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Divide. Write the quotient in lowest terms.

3(1)/(8)÷1(2)/(3)=

Divide. Write the quotient in lowest terms.\newline318÷123= 3 \frac{1}{8} \div 1 \frac{2}{3}=

Full solution

Q. Divide. Write the quotient in lowest terms.\newline318÷123= 3 \frac{1}{8} \div 1 \frac{2}{3}=
  1. Convert to improper fractions: Convert the mixed numbers to improper fractions.\newline3183\frac{1}{8} can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator: (3×8)+1=24+1=25(3 \times 8) + 1 = 24 + 1 = 25. So, 3183\frac{1}{8} becomes 258\frac{25}{8}.\newline1231\frac{2}{3} can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator: (1×3)+2=3+2=5(1 \times 3) + 2 = 3 + 2 = 5. So, 1231\frac{2}{3} becomes 53\frac{5}{3}.
  2. Rewrite as a multiplication problem: Rewrite the division problem as a multiplication problem by multiplying by the reciprocal of the second fraction.\newlineThe division 258÷53\frac{25}{8} \div \frac{5}{3} is equivalent to 258×35\frac{25}{8} \times \frac{3}{5}.
  3. Multiply the numerators and denominators: Multiply the numerators and the denominators.\newlineThe numerator of the resulting fraction is 25×3=7525 \times 3 = 75.\newlineThe denominator of the resulting fraction is 8×5=408 \times 5 = 40.\newlineSo, the multiplication gives us 7540\frac{75}{40}.
  4. Simplify the fraction: Simplify the fraction to its lowest terms.\newlineBoth the numerator and the denominator are divisible by 55.\newlineDividing the numerator by 55 gives us 75÷5=1575 \div 5 = 15.\newlineDividing the denominator by 55 gives us 40÷5=840 \div 5 = 8.\newlineSo, the simplified fraction is 158\frac{15}{8}.
  5. Convert back to a mixed number: Convert the improper fraction back to a mixed number if necessary.\newlineSince 158\frac{15}{8} is an improper fraction, we can convert it to a mixed number.\newline1515 divided by 88 gives us 11 with a remainder of 77.\newlineSo, the mixed number is 1(78)1\left(\frac{7}{8}\right).

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