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Solve the following: 1) 7 2/5 + 8 4/5, 2) 2 5/9 + 7 1/3, 3) 9 3/5 + 5 3/4. Home Work: Solve the following: 1) 2 3/5 - 1 1/2, 2) 9 1/6 - 7 3/5, 3) 3 3/5 - 2 2/3
Mathematics
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Exercise
- To solve :
Convert the mixed numbers to improper fractions.
$$ 7\frac{2}{5} = \frac{7 \times 5 + 2}{5} = \frac{37}{5} $$ $$ 8\frac{4}{3} = \frac{8 \times 3 + 4}{3} = \frac{28}{3} $$Find a common denominator, which is 15.
$$ \frac{37}{5} = \frac{37 \times 3}{5 \times 3} = \frac{111}{15} $$ $$ \frac{28}{3} = \frac{28 \times 5}{3 \times 5} = \frac{140}{15} $$Add the fractions.
$$ \frac{111}{15} + \frac{140}{15} = \frac{111 + 140}{15} = \frac{251}{15} $$Convert the improper fraction back to a mixed number.
$$ \frac{251}{15} = 16\frac{11}{15} $$ The answer is $\boxed{\mathbf{16\frac{11}{15}}}$.2. To solve :
Convert the mixed numbers to improper fractions.
$$ 2\frac{5}{9} = \frac{2 \times 9 + 5}{9} = \frac{23}{9} $$ $$ 7\frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{22}{3} $$Find a common denominator, which is 9.
$$ \frac{22}{3} = \frac{22 \times 3}{3 \times 3} = \frac{66}{9} $$Add the fractions.
$$ \frac{23}{9} + \frac{66}{9} = \frac{23 + 66}{9} = \frac{89}{9} $$Convert the improper fraction back to a mixed number.
$$ \frac{89}{9} = 9\frac{8}{9} $$ The answer is $\boxed{\mathbf{9\frac{8}{9}}}$.3. To solve :
Convert the mixed numbers to improper fractions.
$$ 9\frac{3}{5} = \frac{9 \times 5 + 3}{5} = \frac{48}{5} $$ $$ 5\frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{23}{4} $$Find a common denominator, which is 20.
$$ \frac{48}{5} = \frac{48 \times 4}{5 \times 4} = \frac{192}{20} $$ $$ \frac{23}{4} = \frac{23 \times 5}{4 \times 5} = \frac{115}{20} $$Add the fractions.
$$ \frac{192}{20} + \frac{115}{20} = \frac{192 + 115}{20} = \frac{307}{20} $$Convert the improper fraction back to a mixed number.
$$ \frac{307}{20} = 15\frac{7}{20} $$ The answer is $\boxed{\mathbf{15\frac{7}{20}}}$.Home Work
- To solve :
Convert the mixed numbers to improper fractions.
$$ 2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5} $$ $$ 1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2} $$Find a common denominator, which is 10.
$$ \frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10} $$ $$ \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} $$Subtract the fractions.
$$ \frac{26}{10} - \frac{15}{10} = \frac{26 - 15}{10} = \frac{11}{10} $$Convert the improper fraction back to a mixed number.
$$ \frac{11}{10} = 1\frac{1}{10} $$ The answer is $\boxed{\mathbf{1\frac{1}{10}}}$.2. To solve :
Simplify the first mixed number and convert both to improper fractions.
$$ 9\frac{3}{6} = 9\frac{1}{2} = \frac{9 \times 2 + 1}{2} = \frac{19}{2} $$ $$ 7\frac{3}{5} = \frac{7 \times 5 + 3}{5} = \frac{38}{5} $$Find a common denominator, which is 10.
$$ \frac{19}{2} = \frac{19 \times 5}{2 \times 5} = \frac{95}{10} $$ $$ \frac{38}{5} = \frac{38 \times 2}{5 \times 2} = \frac{76}{10} $$Subtract the fractions.
$$ \frac{95}{10} - \frac{76}{10} = \frac{95 - 76}{10} = \frac{19}{10} $$Convert the improper fraction back to a mixed number.
$$ \frac{19}{10} = 1\frac{9}{10} $$ The answer is $\boxed{\mathbf{1\frac{9}{10}}}$.3. To solve :
Convert the mixed numbers to improper fractions.
$$ 3\frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{18}{5} $$ $$ 2\frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3} $$Find a common denominator, which is 15.
$$ \frac{18}{5} = \frac{18 \times 3}{5 \times 3} = \frac{54}{15} $$
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