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Complete the equation. Write the sum as a mixed number. 1(7)/(9)+(1)/(5)=(80)/(◻)+(9)/(◻)=◻(◻)/(◻)

Complete the equation. Write the sum as a mixed number.\newline179+15=80□+9□=□(□□)1\frac{7}{9}+\frac{1}{5}=\frac{80}{\Box}+\frac{9}{\Box}=\Box\left(\frac{\Box}{\Box}\right)

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Full solution

Q. Complete the equation. Write the sum as a mixed number.\newline179+15=80□+9□=□(□□)1\frac{7}{9}+\frac{1}{5}=\frac{80}{\Box}+\frac{9}{\Box}=\Box\left(\frac{\Box}{\Box}\right)
  1. Convert to improper fraction: Convert mixed number to improper fraction.\newline179=1+79=99+79=1691\frac{7}{9} = 1 + \frac{7}{9} = \frac{9}{9} + \frac{7}{9} = \frac{16}{9}.
  2. Find common denominator: Find a common denominator for 169\frac{16}{9} and 15\frac{1}{5}.\newlineCommon denominator of 99 and 55 is 4545.\newline169=(16×5)(9×5)=8045\frac{16}{9} = \frac{(16\times5)}{(9\times5)} = \frac{80}{45}.\newline15=(1×9)(5×9)=945\frac{1}{5} = \frac{(1\times9)}{(5\times9)} = \frac{9}{45}.
  3. Add fractions: Add the fractions.\newline8045+945=80+945=8945\frac{80}{45} + \frac{9}{45} = \frac{80 + 9}{45} = \frac{89}{45}.
  4. Convert to mixed number: Convert improper fraction to mixed number. 8945=1\frac{89}{45} = 1 whole and 4445\frac{44}{45} left over, so it's 1(4445)1\left(\frac{44}{45}\right).
  5. Complete the equation: Complete the equation with the found values.\newline1(7)9+15=8045+945=1(44)45\frac{1(7)}{9} + \frac{1}{5} = \frac{80}{45} + \frac{9}{45} = \frac{1(44)}{45}.

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