What You Will Learn
- Identify the numerator and denominator of a fraction.
- Understand proper, improper and mixed fractions.
- Find and use equivalent fractions.
- Compare and order fractions.
- Add, subtract, multiply and divide fractions.
- Apply fractions to everyday problems.
What Is a Fraction?
A fraction represents a part of a whole or a part of a group. A fraction is written using two numbers separated by a line.
The 3 is the numerator and the 4 is the denominator.
The denominator tells us how many equal parts make the whole, while the numerator tells us how many of those parts are being considered.
Numerator and Denominator
In a fraction such as 5 / 8, the top number is the numerator and the bottom number is the denominator.
Types of Fractions
The numerator is smaller than the denominator.
The numerator is equal to or greater than the denominator.
A whole number combined with a proper fraction.
Equivalent Fractions
Equivalent fractions have different numbers but represent the same value. We can multiply or divide the numerator and denominator by the same non-zero number.
Each fraction represents one half. The numerator and denominator are multiplied by the same number each time.
Simplifying Fractions
A fraction is in simplest form when the numerator and denominator have no common factor greater than 1.
Divide both 8 and 12 by their common factor, 4, to obtain the simplest form.
Comparing Fractions
Fractions can be compared using >, < and =. When denominators are the same, compare the numerators.
The denominators are equal, so 5 parts are greater than 3 parts.
When denominators are different, you can convert the fractions to equivalent fractions with a common denominator before comparing them.
Adding Fractions
When fractions have the same denominator, add the numerators and keep the denominator.
For fractions with different denominators, first find a common denominator, then convert the fractions before adding.
Subtracting Fractions
Like addition, subtraction with different denominators requires a common denominator.
After subtracting, simplify the result whenever possible.
Multiplying Fractions
To multiply fractions, multiply the numerators together and the denominators together.
Dividing Fractions
To divide by a fraction, multiply by its reciprocal.
The reciprocal of a fraction is found by swapping its numerator and denominator.
Fractions in Everyday Life
Fractions are used when measuring, sharing quantities, reading recipes, telling time and describing parts of a whole.
A recipe can use fractional measurements.
A quarter of an hour is 15 minutes.
Common Mistakes
For same denominators, add the numerators and keep the denominator.
Always check whether the final fraction can be reduced.
When dividing, swap the numerator and denominator of the second fraction.
Quick Practice
Try these questions before checking your answers.
In 7 / 9, identify the numerator and denominator.
Write an equivalent fraction for 1 / 3 with denominator 12.
Simplify 12 / 18.
Calculate: 2 / 5 + 1 / 5.
Calculate: 3 / 4 × 2 / 3.
Summary
- A fraction represents part of a whole or a group.
- The numerator is the top number and the denominator is the bottom number.
- Equivalent fractions have the same value.
- Fractions can be simplified, compared and ordered.
- Different operations follow different fraction rules.
- Always simplify your final answer when possible.