Fraction: Meaning & Types of Fractions – JSS1 Mathematics Lesson Note (First Term)

A fraction is a part of a whole, written as one number over another, such as 3/4.

Behavioural objectives

By the end of the lesson, students should be able to:

1. explain what a fraction is, and name the numerator and the denominator;
2. identify common (regular) fractions, decimal fractions, proper fractions and improper fractions;
3. change an improper fraction to a mixed number and a mixed number to an improper fraction;
4. find equivalent fractions and fill in the missing numbers in them.

What is a fraction?

A fraction is a portion or part of a whole.

• Whole: a complete object, such as a whole loaf of bread or a whole orange.
• Part: one or more equal pieces of the whole.
• Example: the pie below is a whole that can be cut into sectors (slices) to show different fractions.

Whole (1)

Half (1/2)

Half-pie

Three-quarters (3/4)

What are the parts of a fraction?

A fraction has two parts: the numerator at the top and the denominator at the bottom.

• Numerator: the number on top. It tells how many equal parts are taken.
• Denominator: the number at the bottom. It tells how many equal parts make the whole.
• Fraction bar: the line between them. It means “divided by”.

What are the types of fractions?

There are two main types of fractions, common fractions and decimal fractions, and common fractions are proper, improper or mixed.

Common or regular fractions

• Meaning: a fraction written as one whole number over another.
• Examples: ½, ¼, ¾, 3/8 and 5/8.

Decimal fractions

• Meaning: fractions written with a decimal point. They are also called decimals.
• Examples: 0.897 and 7.864.

Proper fractions

• Meaning: the numerator is less than the denominator.
• Value: always less than 1.
• Examples: 2/5 and ¼.

Improper fractions

• Meaning: the numerator is greater than the denominator.
• Value: more than 1.
• Examples: 8/3 and 12/5.

Mixed numbers

• Meaning: a whole number and a proper fraction written together.
• Examples: 2 1/2 and 3 3/4.

How do you change between improper fractions and mixed numbers?

An improper fraction is changed to a mixed number by division, and a mixed number is changed back by multiplication and addition.

How do you change an improper fraction to a mixed number?

1. Divide the numerator by the denominator.
2. Write the quotient as the whole number.
3. Write the remainder as the new numerator.
4. Keep the same denominator.

Example 1: Change 15/4 to a mixed number.

• 15 ÷ 4 = 3 remainder 3.
• The whole number is 3. The remainder 3 is the numerator. The denominator stays 4.
• So 15/4 = 3 3/4.

How do you change a mixed number to an improper fraction?

1. Multiply the whole number by the denominator.
2. Add the numerator to the answer.
3. Write the result over the same denominator.

Example 2: Change 2 3/5 to an improper fraction.

• Multiply: 2 × 5 = 10.
• Add the numerator: 10 + 3 = 13.
• So 2 3/5 = 13/5.

What are equivalent fractions?

Equivalent fractions are fractions that have the same value.

• Examples: ½, 2/4, 3/6, 4/8, 5/10 and 6/12 are all equivalent.
• To make one: multiply the numerator and denominator by the same number.
• To reduce one: divide the numerator and denominator by the same number.
• Lowest terms: a fraction is in its lowest terms when no number except 1 divides both parts. For example, 12/18 ÷ 6 gives 2/3.

Example 1

Convert 2/9 into an equivalent fraction with the denominator 54.

1. Write 2/9 = __/54.
2. Divide the new denominator by the old one to get the multiplier: 54 ÷ 9 = 6.
3. Multiply the numerator by the multiplier: 2 × 6 = 12.
4. So 2/9 = 12/54.

Example 2

Find the missing parts of these fractions: __/10 = 12/__ = 20/50 = __/80

1. Use 20/50 as the reference fraction, because both its numerator and denominator are given.
2. Reduce it: 20/50 = 2/5.
3. For __/10: divide 10 by 5 to get 2. Multiply both parts of 2/5 by 2. So 2/5 = 4/10.
4. For 12/__: divide 12 by the numerator 2 to get 6. Multiply the denominator 5 by 6. So 2/5 = 12/30.
5. For __/80: divide 80 by 5 to get 16. Multiply the numerator 2 by 16. So 2/5 = 32/80.
6. Answer: 4/10 = 12/30 = 20/50 = 32/80.

Evaluation

1. Express each of the following fractions as a mixed number: (a) 9/5 (b) 15/2
2. Express each of the following fractions as an improper fraction: (a) 11/2 (b) 43/8
3. Copy and complete each of the following:
   1. 3/5 = __/15
   2. 4/7 = 12/__ = __/35 = __/49 = 44/__
4. State whether each is a proper fraction, an improper fraction or a mixed number: (a) 3/7 (b) 9/4 (c) 2 1/3

Assignment

Change 5 2/3 to an improper fraction, then write three fractions equivalent to 3/4.