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Complete the equation. Write the sum as a mixed number. 2(1)/(2)+(8)/(9)=(45)/(◻)+(16)/(◻)=◻(◻)/(◻)

Complete the equation. Write the sum as a mixed number.\newline212+89=45□+16□=□□□ 2 \frac{1}{2}+\frac{8}{9}=\frac{45}{\square}+\frac{16}{\square}=\square \frac{\square}{\square}

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Full solution

Q. Complete the equation. Write the sum as a mixed number.\newline212+89=45□+16□=□□□ 2 \frac{1}{2}+\frac{8}{9}=\frac{45}{\square}+\frac{16}{\square}=\square \frac{\square}{\square}
  1. Convert to improper fraction: Convert the mixed number to an improper fraction.\newline2122\frac{1}{2} = 2×2+12\frac{2\times 2 + 1}{2} = 52\frac{5}{2}.
  2. Add fractions: Add the improper fraction to the other fraction.\newline52+89\frac{5}{2} + \frac{8}{9}.\newlineTo add, find a common denominator. The least common multiple of 22 and 99 is 1818.\newline52=(5×9)(2×9)=4518\frac{5}{2} = \frac{(5\times9)}{(2\times9)} = \frac{45}{18}.\newline89=(8×2)(9×2)=1618\frac{8}{9} = \frac{(8\times2)}{(9\times2)} = \frac{16}{18}.\newlineNow, add the fractions: 4518+1618=6118\frac{45}{18} + \frac{16}{18} = \frac{61}{18}.
  3. Convert to mixed number: Convert the improper fraction 6118\frac{61}{18} to a mixed number.\newline6118=3\frac{61}{18} = 3 remainder 77, so it's 3(718)3\left(\frac{7}{18}\right).
  4. Fill in blanks: Fill in the blanks in the original equation.\newline2(12)+89=4518+1618=3(718)2\left(\frac{1}{2}\right) + \frac{8}{9} = \frac{45}{18} + \frac{16}{18} = 3\left(\frac{7}{18}\right).

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