19/8 divided by 1/4 in Fraction Form

The result of 19/8 divided by 1/4 is: 9 1/2

Step-by-Step Solution

Step 1: Understand the Problem

We need to divide the fraction $\frac{1}{9} 8$ by $\frac{1}{4}$ .

Step 2: Use the Division Rule

To divide fractions, we multiply by the reciprocal of the second fraction:
$\frac{1}{9} 8 \div \frac{1}{4} = \frac{1}{9} 8 \times \frac{4}{1}$

Step 3: Multiply the Fractions

Multiply the numerators: 19 × 4 = 76
Multiply the denominators: 8 × 1 = 8

Step 4: Simplify the Fraction

We can simplify $\frac{7}{6} 8$ to its lowest form.
The greatest common divisor (GCD) of 76 and 8 is 4.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{9} 2$ .

Step 5: Convert to Mixed Number

The fraction $\frac{1}{9} 2$ can be written as the mixed number $9 \frac{1}{2}$ .

Final Answer

The result of 19/8 divided by 1/4 is:

\frac{19}{8} \div \frac{1}{4} = 9 \frac{1}{2}

Understanding Fraction Division

How to Divide Fractions

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

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a d}{b c}$

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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