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Compare mixed numbers when the denominators of fractional parts are different

I can compare and order mixed numbers when the whole and the numerator of the fractional part is the same.

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Lesson 5 of 5

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Year 4

Compare mixed numbers when the denominators of fractional parts are different

I can compare and order mixed numbers when the whole and the numerator of the fractional part is the same.

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Lesson details

Key learning points

If mixed numbers have the same whole number parts, then the size of the fractional parts determines the greater number.
When we compare fractions that have the same numerator, the greater the denominator, the smaller the fraction.
Knowledge of comparing proper fractions can help when comparing mixed numbers.

Keywords

Mixed number - A mixed number is a whole number and a fraction combined.

Common misconception

Children may compare the fractional part of the mixed number first rather than the more significant whole number part.

What do you notice? If the whole number is the same, we need to look at the fractional part. If the numerators are the same, we need to compare the denominators - the smaller the denominator the greater the fraction.

Support children to make connections between the ordering and comparing of mixed numbers and ordering and comparing of unit fractions and proper fractions that have the same numerator. Children need to understand, that with mixed numbers, the whole number part is the most significant part.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
Starting with the smallest, put these numbers in order.

1 - 101

2 - 110

3 - 111

4 - 1,000

5 - 1,001

6 - 1,110

Q2.
Which fraction shows how much of the bar has been shaded grey?

$$ {4} \over {5}$$

$$ {5} \over {4}$$

$$ {4} \over {9}$$

Correct answer: $$ {5} \over {9}$$

Q3.
Look at the part-part-whole model. What is the value of the fractional part of this mixed number?

Correct answer: $$ {4} \over {6}$$ -

$$ {6} \over {4}$$

$$ {3} \over {6}$$

Q4.
Look at these numbers. Which is the greatest?

$$4{{1} \over {5}}$$

$$5{{1} \over {5}}$$

Correct answer: $$6{{3} \over {6}}$$

Q5.
Starting with the smallest, put these numbers in order.

1 - 0

2 - $$ {1} \over {20}$$

3 - $$ {1} \over {15}$$

4 - $$ {1} \over {10}$$

5 - $$ {1} \over {5}$$

6 - 1

Q6.
Starting with the smallest, put these numbers in order.

1 - 3

2 - $$3{{1} \over {9}}$$

3 - $$3{{6} \over {9}}$$

4 - $$3{{7} \over {9}}$$

5 - $$3{{8} \over {9}}$$

6 - 4

Assessment exit quiz

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6 Questions

Q1.
Look at these representations of fractions and complete the sentence using ‘greater’ or ‘smaller’: $$ {2} \over {6}$$ is than $$ {2} \over {5}$$

Correct Answer: smaller

Q2.
Which symbol makes this statement true? $$ {2} \over {9}$$ ___ $$ {2} \over {7}$$

Correct answer: <

Q3.
Starting with the smallest, put these numbers in order.

1 - 0

2 - $$ {10} \over {100}$$

3 - $$ {10} \over {50}$$

4 - $$ {10} \over {25}$$

5 - $$ {10} \over {20}$$

6 - 1

Q4.
Which symbol makes this statement true? $$9{{6} \over {8}}$$ ___ $$9{{6} \over {10}}$$

Correct answer: >

Q5.
Starting with the smallest, put these numbers in order.

1 - 7

2 - $$7{{6} \over {10}}$$

3 - $$7{{6} \over {9}}$$

4 - $$7{{6} \over {8}}$$

5 - $$7{{6} \over {7}}$$

6 - 8

Q6.
Andeep has spilt his drink on his homework. What could the missing digit be?

Correct answer: 8

Correct answer: 9

Lesson appears in

UnitMaths / Compare and order mixed numbers and position on a number line

Maths

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Compare mixed numbers when the denominators of fractional parts are different

Compare mixed numbers when the denominators of fractional parts are different

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Starting with the smallest, put these numbers in order.

Q2.Which fraction shows how much of the bar has been shaded grey?

Q3.Look at the part-part-whole model. What is the value of the fractional part of this mixed number?

Q4.Look at these numbers. Which is the greatest?

Q5.Starting with the smallest, put these numbers in order.

Q6.Starting with the smallest, put these numbers in order.

Assessment exit quiz

6 Questions

Q1.Look at these representations of fractions and complete the sentence using ‘greater’ or ‘smaller’: $$ {2} \over {6}$$ is than $$ {2} \over {5}$$

Q2.Which symbol makes this statement true? $$ {2} \over {9}$$ ___ $$ {2} \over {7}$$

Q3.Starting with the smallest, put these numbers in order.

Q4.Which symbol makes this statement true? $$9{{6} \over {8}}$$ ___ $$9{{6} \over {10}}$$

Q5.Starting with the smallest, put these numbers in order.

Q6.Andeep has spilt his drink on his homework. What could the missing digit be?

Lesson appears in

UnitMaths / Compare and order mixed numbers and position on a number line

Maths

Q1.
Starting with the smallest, put these numbers in order.

Q2.
Which fraction shows how much of the bar has been shaded grey?

Q3.
Look at the part-part-whole model. What is the value of the fractional part of this mixed number?

Q4.
Look at these numbers. Which is the greatest?

Q5.
Starting with the smallest, put these numbers in order.

Q6.
Starting with the smallest, put these numbers in order.

Q1.
Look at these representations of fractions and complete the sentence using ‘greater’ or ‘smaller’: $$ {2} \over {6}$$ is than $$ {2} \over {5}$$

Q2.
Which symbol makes this statement true? $$ {2} \over {9}$$ ___ $$ {2} \over {7}$$

Q3.
Starting with the smallest, put these numbers in order.

Q4.
Which symbol makes this statement true? $$9{{6} \over {8}}$$ ___ $$9{{6} \over {10}}$$

Q5.
Starting with the smallest, put these numbers in order.

Q6.
Andeep has spilt his drink on his homework. What could the missing digit be?