Simplest Form Fractions

Simplifying Fractions with Variables

Concept

A fraction is in simplest form when the numerator and denominator share no common factors and cannot be reduced any further.

Rules

To simplify a fraction, divide the numerator and the denominator by their greatest common factor.

Example

Write the fraction in its simplest form.
$\fn_phv \frac{15}{40}$

Solution

To simplify $\fn_phv \frac{15}{40}$ , find the greatest common factor for the numerator and denominator.
The factors for 15 are: 1, 3, 5, 15
The factors for 40 are: 1, 2, 4, 5, 8, 10, 20, 40
The greatest common factor for both 15 and 40 is 5.
Divide both 15 and 40 by 5 to simplify the fraction.
$\fn_phv \frac{15\div 5}{40\div 5}={\color{Red} \frac{3}{8}}$

Practice Simplest Form Fractions

Practice Problem 1

Write each fraction in its simplest form.
Fill in the missing number.

Practice Problem 2

Write each fraction in its simplest form.

Practice Problem 3

Add. Write the sum in the simplest form.

Practice Problem 4

Subtract. Write the difference in the simplest form.

Factor is one of two or more numbers that divides a given number without a remainder.

Greatest Common Factor (GCF) – is the largest positive integer that divides evenly into all numbers with zero remainders. “

Pre-requisite Skills
Identify Multiples
Greatest Common Factor
Prime and Composite Numbers
Equivalent Fractions

Related Skills
Least Common Multiple (LCM)
Add and Subtract Fractions with Like Denominators
Add and Subtract Fractions with Unlike Denominators
Estimate Sums and Difference of Mixed Numbers
Estimate Products of Fractions
Multiply Fractions
Multiply Mixed Numbers
Compare Fractions
Multiply Rational Numbers
Divide Rational Numbers