Solve: 3/4 Divided by 1 1/3 - Mixed Number Division

Question

34:113= \frac{3}{4}:1\frac{1}{3}=

Video Solution

Step-by-Step Solution

To solve this division problem, we will follow these steps:

  • Step 1: Convert the mixed number to an improper fraction.
  • Step 2: Replace division with multiplication by the reciprocal.
  • Step 3: Perform the multiplication and simplify the result.

Let's begin with the solution:

Step 1: Convert the mixed number 113 1\frac{1}{3} into an improper fraction.

To convert, multiply 1 (the whole number) by 3 (the denominator) and add 1 (the numerator):

1×3+1=3+1=4 1 \times 3 + 1 = 3 + 1 = 4

Therefore, 113=43 1\frac{1}{3} = \frac{4}{3} .

Step 2: Write the division problem as multiplication by the reciprocal of 43 \frac{4}{3} .

The reciprocal of 43 \frac{4}{3} is 34 \frac{3}{4} . So,

34÷113=34×34 \frac{3}{4} \div 1\frac{1}{3} = \frac{3}{4} \times \frac{3}{4} .

Step 3: Multiply the fractions and simplify if possible.

Multiply the numerators and the denominators:

Numerators: 3×3=9 \text{Numerators: } 3 \times 3 = 9

Denominators: 4×4=16 \text{Denominators: } 4 \times 4 = 16

Thus, 34×34=916 \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} .

No further simplification is required as 9 and 16 are relatively prime.

Therefore, the solution to the problem is 916 \frac{9}{16} .

Answer

916 \frac{9}{16}