1/8 divided by 3/4 in simplest form
The Correct answer and Explanation is :
The correct answer is: ( \frac{1}{6} )
To divide fractions, you multiply by the reciprocal (inverse) of the second fraction. Here’s how you do it:
Step-by-Step Solution:
- Step 1: Write the problem:
( \frac{1}{8} \div \frac{3}{4} ) - Step 2: Change the division into multiplication by taking the reciprocal of the second fraction. The reciprocal of ( \frac{3}{4} ) is ( \frac{4}{3} ). ( \frac{1}{8} \times \frac{4}{3} )
- Step 3: Multiply the numerators (top numbers) and the denominators (bottom numbers):
Numerator: ( 1 \times 4 = 4 )
Denominator: ( 8 \times 3 = 24 ) So, ( \frac{1}{8} \div \frac{3}{4} ) becomes ( \frac{4}{24} ). - Step 4: Simplify the fraction ( \frac{4}{24} ).
Both the numerator and the denominator can be divided by 4 (the greatest common factor): ( \frac{4}{24} = \frac{4 \div 4}{24 \div 4} = \frac{1}{6} ). Therefore, the simplest form of ( \frac{1}{8} \div \frac{3}{4} ) is ( \frac{1}{6} ).
Explanation:
Dividing fractions can be confusing at first, but it follows a simple rule: multiply by the reciprocal of the divisor (the second fraction). The reciprocal is obtained by flipping the fraction (interchanging its numerator and denominator).
In this example, you start with ( \frac{1}{8} ) divided by ( \frac{3}{4} ). When you divide fractions, you multiply the first fraction by the reciprocal of the second. By flipping ( \frac{3}{4} ) to ( \frac{4}{3} ), the division becomes a multiplication problem.
Multiplying two fractions is straightforward: multiply the numerators and then the denominators. After this step, you simplify the result by dividing both the numerator and the denominator by their greatest common factor, yielding the answer ( \frac{1}{6} ).
This approach works for any fraction division problem. Understanding the reciprocal method ensures you can handle more complex fraction operations with confidence.