4 2/3 divided by 3/4

Understand the Problem

The question is asking us to perform the division of the mixed number 4 2/3 by the fraction 3/4. We will convert the mixed number to an improper fraction, then apply the division operation by multiplying by the reciprocal of the divisor.

Answer

$6 \frac{2}{9}$

Steps to Solve

Convert the mixed number to an improper fraction

To convert the mixed number (4 \frac{2}{3}) into an improper fraction, we multiply the whole number by the denominator and add the numerator.

[ 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} ]

Identify the divisor and find its reciprocal

The divisor is the fraction (\frac{3}{4}). The reciprocal of a fraction is obtained by swapping the numerator and the denominator. Thus, the reciprocal of (\frac{3}{4}) is (\frac{4}{3}).

Multiply the improper fraction by the reciprocal

Now we multiply the improper fraction (\frac{14}{3}) by the reciprocal (\frac{4}{3}):

[ \frac{14}{3} \times \frac{4}{3} = \frac{14 \times 4}{3 \times 3} = \frac{56}{9} ]

Convert the improper fraction back to a mixed number (if needed)

To convert (\frac{56}{9}) back into a mixed number, we divide (56) by (9):

[ 56 \div 9 = 6 \quad \text{(whole number)} ] [ 56 - (9 \times 6) = 2 \quad \text{(remainder)} ]

So, (\frac{56}{9}) can be expressed as the mixed number (6 \frac{2}{9}).

The result of dividing (4 \frac{2}{3}) by (\frac{3}{4}) is (6 \frac{2}{9}).

More Information

Dividing a mixed number by a fraction involves converting the mixed number to an improper fraction and then multiplying by the reciprocal. This method can be particularly useful in various real-life situations, such as recipe adjustments or when measuring.

Tips

Not converting the mixed number to an improper fraction before starting the division.
Forgetting to take the reciprocal of the divisor.
Errors in arithmetic during multiplication or conversion back to a mixed number.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!