}{5} = \frac{12}{45}$)
f) (partial)
g) $\frac{5}{12} \div \frac{7}{10} = \frac{35}{120}$
h) $\frac{10}{5} \div \frac{6}{15} = \frac{60}{75}$

Answer:

Let's solve each problem step by step:

Part g: $\boldsymbol{\frac{11}{12} - \frac{3}{4}}$

Step 1: Find a common denominator

The denominators are 12 and 4. The least common denominator (LCD) of 12 and 4 is 12.
Rewrite $\frac{3}{4}$ with denominator 12: $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

Step 2: Subtract the fractions

$\frac{11}{12} - \frac{9}{12} = \frac{11 - 9}{12} = \frac{2}{12}$

Step 3: Simplify the result

Simplify $\frac{2}{12}$ by dividing numerator and denominator by their greatest common divisor (GCD), which is 2: $\frac{2 \div 2}{12 \div 2} = \frac{1}{6}$

Part h: $\boldsymbol{\frac{8}{10} - \frac{2}{5} - \frac{1}{2}}$

Step 1: Find a common denominator

The denominators are 10, 5, and 2. The LCD of 10, 5, and 2 is 10.
Rewrite $\frac{2}{5}$ and $\frac{1}{2}$ with denominator 10:
$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$
$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$

Step 2: Subtract the fractions

$\frac{8}{10} - \frac{4}{10} - \frac{5}{10} = \frac{8 - 4 - 5}{10} = \frac{-1}{10}$ (or $-\frac{1}{10}$)

Part a: $\boldsymbol{\frac{5}{9} \times \frac{2}{7}}$

Step 1: Multiply the numerators and denominators

$\frac{5 \times 2}{9 \times 7} = \frac{10}{63}$
(This fraction is already in lowest terms since 10 and 63 have no common divisors other than 1.)

Part b: $\boldsymbol{\frac{2}{15} \times \frac{3}{10}}$

Step 1: Multiply the numerators and denominators

$\frac{2 \times 3}{15 \times 10} = \frac{6}{150}$

Step 2: Simplify the result

Divide numerator and denominator by their GCD (which is 6): $\frac{6 \div 6}{150 \div 6} = \frac{1}{25}$

Part d: $\boldsymbol{\frac{2}{5} \times \frac{3}{4} \times \frac{1}{2}}$

Step 1: Multiply the first two fractions

$\frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20}$ (simplify to $\frac{3}{10}$)

Step 2: Multiply the result by the third fraction

$\frac{3}{10} \times \frac{1}{2} = \frac{3 \times 1}{10 \times 2} = \frac{3}{20}$

Part e: $\boldsymbol{\frac{2}{9} \div \frac{5}{6}}$

Step 1: Recall the rule for dividing fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So, $\frac{2}{9} \div \frac{5}{6} = \frac{2}{9} \times \frac{6}{5}$

Step 2: Multiply the numerators and denominators

$\frac{2 \times 6}{9 \times 5} = \frac{12}{45}$

Step 3: Simplify the result

Divide numerator and denominator by their GCD (which is 3): $\frac{12 \div 3}{45 \div 3} = \frac{4}{15}$

Part g (second g): $\boldsymbol{\frac{5}{12} \div \frac{7}{10}}$

Step 1: Use the reciprocal rule

$\frac{5}{12} \div \frac{7}{10} = \frac{5}{12} \times \frac{10}{7}$

Step 2: Multiply the numerators and denominators

$\frac{5 \times 10}{12 \times 7} = \frac{50}{84}$

Step 3: Simplify the result

Divide numerator and denominator by their GCD (which is 2): $\frac{50 \div 2}{84 \div 2} = \frac{25}{42}$

Part h (second h): $\boldsymbol{\frac{10}{5} \div \frac{6}{15}}$

Step 1: Simplify $\frac{10}{5}$ first

$\frac{10}{5} = 2$

Step 2: Use the reciprocal rule

$2 \div \frac{6}{15} = 2 \times \frac{15}{6}$

Step 3: Multiply and simplify

$2 \times \frac{15}{6} = \frac{30}{6} = 5$

Final Answers:

• g) $\frac{11}{12} - \frac{3}{4} = \boldsymbol{\frac{1}{6}}$
• h) $\frac{8}{10} - \frac{2}{5} - \frac{1}{2} = \boldsymbol{-\frac{1}{10}}$
• a) $\frac{5}{9} \times \frac{2}{7} = \boldsymbol{\frac{10}{63}}$
• b) $\frac{2}{15} \times \frac{3}{10} = \boldsymbol{\frac{1}{25}}$
• d) $\frac{2}{5} \times \frac{3}{4} \times \frac{1}{2} = \boldsymbol{\frac{3}{20}}$
• e) $\frac{2}{9} \div \frac{5}{6} = \boldsymbol{\frac{4}{15}}$
• g) $\frac{5}{12} \div \frac{7}{10} = \boldsymbol{\frac{25}{42}}$
• h) $\frac{10}{5} \div \frac{6}{15} = \boldsymbol{5}$