An improper fraction is a fraction where the numerator is greater than the denominator.

A proper fraction is a fraction where the numerator is less than the denominator.

Order sets of non-related fractions using a range of strategies

Maths

Explain how to compare non-related fractions finding equivalent fractions with common denominators

Explain how to compare pairs of non-related fractions by comparing to a half

Explain how to compare pairs of non-related fractions using fraction sense

Explain which strategy for comparing non-related fractions is most efficient

In this unit pupils will use their fraction sense to explain how to compare pairs of non-related fractions either by converting to common denominators or using fraction knowledge and understanding. In the future unit pupils will learn how to multiply 2 unit fractions and 2 non-unit fractions They will learn how to divide a unit fraction and a non-unit fraction by a whole number 

In the prior unit pupils explained how to write a fraction in its simplest form when solving addition and subtraction problems and added and subtracted related fractions.  In this unit pupils will use their fraction sense to explain how to compare pairs of non-related fractions either by converting to common denominators or using fraction knowledge and understanding.

In this unit pupils will use their fraction sense to explain how to compare pairs of non-related fractions either by converting to common denominators or using fraction knowledge and understanding.

Comparing fractions

$$ {1} \over {4}$$        $$ {1} \over {3}$$        $$ {1} \over {2}$$

$$ {1} \over {8}$$        $$ {1} \over {4}$$        $$ {1} \over {6}$$

$$ {1} \over {8}$$        $$ {2} \over {7}$$        $$ {3} \over {6}$$

$$ {9} \over {9}$$        $$ {9} \over {10}$$       $$ {9} \over {11}$$

Tick the sequences where the fractions are increasing in size each time.

$$ {1} \over {9}$$        $$ {1} \over {8}$$        $$ {1} \over {7}$$

$$ {2} \over {5}$$        $$ {3} \over {4}$$        $$ {4} \over {1}$$

$$ {1} \over {8}$$        $$ {1} \over {9}$$        $$ {1} \over {10}$$

$$ {3} \over {9}$$        $$ {4} \over {10}$$        $$ {5} \over {11}$$

Tick the sequence where the fractions are decreasing in size each time.

Order the fractions from largest to smallest.

Tick the largest fraction and the smallest fraction in this list.

Tick the fractions that could fit in the gap in this increasing sequence. $$ {2} \over {3}$$   $$ {5} \over {6}$$   __________  $$ {9} \over {10}$$

a fraction with a numerator that is larger than the denominator.

a fraction that has the same numerator and denominator.

a fraction with a denominator that is larger than the numerator.

Use reasoning to compare these two fractions: $$ {2} \over {10}$$ ___ $$ {6} \over {7}$$

Use reasoning to identify which of these fractions is greater than $$ {2} \over {5}$$ 

Use reasoning to identify the fraction which would complete the inequality:  $$ {5} \over {7}$$ > _____

Use reasoning to compare these two fractions: $$ {9} \over {10}$$ ___ $$ {6} \over {7}$$

Use reasoning to compare these two fractions: $$ {4} \over {7}$$ ___ $$ {5} \over {8}$$

Starter Quiz

An improper fraction is: