What Are Fractions?
Before we dive into operations, let's make sure we're confident about what fractions actually are.
A fraction represents a part of a whole. It is written as , where is the numerator (how many parts we have) and is the denominator (how many equal parts the whole is divided into).
Think of a pizza cut into 8 equal slices. If you eat 3 slices, you've eaten of the pizza.
- The numerator (top number) tells you how many parts you're talking about.
- The denominator (bottom number) tells you how many equal parts make up the whole.
A fraction where the numerator is smaller than the denominator, e.g. . Its value is less than 1.
A fraction where the numerator is equal to or greater than the denominator, e.g. . Its value is 1 or greater.
A number made up of a whole number and a proper fraction, e.g. .
To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder goes over the original denominator. For example, because remainder .
Equivalent Fractions and Simplifying
Two fractions are equivalent if they represent the same amount, even though they look different.
Fractions that have the same value but different numerators and denominators. You create them by multiplying or dividing both the numerator and denominator by the same number.
For example:
All of these represent exactly half.
Dividing the numerator and denominator by their highest common factor (HCF) to write the fraction in its simplest form.
Simplify
- Find the HCF of 12 and 18. Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The HCF is 6.
- Divide both numerator and denominator by 6:
So in simplest form.
Equivalent fractions are like different ways of saying the same thing. Saying "half a pizza" and "four-eighths of a pizza" describe the exact same amount of pizza — just using different-sized slices!
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