3/4 divided by 1/6 in Fraction Form

The result of 3/4 divided by 1/6 is: 4 1/2

Step-by-Step Solution

Step 1: Understand the Problem

We need to divide the fraction \(\frac34\) by \(\frac16\).

Step 2: Use the Division Rule

To divide fractions, we multiply by the reciprocal of the second fraction:
\(\frac34 \div \frac16 = \frac34 \times \frac61\)

Step 3: Multiply the Fractions

Multiply the numerators: 3 × 6 = 18
Multiply the denominators: 4 × 1 = 4

Step 4: Simplify the Fraction

We can simplify \(\frac184\) to its lowest form.
The greatest common divisor (GCD) of 18 and 4 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac92\).

Step 5: Convert to Mixed Number

The fraction \(\frac92\) can be written as the mixed number \(4\frac12\).

Final Answer

The result of 3/4 divided by 1/6 is:

\[ \frac{3}{4} \div \frac{1}{6} = 4\frac12 \]

Understanding Fraction Division

How to Divide Fractions

To divide fractions, you multiply by the reciprocal of the divisor:

\( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc} \)

This technique is often remembered as "keep, change, flip" - keep the first fraction, change division to multiplication, and flip the second fraction.

Why Simplify Fractions?

Simplifying fractions makes them easier to work with and understand. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.

To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).

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