17/4 divided by 45/3 in Fraction Form

The result of 17/4 divided by 45/3 is: 17/60

Step-by-Step Solution

Step 1: Understand the Problem

We need to divide the fraction $\frac{1}{7} 4$ by $\frac{4}{5} 3$ .

Step 2: Use the Division Rule

To divide fractions, we multiply by the reciprocal of the second fraction:
$\frac{1}{7} 4 \div \frac{4}{5} 3 = \frac{1}{7} 4 \times \frac{3}{4} 5$

Step 3: Multiply the Fractions

Multiply the numerators: 17 × 3 = 51
Multiply the denominators: 4 × 45 = 180

Step 4: Simplify the Fraction

We can simplify $\frac{5}{1} 180$ to its lowest form.
The greatest common divisor (GCD) of 51 and 180 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{7} 60$ .

Final Answer

The result of 17/4 divided by 45/3 is:

\frac{17}{4} \div \frac{45}{3} = \frac{1}{7} 60

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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