What you will learn
- Show a fraction with a shape, a set and a number line, and write it in words and in symbols.
- Find equivalent fractions with a fraction wall and with a rule, and spot fraction patterns.
- Write a fraction in its lowest terms.
A fraction is a part of a whole. When Mummy cuts a coconut sweet bread into 8 equal slices, each slice is one eighth of the loaf. In this lesson you will name fractions, find fractions that are the same size even though they look different, and write fractions in their simplest form, called lowest terms.
Naming fractions
The bottom number of a fraction is the denominator. It tells how many equal parts the whole is cut into. The top number is the numerator. It tells how many of those parts we are talking about. In 34, the denominator is 4 and the numerator is 3. We say three quarters. You may also see it written on one line as 3/4, and that is how the quiz writes fractions.
We can show the same fraction in three ways: part of a shape (area), part of a set of things, or a point on a number line.
Area: 3 of 4 equal parts
Area: 3 of 4 equal slices
Set: 3 of 4 mangoes are ripe
Number line: 0 to 1 in quarters, the arrow is at 34
Worked example 1
Granny made 10 pastelles for Christmas. 3 are chicken and the rest are beef. What fraction of the pastelles are chicken? What fraction are beef?
Show me how
There are 10 pastelles in all, so the denominator is 10.
3 are chicken: 310, three tenths.
10 − 3 = 7 are beef: 710, seven tenths.
Equivalent fractions
Equivalent fractions are fractions that name the same amount. Look at the fraction wall. One half covers exactly the same length as two quarters and as four eighths.
12 = 24 = 48
We record it with the equal sign: 12 = 24. When two fractions are not the same size we use the not equal to sign: 12 ≠ 13.
Worked example 2
Use the fraction wall to find a fraction equal to 13.
Show me how
Find the row of thirds and the row of sixths.
One third lines up exactly with two sixths.
So 13 = 26.
13 = 26
The pattern and the rule
Write the fractions that are equal to one half in a list: 12, 24, 36, 48, 510. Look for the pattern. The numerators count up in ones and the denominators count up in twos. Every time, the denominator is double the numerator.
The rule: multiply the numerator and the denominator by the same number and you get an equivalent fraction. Cutting every piece into 2 makes twice as many pieces, but the amount shaded stays the same.
Worked example 3
Fill the box: 34 = 8
Show me how
The denominator went from 4 to 8, so it was multiplied by 2.
Do the same to the numerator: 3 × 2 = 6.
So 34 = 68.
Watch out! A common mistake
Do not add the same number to the top and the bottom. Adding 1 to both parts of 12 gives 23, and two thirds is much bigger than one half. Always multiply or divide, never add or take away.
Lowest terms
A fraction is in its lowest terms when no number except 1 divides into both the numerator and the denominator. To write a fraction in lowest terms, divide the numerator and the denominator by the same number. Keep going until you cannot divide again. Try 2, then 3, then 5.
Worked example 4
Write 610 in lowest terms.
Show me how
6 and 10 are both even, so divide both by 2.
6 ÷ 2 = 3 and 10 ÷ 2 = 5.
Nothing except 1 divides into 3 and 5, so 610 = 35 in lowest terms.
48 → 12 in lowest terms. 39 → 13. 810 → 45.
Try it
TRY ITFraction lab
Name the fraction, find the missing number, write a fraction in lowest terms, continue a pattern, or decide if two fractions are equal.
Let’s practise
Work out each one in your copybook. Open Hint if you are stuck, then open Show answer to check your working.
1. A bar is cut into 5 equal parts and 2 parts are shaded. Write the fraction in symbols and in words.
Hint
The denominator is the number of equal parts in all.
Show answer
25, two fifths
2. There are 8 mangoes in a bag and 3 are ripe. What fraction of the mangoes are ripe?
Hint
How many mangoes are there in all?
Show answer
38 of the mangoes are ripe.
3. Use the fraction wall to fill the gaps: 12 = ?/4 = ?/8.
Hint
Find the row of quarters and the row of eighths.
Show answer
12 = 24 = 48
4. Fill the box: 23 = /6.
Hint
3 × 2 = 6, so multiply the numerator by 2 as well.
Show answer
4, because 23 = 46.
5. Write three fractions that are equivalent to 15.
Hint
Multiply the top and the bottom by 2, then by 3, then by 4.
Show answer
210, 315 and 420 (other answers are possible)
6. Continue the pattern: 14, 28, 312, ___, ___. What is the rule?
Hint
Look at the numerators, then the denominators.
Show answer
416, 520. The numerators go up by 1 and the denominators go up by 4.
7. Write 48 in lowest terms.
Hint
Divide the top and the bottom by 4.
Show answer
12
8. Is 24 equal to 36? Write = or ≠ between them.
Hint
Write each one in lowest terms.
Show answer
24 = 36, because both are equal to 12.
Quiz
Lesson quiz: 10 questions
Answer every question, then press Check my answers. Score 8 or more to earn the Fraction Finder badge.
Equivalent fractions and lowest terms: worksheet
Name: ____________________ Date: ______________
Part A: Let’s practise
1. A bar is cut into 5 equal parts and 2 parts are shaded. Write the fraction in symbols and in words.
2. There are 8 mangoes in a bag and 3 are ripe. What fraction of the mangoes are ripe?
3. Use the fraction wall to fill the gaps: 12 = ?/4 = ?/8.
4. Fill the box: 23 = /6.
5. Write three fractions that are equivalent to 15.
6. Continue the pattern: 14, 28, 312, ___, ___. What is the rule?
7. Write 48 in lowest terms.
8. Is 24 equal to 36? Write = or ≠ between them.
Part B: Quiz
1. In the fraction 5/7, what is the numerator?
2. Which fraction is three quarters?
(a) 4/3
(b) 3/4
(c) 3/8
(d) 1/4
3. A box of 10 pastelles has 7 beef pastelles. What fraction of the pastelles are beef?
(a) 3/10
(b) 10/7
(c) 7/10
(d) 7/3
4. 1/2 = 4/8
True or False? Circle one: True / False
5. Fill the gap: 1/3 = ?/9
6. Which fraction is NOT equivalent to 1/2?
(a) 2/4
(b) 5/10
(c) 3/6
(d) 2/3
7. Fill the gap: 3/5 = 6/?
8. What is 6/8 in lowest terms?
(a) 3/4
(b) 2/3
(c) 12/16
(d) 1/2
9. What comes next in the pattern 1/3, 2/6, 3/9, …?
(a) 4/10
(b) 3/12
(c) 4/12
(d) 5/12
10. Adding 1 to the top and to the bottom of 1/2 gives an equivalent fraction.
True or False? Circle one: True / False
Answers (for the adult)
Part A
1. 25, two fifths
2. 38 of the mangoes are ripe.
3. 12 = 24 = 48
4. 4, because 23 = 46.
5. 210, 315 and 420 (other answers are possible)
6. 416, 520. The numerators go up by 1 and the denominators go up by 4.
7. 12
8. 24 = 36, because both are equal to 12.
Part B
1. 5
2. (b) 3/4
3. (c) 7/10
4. True
5. 3
6. (d) 2/3
7. 10
8. (a) 3/4
9. (c) 4/12
10. False
Recap
- The denominator (bottom) tells how many equal parts. The numerator (top) tells how many parts we take.
- A fraction can be part of a shape, part of a set or a point on a number line.
- Equivalent fractions name the same amount: 12 = 24 = 48.
- Multiply or divide the top and the bottom by the same number to make an equivalent fraction.
- Lowest terms: divide until only 1 goes into both numbers. 610 = 35.
Words to know
- fraction
- A part of a whole or a part of a set.
Example: One slice of a pizza cut into 6 is 16 of the pizza. - numerator
- The top number of a fraction.
Example: In 35 the numerator is 3. - denominator
- The bottom number. It tells how many equal parts make the whole.
Example: In 35 the denominator is 5. - equivalent fractions
- Fractions that name the same amount.
Example: 12 and 510 are equivalent fractions. - lowest terms
- A fraction that cannot be divided any more by the same number on top and bottom.
Example: 48 in lowest terms is 12.
Try it at home
- Make a fraction wall: fold paper strips into halves, quarters and eighths, colour them and stick them under one whole strip.
- When the family shares a roti, a pizza or a sweet bread, say what fraction each person gets. If 2 out of 4 pieces are left, say it another way.
Test tips
Tips for class tests
- Check that the parts are equal before you name a fraction.
- Whatever you do to the top, do the same to the bottom.
- For lowest terms, try dividing by 2, then 3, then 5.
For parents and teachers
After this lesson, your child should be able to:
- represent fractions with area, set and linear models and name them in words and symbols;
- find and record equivalent fractions using a fraction wall and the multiplying rule, and describe the pattern;
- reduce a fraction to its lowest terms.
Paper folding and sharing food at home are the best models. Ask your child to explain why 24 and 12 are the same amount, not just to apply the rule.
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Previous: Mental Maths Strategies – Standard 3 Maths
Next: Comparing Fractions, Improper Fractions and Mixed Numbers – Standard 3 Maths
Course: Standard 3 Maths
Updates
2026/11/05
– First version of this lesson.
Attributions to media used in this post:
Trinidad coconut sweetbread in pans.jpg – Lyn’s Caribbean Kitchen – CC BY 3.0 (via Wikimedia Commons)
© 2026 Vedesh Kungebeharry. All rights reserved.
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