Solve Mixed Number Division: 1⅔ ÷ ¾ Step-by-Step

Video Solution

Solution Steps

00:00 Solve

00:04 Convert mixed number to fraction

00:09 Calculate the numerator and put it back in the exercise

00:19 Convert division to multiplication by reciprocal

00:31 Make sure to multiply numerator by numerator and denominator by denominator

00:36 Calculate the multiplications

00:41 Now convert to mixed number

00:46 Break down 36 into 21 plus 15

00:57 Break down the fraction into whole number and remainder

01:01 Convert whole fraction to whole number, and combine into mixed number

01:10 Simplify what's possible

01:17 And this is the solution to the question

Step-by-Step Solution

To solve the division of the mixed fraction $1\frac{2}{7}$ by the fraction $\frac{3}{4}$ , follow these steps:

Step 1: Convert the mixed fraction to an improper fraction: $1\frac{2}{7} = \frac{9}{7}$ .
Step 2: Determine the reciprocal of the divisor fraction: $\text{Reciprocal of } \frac{3}{4} = \frac{4}{3}$ .
Step 3: Multiply the improper fraction by the reciprocal of the divisor: $\frac{9}{7} \times \frac{4}{3} = \frac{36}{21}$ .
Step 4: Simplify the resulting fraction: The greatest common divisor of 36 and 21 is 3. Thus, $\frac{36}{21} = \frac{12}{7}$ .
Step 5: Convert back to a mixed number: The improper fraction $\frac{12}{7} = 1\frac{5}{7}$ .

Therefore, the solution to the problem is $1\frac{5}{7}$ .