Question

fractions worksheet
find the sum.

1. $4\frac{5}{6} + \frac{4}{5} =$
2. $8\frac{1}{2} + \frac{1}{6} =$
3. $3\frac{5}{8} + \frac{1}{2} =$
4. $1\frac{6}{10} + \frac{1}{4} =$
5. $7\frac{1}{5} + \frac{7}{11} =$
6. $1\frac{1}{4} + \frac{4}{10} =$
7. $8\frac{1}{7} + \frac{8}{9} =$
8. $6\frac{4}{9} + \frac{1}{3} =$
9. $8\frac{3}{6} + \frac{8}{11} =$
10. $7\frac{3}{9} + \frac{3}{7} =$
11. $8\frac{1}{5} + \frac{1}{2} =$
12. $5\frac{3}{4} + \frac{5}{8} =$
13. $9\frac{9}{12} + \frac{1}{3} =$
14. $3\frac{6}{8} + \frac{5}{11} =$

Explanation:

Step1: Convert mixed number to improper fraction

$4\frac{5}{6} = \frac{4\times6 + 5}{6} = \frac{29}{6}$

Step2: Find common denominator (30)

$\frac{29}{6} = \frac{29\times5}{6\times5} = \frac{145}{30}$, $\frac{4}{5} = \frac{4\times6}{5\times6} = \frac{24}{30}$

Step3: Add fractions and simplify

$\frac{145}{30} + \frac{24}{30} = \frac{169}{30} = 5\frac{19}{30}$

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Step1: Convert mixed number to improper fraction

$8\frac{1}{2} = \frac{8\times2 + 1}{2} = \frac{17}{2}$

Step2: Find common denominator (6)

$\frac{17}{2} = \frac{17\times3}{2\times3} = \frac{51}{6}$

Step3: Add fractions and simplify

$\frac{51}{6} + \frac{1}{6} = \frac{52}{6} = 8\frac{2}{3}$

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Step1: Convert mixed number to improper fraction

$3\frac{5}{8} = \frac{3\times8 + 5}{8} = \frac{29}{8}$

Step2: Find common denominator (8)

$\frac{1}{2} = \frac{1\times4}{2\times4} = \frac{4}{8}$

Step3: Add fractions and simplify

$\frac{29}{8} + \frac{4}{8} = \frac{33}{8} = 4\frac{1}{8}$

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Step1: Convert mixed number to improper fraction

$1\frac{6}{10} = \frac{1\times10 + 6}{10} = \frac{16}{10} = \frac{8}{5}$

Step2: Find common denominator (20)

$\frac{8}{5} = \frac{8\times4}{5\times4} = \frac{32}{20}$, $\frac{1}{4} = \frac{1\times5}{4\times5} = \frac{5}{20}$

Step3: Add fractions and simplify

$\frac{32}{20} + \frac{5}{20} = \frac{37}{20} = 1\frac{17}{20}$

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Step1: Convert mixed number to improper fraction

$7\frac{1}{5} = \frac{7\times5 + 1}{5} = \frac{36}{5}$

Step2: Find common denominator (55)

$\frac{36}{5} = \frac{36\times11}{5\times11} = \frac{396}{55}$, $\frac{7}{11} = \frac{7\times5}{11\times5} = \frac{35}{55}$

Step3: Add fractions and simplify

$\frac{396}{55} + \frac{35}{55} = \frac{431}{55} = 7\frac{46}{55}$

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Step1: Convert mixed number to improper fraction

$1\frac{1}{4} = \frac{1\times4 + 1}{4} = \frac{5}{4}$

Step2: Simplify and find common denominator (20)

$\frac{4}{10} = \frac{2}{5}$, $\frac{5}{4} = \frac{25}{20}$, $\frac{2}{5} = \frac{8}{20}$

Step3: Add fractions and simplify

$\frac{25}{20} + \frac{8}{20} = \frac{33}{20} = 1\frac{13}{20}$

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Step1: Convert mixed number to improper fraction

$8\frac{1}{7} = \frac{8\times7 + 1}{7} = \frac{57}{7}$

Step2: Find common denominator (63)

$\frac{57}{7} = \frac{57\times9}{7\times9} = \frac{513}{63}$, $\frac{8}{9} = \frac{8\times7}{9\times7} = \frac{56}{63}$

Step3: Add fractions and simplify

$\frac{513}{63} + \frac{56}{63} = \frac{569}{63} = 9\frac{2}{63}$

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Step1: Convert mixed number to improper fraction

$6\frac{4}{9} = \frac{6\times9 + 4}{9} = \frac{58}{9}$

Step2: Find common denominator (9)

$\frac{1}{3} = \frac{1\times3}{3\times3} = \frac{3}{9}$

Step3: Add fractions and simplify

$\frac{58}{9} + \frac{3}{9} = \frac{61}{9} = 6\frac{7}{9}$

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Step1: Simplify mixed number fraction

$8\frac{3}{6} = 8\frac{1}{2} = \frac{17}{2}$

Step2: Find common denominator (22)

$\frac{17}{2} = \frac{17\times11}{2\times11} = \frac{187}{22}$, $\frac{8}{11} = \frac{8\times2}{11\times2} = \frac{16}{22}$

Step3: Add fractions and simplify

$\frac{187}{22} + \frac{16}{22} = \frac{203}{22} = 9\frac{5}{22}$

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Step1: Simplify mixed number fraction

$7\frac{3}{9} = 7\frac{1}{3} = \frac{22}{3}$

Step2: Find common denominator (21)

$\frac{22}{3} = \frac{22\times7}{3\times7} = \frac{154}{21}$, $\frac{3}{7} = \frac{3\times3}{7\times3} = \frac{9}{21}$

Step3: Add fractions and simplify

$\frac{154}{21} + \frac{9}{21} = \frac{163}{21} = 7\frac{16}{21}$

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Step1: Convert mixed number to improper fraction

$8\frac{1}{5} = \frac{8\times5 + 1}{5} = \frac{41}{5}$

Step2: Find common denominator (10)

$\frac{41}{5} = \frac{41\times2}{5\times2} = \frac{82}{10}$, $\frac{1}{2} = \frac{1\times5}{2\times5} = \frac{5}{10}$

Step3: Add fractions and simplify

$\frac{82}{10} + \frac{5}{10} = \frac{87}{10} = 8\frac{7}{10}$

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Step1: Convert mixed number to improper fraction

$5\frac{3}{4} = \frac{5\times4 + 3}{4} = \frac{23}{4}$

Step2: Find common denominator (8)

$\frac{23}{4} = \frac{23\times2}{4\times2} = \frac{46}{8}$

Step3: Add fractions and simplify

$\frac{46}{8} + \frac{5}{8} = \frac{51}{8} = 6\frac{3}{8}$

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Step1: Simplify mixed number fraction

$9\frac{9}{12} = 9\frac{3}{4} = \frac{39}{4}$

Step2: Find common denominator (12)

$\frac{39}{4} = \frac{39\times3}{4\times3} = \frac{117}{12}$, $\frac{1}{3} = \frac{1\times4}{3\times4} = \frac{4}{12}$

Step3: Add fractions and simplify

$\frac{117}{12} + \frac{4}{12} = \frac{121}{12} = 10\frac{1}{12}$

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Step1: Simplify mixed number fraction

$3\frac{6}{8} = 3\frac{3}{4} = \frac{15}{4}$

Step2: Find common denominator (44)

$\frac{15}{4} = \frac{15\times11}{4\times11} = \frac{165}{44}$, $\frac{5}{11} = \frac{5\times4}{11\times4} = \frac{20}{44}$

Step3: Add fractions and simplify

$\frac{165}{44} + \frac{20}{44} = \frac{185}{44} = 4\frac{9}{44}$

Answer:

1. $5\frac{19}{30}$
2. $8\frac{2}{3}$
3. $4\frac{1}{8}$
4. $1\frac{17}{20}$
5. $7\frac{46}{55}$
6. $1\frac{13}{20}$
7. $9\frac{2}{63}$
8. $6\frac{7}{9}$
9. $9\frac{5}{22}$
10. $7\frac{16}{21}$
11. $8\frac{7}{10}$
12. $6\frac{3}{8}$
13. $10\frac{1}{12}$
14. $4\frac{9}{44}$