Solve: (3/4 ÷ 5/4) + 1/2 - Mixed Fraction Operations

Question

Solve the following exercise:

34:54+12=? \frac{3}{4}:\frac{5}{4}+\frac{1}{2}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the division 34:54 \frac{3}{4} : \frac{5}{4} .
  • Step 2: Use the formula ab:cd=ab×dc\frac{a}{b} : \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}.
  • Step 3: Simplify the division result.
  • Step 4: Add 12 \frac{1}{2} to the result of the division.
  • Step 5: Simplify the addition result to get the final answer.

Now, let's work through each step:

Step 1: We need to calculate 34:54 \frac{3}{4} : \frac{5}{4} . Using the division of fractions formula, this becomes:

34×45=3×44×5=1220 \frac{3}{4} \times \frac{4}{5} = \frac{3 \times 4}{4 \times 5} = \frac{12}{20} .

Step 2: Simplify 1220 \frac{12}{20} . Divide the numerator and the denominator by their greatest common divisor, which is 4:

12÷420÷4=35 \frac{12 \div 4}{20 \div 4} = \frac{3}{5} .

Step 3: Add 12 \frac{1}{2} to the result 35\frac{3}{5}:

The common denominator for addition is 10. Therefore:

35=3×25×2=610 \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} and 12=1×52×5=510 \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} .

Add these two fractions:

610+510=6+510=1110 \frac{6}{10} + \frac{5}{10} = \frac{6 + 5}{10} = \frac{11}{10} .

Therefore, the solution to the problem is 1110 \frac{11}{10} .

Answer

1110 \frac{11}{10}