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Divide. Write the quotient in lowest terms.

8÷1(4)/(5)=

Divide. Write the quotient in lowest terms.\newline8÷145= 8 \div 1 \frac{4}{5}=

Full solution

Q. Divide. Write the quotient in lowest terms.\newline8÷145= 8 \div 1 \frac{4}{5}=
  1. Identify numbers: Identify the numbers involved in the division.\newlineWe have the whole number 88 and the mixed number 1(45)1\left(\frac{4}{5}\right). We need to divide 88 by 1(45)1\left(\frac{4}{5}\right).
  2. Convert to improper fraction: Convert the mixed number to an improper fraction. 1(45)1\left(\frac{4}{5}\right) can be converted to an improper fraction by multiplying the whole number part by the denominator of the fraction part and then adding the numerator of the fraction part. 1(45)=(1×5)+4=5+4=951\left(\frac{4}{5}\right) = (1 \times 5) + 4 = 5 + 4 = \frac{9}{5}
  3. Rewrite using improper fraction: Rewrite the division problem using the improper fraction.\newlineNow the division problem is 8÷958 \div \frac{9}{5}.
  4. Convert to multiplication: Convert the division problem to a multiplication problem by using the reciprocal of the divisor.\newlineTo divide by a fraction, we multiply by its reciprocal. The reciprocal of 95\frac{9}{5} is 59\frac{5}{9}.\newlineSo, 8÷958 \div \frac{9}{5} becomes 8×59.8 \times \frac{5}{9}.
  5. Perform multiplication: Perform the multiplication.\newlineNow we multiply the whole number by the fraction.\newline8×59=(8×5)/9=4098 \times \frac{5}{9} = \left(8 \times 5\right) / 9 = \frac{40}{9}
  6. Simplify fraction: Simplify the fraction, if possible.\newlineThe fraction 409\frac{40}{9} is already in its simplest form because 4040 and 99 have no common factors other than 11.

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