# Fractions and mixed numerals

(a) Convert the following mixed numbers to improper fractions.
i. 3 5/8
ii. 7 7/6
(b) Convert the following improper fraction to mixed number.
i. 13/4
ii. 78/5
(c) Simplify these fractions to their lowest terms.
i. 36/42
ii. 27/45

2. evaluate following expressions with fractions and mixed numerals:
i. 1/2 - 3/5 + 4/7=
ii. 1/2 ÷ 3/5 × 4/7=
iii. (4/7 + 1/2) ÷ 5 3/7=
iv. 2/5 × 2 1/3 + 3/2=
v. 20 - (4 × 2/7 ÷ 2/21)

a1 =  3.625
a2 =  8.1667
b1 =  3.25
b2 =  15.6
c1 =  0.8571
c2 =  0.6
d1 =  0.4714
d2 =  0.4762
d3 =  0.1974
d4 =  2.4333
d5 =  8

### Step-by-step explanation:

${b}_{1}=\frac{13}{4}=3\frac{1}{4}=3.25$
${b}_{2}=\frac{78}{5}=15\frac{3}{5}=15.6$
${c}_{1}=\frac{36}{42}=\frac{6}{7}=0.8571$
${c}_{2}=\frac{27}{45}=\frac{3}{5}=0.6$
${d}_{1}=\frac{1}{2}-\frac{3}{5}+\frac{4}{7}=\frac{33}{70}=0.4714$
${d}_{3}=\left(\frac{4}{7}+\frac{1}{2}\right)\mathrm{/}5\frac{3}{7}=\frac{15}{76}=0.1974$

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