Q. \( = \dfrac{4}{5} \times 2\dfrac{2}{3}.\)
Answer
Convert the mixed number to an improper fraction.
\(2\frac{2}{3}=\frac{8}{3}\)
Now multiply.
\(\frac{4}{5}\times 2\frac{2}{3}=\frac{4}{5}\times\frac{8}{3}\)
Multiply the numerators and denominators.
\(\frac{4}{5}\times\frac{8}{3}=\frac{32}{15}\)
Convert the improper fraction to a mixed number.
\(\frac{32}{15}=2\frac{2}{15}\)
Final result: \(2\frac{2}{15}\)
Detailed Explanation
- Write the problem clearly
\[ \; ? = \dfrac{4}{5} \times 2\dfrac{2}{3} \; . \] - Convert the mixed number to an improper fraction
Multiply the whole-number part by the denominator, then add the numerator. The denominator stays the same.
Whole part times denominator: 2 \times 3 = 6.
Add the numerator: 6 + 2 = 8.
Therefore,
\[ 2\dfrac{2}{3} = \dfrac{8}{3}. \] - Replace and multiply the fractions
Replace the mixed number with its improper fraction and multiply numerators and denominators separately:
\[ \dfrac{4}{5} \times \dfrac{8}{3} = \dfrac{4 \times 8}{5 \times 3} = \dfrac{32}{15}. \] - Simplify the result
Check for common factors between numerator and denominator. The greatest common divisor of 32 and 15 is 1, so the fraction is already in lowest terms.
Convert to a mixed number by dividing 32 by 15: 15 goes into 32 two times with remainder 2. Thus,
\[ \dfrac{32}{15} = 2\dfrac{2}{15}. \] - Final answer
\[ \dfrac{4}{5} \times 2\dfrac{2}{3} = \dfrac{32}{15} = 2\dfrac{2}{15}. \]
See full solution
Arithmetic FAQs
How do I convert \(2\dfrac{2}{3}\) to an improper fraction?
Multiply the whole number by the denominator and add the numerator: \(2\times3+2=8\), so \(2\dfrac{2}{3}=\dfrac{8}{3}\)..
How do I compute \(\dfrac{4}{5}\times 2\dfrac{2}{3}\)?
Convert the mixed number: \(\dfrac{4}{5}\times\dfrac{8}{3}\) then multiply: \(\dfrac{4\cdot8}{5\cdot3}=\dfrac{32}{15}\).
Can I simplify before multiplying?
You may cancel common factors between any numerator and the opposite denominator. Here there are no cross-factors, so no simplification; multiply to get \(\dfrac{32}{15}\)..
How do I write \(\dfrac{32}{15}\) as a mixed number?
Divide 32 by 15: \(32=15\cdot2+2\), so \(\dfrac{32}{15}=2\dfrac{2}{15}\)..
What is the decimal value of the result?
\( \dfrac{32}{15}=2.1333\ldots \) which can be written as \( 2.1\overline{3}\ldots \) .
What are common mistakes to avoid?.
What are common mistakes to avoid?.
How can I check my answer quickly?
Convert to decimals: \(0.8\times2.666\ldots=2.133\ldots\), which matches \(\dfrac{32}{15}\) or \(2\dfrac{2}{15}\)..
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