Question

adding and subtracting using fractions
a) $\frac{1}{6} + \frac{1}{6}$
b) $\frac{7}{10} - \frac{3}{10}$
c) $\frac{1}{2} + \frac{1}{4}$
d) $\frac{7}{10} - \frac{2}{5}$
e) $\frac{3}{4} + \frac{5}{6}$
f) $\frac{17}{9} - \frac{11}{12}$
g) $\frac{2}{3} + \frac{1}{4} - \frac{7}{12}$
h) $\frac{11}{15} - \frac{3}{20} + \frac{7}{4}$
i) $\frac{13}{8} + \frac{7}{12} - \frac{7}{6}$
j) $3\frac{2}{5} - 1\frac{7}{10}$
k) $7\frac{7}{12} - 5\frac{11}{18}$
l) $3\frac{3}{14} + \frac{16}{7} - 5\frac{1}{2}$

Explanation:

Step1: Add like denominators

$\frac{1}{6} + \frac{1}{6} = \frac{1+1}{6} = \frac{2}{6}$

Step2: Simplify the fraction

$\frac{2}{6} = \frac{1}{3}$

Step1: Subtract like denominators

$\frac{7}{10} - \frac{3}{10} = \frac{7-3}{10} = \frac{4}{10}$

Step2: Simplify the fraction

$\frac{4}{10} = \frac{2}{5}$

Step1: Find common denominator (4)

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

Step2: Add the fractions

$\frac{2}{4} + \frac{1}{4} = \frac{2+1}{4} = \frac{3}{4}$

Step1: Find common denominator (10)

$\frac{2}{5} = \frac{4}{10}$

Step2: Subtract the fractions

$\frac{7}{10} - \frac{4}{10} = \frac{7-4}{10} = \frac{3}{10}$

Step1: Find common denominator (12)

$\frac{3}{4} = \frac{9}{12}, \frac{5}{6} = \frac{10}{12}$

Step2: Add the fractions

$\frac{9}{12} + \frac{10}{12} = \frac{9+10}{12} = \frac{19}{12}$

Step1: Find common denominator (36)

$\frac{17}{9} = \frac{68}{36}, \frac{11}{12} = \frac{33}{36}$

Step2: Subtract the fractions

$\frac{68}{36} - \frac{33}{36} = \frac{68-33}{36} = \frac{35}{36}$

Step1: Find common denominator (12)

$\frac{2}{3} = \frac{8}{12}, \frac{1}{4} = \frac{3}{12}$

Step2: Add first two fractions

$\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

Step3: Subtract the final fraction

$\frac{11}{12} - \frac{7}{12} = \frac{11-7}{12} = \frac{4}{12} = \frac{1}{3}$

Step1: Find common denominator (60)

$\frac{11}{15} = \frac{44}{60}, \frac{3}{20} = \frac{9}{60}, \frac{7}{4} = \frac{105}{60}$

Step2: Subtract second fraction

$\frac{44}{60} - \frac{9}{60} = \frac{35}{60}$

Step3: Add the final fraction

$\frac{35}{60} + \frac{105}{60} = \frac{140}{60} = \frac{7}{3}$

Step1: Find common denominator (24)

$\frac{13}{8} = \frac{39}{24}, \frac{7}{12} = \frac{14}{24}, \frac{7}{6} = \frac{28}{24}$

Step2: Add first two fractions

$\frac{39}{24} + \frac{14}{24} = \frac{53}{24}$

Step3: Subtract the final fraction

$\frac{53}{24} - \frac{28}{24} = \frac{25}{24}$

Step1: Convert to improper fractions

$3\frac{2}{5} = \frac{17}{5}, 1\frac{7}{10} = \frac{17}{10}$

Step2: Find common denominator (10)

$\frac{17}{5} = \frac{34}{10}$

Step3: Subtract the fractions

$\frac{34}{10} - \frac{17}{10} = \frac{17}{10} = 1\frac{7}{10}$

Step1: Convert to improper fractions

$7\frac{7}{12} = \frac{91}{12}, 5\frac{11}{18} = \frac{101}{18}$

Step2: Find common denominator (36)

$\frac{91}{12} = \frac{273}{36}, \frac{101}{18} = \frac{202}{36}$

Step3: Subtract the fractions

$\frac{273}{36} - \frac{202}{36} = \frac{71}{36} = 1\frac{35}{36}$

Step1: Convert to improper fractions

$3\frac{3}{14} = \frac{45}{14}, 5\frac{1}{2} = \frac{11}{2}$

Step2: Find common denominator (14)

$\frac{16}{7} = \frac{32}{14}, \frac{11}{2} = \frac{77}{14}$

Step3: Add first two fractions

$\frac{45}{14} + \frac{32}{14} = \frac{77}{14}$

Step4: Subtract the final fraction

$\frac{77}{14} - \frac{77}{14} = 0$

Answer:

a) $\frac{1}{3}$
b) $\frac{2}{5}$
c) $\frac{3}{4}$
d) $\frac{3}{10}$
e) $\frac{19}{12}$
f) $\frac{35}{36}$
g) $\frac{1}{3}$
h) $\frac{7}{3}$
i) $\frac{25}{24}$
j) $1\frac{7}{10}$
k) $1\frac{35}{36}$
l) $0$