Solving Fraction Problems: 15/16 × 3/8 ÷ 3/4
Fraction problems can be challenging, especially when dealing with multiplication and division of fractions. In this article, we will solve the problem 15/16 × 3/8 ÷ 3/4 step by step.
Understanding the Problem
The problem 15/16 × 3/8 ÷ 3/4 involves two operations: multiplication and division. To solve this problem, we need to follow the order of operations (PEMDAS):
- Multiply 15/16 and 3/8
- Divide the result by 3/4
Step 1: Multiplication
To multiply two fractions, we need to multiply the numerators (numbers on top) and multiply the denominators (numbers on the bottom), then simplify the result.
$\frac{15}{16} \times \frac{3}{8} = \frac{15 \times 3}{16 \times 8} = \frac{45}{128}$
Step 2: Division
To divide a fraction by another fraction, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply.
$\frac{45}{128} \div \frac{3}{4} = \frac{45}{128} \times \frac{4}{3} = \frac{45 \times 4}{128 \times 3} = \frac{180}{384}$
Simplification
We can simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 12.
$\frac{180}{384} = \frac{180 \div 12}{384 \div 12} = \frac{15}{32}$
Final Answer
The final answer to the problem 15/16 × 3/8 ÷ 3/4 is 15/32.
