Question

1. reduce the following fractions:

a) \\(\frac{21}{42}\\)
b) \\(\frac{16}{36}\\)
c) \\(\frac{-36}{42}\\)
d) \\(\frac{-16}{-21}\\)

1. change the following mixed numbers to improper fractions:

a) \\(2\frac{1}{5}\\)
b) \\(3\frac{6}{7}\\)

1. simplify:

a) \\(\frac{3}{7}\bullet\frac{4}{5}\\)
b) \\(\frac{7}{4}\div\frac{2}{7}\\)
c) \\(\frac{6}{7}\div\frac{2}{5}\\)
d) \\(\frac{4}{11}+\frac{5}{11}\\)
e) \\(\frac{5}{6}+\frac{3}{4}\\)
f) \\(\frac{2}{7}-\frac{3}{5}\\)

Explanation:

Problem 12: Reduce the following fractions

a) $\boldsymbol{\frac{21}{42}}$

Step1: Find GCD of 21 and 42

GCD(21, 42) = 21

Step2: Divide numerator and denominator by GCD

$\frac{21 \div 21}{42 \div 21} = \frac{1}{2}$

b) $\boldsymbol{\frac{16}{36}}$

Step1: Find GCD of 16 and 36

GCD(16, 36) = 4

Step2: Divide numerator and denominator by GCD

$\frac{16 \div 4}{36 \div 4} = \frac{4}{9}$

c) $\boldsymbol{-\frac{36}{42}}$

Step1: Find GCD of 36 and 42

GCD(36, 42) = 6

Step2: Divide numerator and denominator by GCD (and keep the negative sign)

$-\frac{36 \div 6}{42 \div 6} = -\frac{6}{7}$

d) $\boldsymbol{\frac{-16}{-21}}$

Answer:

s:

1. a) $\boldsymbol{\frac{1}{2}}$; b) $\boldsymbol{\frac{4}{9}}$; c) $\boldsymbol{-\frac{6}{7}}$; d) $\boldsymbol{\frac{16}{21}}$
2. a) $\boldsymbol{\frac{11}{5}}$; b) $\boldsymbol{\frac{27}{7}}$
3. a) $\boldsymbol{\frac{12}{35}}$; b) $\boldsymbol{\frac{49}{8}}$; c) $\boldsymbol{\frac{15}{7}}$; d) $\boldsymbol{\frac{9}{11}}$; e) $\boldsymbol{\frac{19}{12}}$; f) $\boldsymbol{-\frac{11}{35}}$