A factor is a term which exactly divides another term.

The highest common factor is the common factor which can be divided by all other possible common factors.

Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.

Simplifying fractions

Maths

In this unit, pupils have explored the structure of fractions and their relationship with decimals and integers. This is built on in the future unit where pupils deepen their understanding of the arithmetic procedures involving fractions and integers.

In this unit, pupils will be asked to compare and order both fractions and decimals and will assess when conversion is required. Fluency in working with decimals and integers is an important skill which is developed in the prior unit.

This unit develops understanding and manipulation of fractions, including conversion between fractions to terminating and recurring decimals. Pupils then learn strategies to order fractions of increasing complexity.

Comparing and ordering fractions and decimals (positive and negative)

Complete the statement. A {{ }} is a term which exactly divides another term.

Select all the fractions that simplify to $$2 \over 3$$.

Which of the following factors of 24 and 90 is the best choice to efficiently simplify $$24\over90$$?

$$\frac{2^2 \times 3^2 \times 5}{2^2 \times 5^2 \times7}$$

$$\frac{2^3 \times 3^2 \times 5}{2^2 \times 5 \times7}$$

$$\frac{2^3 \times 3^2 \times 5^2}{2^2 \times 5^2 \times7^2}$$

$$\frac{2^3 \times 3^2 \times 5}{2^2 \times 5^2 \times7}$$

$$\frac{2^3 \times 3 \times 5}{2^2 \times 5 \times7}$$

Which of these fractions is equivalent to $$360 \over 700$$

Match each fraction to its simplified equivalent fraction. Use the fact that $$120 = 2^3 \times 3 \times 5$$; $$84 = 2^2 \times 3 \times 7$$ and $$210 = 2 \times 3 \times 5 \times 7$$ 

What word should go in the blank spaces to complete the following statement? Terminating __________ have a finite number of __________ places. 

Write $$0.825$$ as a simplified fraction.

The fraction which is halfway between 0.2 and 0.9 is $$\square \over 20$$. What number should be written in the square? {{ }} 

Which of the following are equivalent to $$5.555$$ ?

Match each decimal to a fraction with the denominator in exponential form.

Sofia writes  $$12.34 = \frac {1234}{10^ \square}$$.   What number should she write in the box to make her statement true? {{ }}

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