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Divide. Write the quotient in lowest terms.

1(7)/(9)÷(4)/(5)=

Divide. Write the quotient in lowest terms.\newline179÷45= 1 \frac{7}{9} \div \frac{4}{5}=

Full solution

Q. Divide. Write the quotient in lowest terms.\newline179÷45= 1 \frac{7}{9} \div \frac{4}{5}=
  1. Write division problem as fraction: Write the division problem as a fraction.\newlineWe have the division problem 1(7)9÷45\frac{1(7)}{9} \div \frac{4}{5}. First, we need to express the mixed number 1(7)/91(7)/9 as an improper fraction.\newline1(7)/9=99+79=1691(7)/9 = \frac{9}{9} + \frac{7}{9} = \frac{16}{9}.\newlineNow, we can rewrite the division problem as (169)÷(45)(\frac{16}{9}) \div (\frac{4}{5}).
  2. Convert to multiplication problem: Convert the division problem into a multiplication problem by multiplying by the reciprocal of the second fraction.\newlineTo divide by a fraction, we multiply by its reciprocal. The reciprocal of 45\frac{4}{5} is 54\frac{5}{4}.\newlineSo, 169\frac{16}{9} ÷\div 45\frac{4}{5} becomes 169\frac{16}{9} \cdot 54\frac{5}{4}.
  3. Multiply numerators and denominators: Multiply the numerators and the denominators.\newlineNow, we multiply the numerators together and the denominators together.\newline(169)×(54)=(16×59×4)=8036(\frac{16}{9}) \times (\frac{5}{4}) = (\frac{16 \times 5}{9 \times 4}) = \frac{80}{36}.
  4. Simplify fraction to lowest terms: Simplify the fraction to its lowest terms.\newlineTo simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and the denominator and divide both by it.\newlineThe GCF of 8080 and 3636 is 44.\newline80÷4=2080 \div 4 = 20, and 36÷4=936 \div 4 = 9.\newlineSo, 8036\frac{80}{36} simplifies to 209\frac{20}{9}.
  5. Check for further simplification: Check if the fraction can be simplified further.\newlineThe numbers 2020 and 99 do not have any common factors other than 11, so the fraction is already in its simplest form.

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