Question

fractions worksheet
1 a. $\frac{4}{8}+\frac{1}{6}=$
1 b. $\frac{5}{11}+\frac{8}{10}=$
2 a. $\frac{9}{11}+\frac{9}{11}=$
2 b. $\frac{11}{8}+\frac{5}{3}=$
3 a. $\frac{6}{5}+\frac{3}{9}=$
3 b. $\frac{9}{2}+\frac{4}{12}=$
4 a. $\frac{4}{7}+\frac{10}{6}=$
4 b. $\frac{8}{12}+\frac{11}{7}=$
5 a. $\frac{11}{4}-\frac{10}{11}=$
5 b. $\frac{1}{3}+\frac{5}{7}=$
6 a. $\frac{1}{2}-\frac{1}{8}=$
6 b. $\frac{7}{9}+\frac{4}{7}=$

Explanation:

Step1: Find common denominator for 1a

The common denominator of 8 and 6 is 24.
$\frac{4}{8}+\frac{1}{6}=\frac{4\times3}{8\times3}+\frac{1\times4}{6\times4}=\frac{12}{24}+\frac{4}{24}$

Step2: Add the fractions for 1a

$\frac{12}{24}+\frac{4}{24}=\frac{12 + 4}{24}=\frac{16}{24}=\frac{2}{3}$

Step3: Find common denominator for 1b

The common denominator of 11 and 10 is 110.
$\frac{5}{11}+\frac{8}{10}=\frac{5\times10}{11\times10}+\frac{8\times11}{10\times11}=\frac{50}{110}+\frac{88}{110}$

Step4: Add the fractions for 1b

$\frac{50}{110}+\frac{88}{110}=\frac{50+88}{110}=\frac{138}{110}=\frac{69}{55}$

Step5: For 2a

Since the denominators are the same, just add the numerators.
$\frac{9}{11}+\frac{9}{11}=\frac{9 + 9}{11}=\frac{18}{11}$

Step6: Find common denominator for 2b

The common denominator of 8 and 3 is 24.
$\frac{11}{8}+\frac{5}{3}=\frac{11\times3}{8\times3}+\frac{5\times8}{3\times8}=\frac{33}{24}+\frac{40}{24}=\frac{33 + 40}{24}=\frac{73}{24}$

Step7: Find common denominator for 3a

The common denominator of 5 and 9 is 45.
$\frac{6}{5}+\frac{3}{9}=\frac{6\times9}{5\times9}+\frac{3\times5}{9\times5}=\frac{54}{45}+\frac{15}{45}=\frac{54+15}{45}=\frac{69}{45}=\frac{23}{15}$

Step8: Find common denominator for 3b

The common denominator of 2 and 12 is 12.
$\frac{9}{2}+\frac{4}{12}=\frac{9\times6}{2\times6}+\frac{4}{12}=\frac{54}{12}+\frac{4}{12}=\frac{54 + 4}{12}=\frac{58}{12}=\frac{29}{6}$

Step9: Find common denominator for 4a

The common denominator of 7 and 6 is 42.
$\frac{4}{7}+\frac{10}{6}=\frac{4\times6}{7\times6}+\frac{10\times7}{6\times7}=\frac{24}{42}+\frac{70}{42}=\frac{24 + 70}{42}=\frac{94}{42}=\frac{47}{21}$

Step10: Find common denominator for 4b

The common denominator of 12 and 7 is 84.
$\frac{8}{12}+\frac{11}{7}=\frac{8\times7}{12\times7}+\frac{11\times12}{7\times12}=\frac{56}{84}+\frac{132}{84}=\frac{56+132}{84}=\frac{188}{84}=\frac{47}{21}$

Step11: Find common denominator for 5a

The common denominator of 4 and 11 is 44.
$\frac{11}{4}-\frac{10}{11}=\frac{11\times11}{4\times11}-\frac{10\times4}{11\times4}=\frac{121}{44}-\frac{40}{44}=\frac{121-40}{44}=\frac{81}{44}$

Step12: Find common denominator for 5b

The common denominator of 3 and 7 is 21.
$\frac{1}{3}+\frac{5}{7}=\frac{1\times7}{3\times7}+\frac{5\times3}{7\times3}=\frac{7}{21}+\frac{15}{21}=\frac{7 + 15}{21}=\frac{22}{21}$

Step13: Find common denominator for 6a

The common denominator of 2 and 8 is 8.
$\frac{1}{2}-\frac{1}{8}=\frac{1\times4}{2\times4}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{4 - 1}{8}=\frac{3}{8}$

Step14: Find common denominator for 6b

The common denominator of 9 and 7 is 63.
$\frac{7}{9}+\frac{4}{7}=\frac{7\times7}{9\times7}+\frac{4\times9}{7\times9}=\frac{49}{63}+\frac{36}{63}=\frac{49+36}{63}=\frac{85}{63}$

Answer:

1a. $\frac{2}{3}$
1b. $\frac{69}{55}$
2a. $\frac{18}{11}$
2b. $\frac{73}{24}$
3a. $\frac{23}{15}$
3b. $\frac{29}{6}$
4a. $\frac{47}{21}$
4b. $\frac{47}{21}$
5a. $\frac{81}{44}$
5b. $\frac{22}{21}$
6a. $\frac{3}{8}$
6b. $\frac{85}{63}$