FRACTIONS · TEXTBOOK LESSON
A fraction represents equal parts of a whole, a point on a number line, or a division. Fractions can be equivalent even when their numerators and denominators look different.
Learning objectives
By the end of this lesson, you should be able to:
- Identify numerator and denominator.
- Generate and simplify equivalent fractions.
- Compare and order fractions.
- Perform arithmetic with fractions using valid common-denominator methods.
1. Key vocabulary and definition
Definition
In the fraction a/b, a is the numerator and b is the denominator. The denominator tells how many equal parts make one whole; the numerator tells how many of those parts are being considered.
numeratordenominatorequivalentsimplifyimproper fractionmixed number
2. Essential facts and rules
These are the facts you should know before attempting the worked example.
Key mathematical facts
- Multiplying or dividing numerator and denominator by the same non-zero number gives an equivalent fraction.
- Fractions can only be added directly when they refer to equal-sized parts, so a common denominator is needed.
- To divide by a fraction, multiply by its reciprocal.
3. Standard method
A reliable method helps prevent errors and makes your reasoning easy to follow.
1
Simplify fractions where helpful.
2
For addition or subtraction, find a common denominator.
3
Convert each fraction to an equivalent fraction with that denominator.
4
Operate on the numerators while keeping the denominator.
5
Simplify the final answer and convert to a mixed number if appropriate.
4. Worked example
Worked example
Calculate 3/4 + 2/3.
1
The lowest common denominator of 4 and 3 is 12.
2
3/4 = 9/12 and 2/3 = 8/12.
3
9/12 + 8/12 = 17/12.
4
17/12 = 1 5/12.
5. Common mistakes
Watch out for these
- Starting calculations before deciding what the question is asking.
- Skipping important steps or changing notation midway through a solution.
- Accepting an answer without checking whether its size, sign or unit is sensible.
6. Video lesson
This topic is ready for a matching video lesson. The written textbook lesson is fully available now; additional videos can be added to the same lesson template.
7. Practice exercise
Complete these without looking at the answers first.
- Simplify 12/18.
- Calculate 2/5 + 1/10.
- Calculate 7/8 - 1/4.
- Find 3/5 of 40.
- Convert 2 3/4 to an improper fraction.
Show answers
- 2/3
- 1/2
- 5/8
- 24
- 11/4
8. Chapter summary
- Understand the underlying idea before memorising a procedure.
- Use precise mathematical notation and show a logical method.
- Always check the final result.