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Year 7

Ordering positive and negative fractions and decimals

I can order a variety of positive and negative fractions and decimals using appropriate methods of conversion and recognising when conversion to a common format is not required.

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Year 7

Ordering positive and negative fractions and decimals

I can order a variety of positive and negative fractions and decimals using appropriate methods of conversion and recognising when conversion to a common format is not required.

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Lesson details

Key learning points

  1. There are multiple methods to order a list of positive and negative decimals.
  2. There are multiple methods to order a list of positive and negative fractions.
  3. There are multiple ways to order a list that contains positive and negative decimals and fractions.
  4. Some methods are more time consuming than others.
  5. Identifying the most efficient method to compare and order fractions and decimals can save time.

Keywords

  • Absolute value - The absolute value of a number is its distance from zero.

Common misconception

Changing all fractions and decimals to a common format without considering obvious comparisons.

This could be an opportunity to talk about familiar conversions including halves, quarters and fifths.

During any of the learning cycles when looking at ordering without converting ask pupils to come to the board and estimate where some common fractions and decimals are on a number line. Choose a mixture of positives and negatives.
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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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Starter quiz

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6 Questions

Q1.
True or false? An improper fraction has a numerator which is greater than its denominator.
Correct answer: True
False
Q2.
In which of the following would it be easier to compare the denominators?
$$\frac{4}{7}$$ and $$\frac{12}{39}$$
Correct answer: $$\frac{101}{120}$$ and $$\frac{103}{240}$$
Correct answer: $$\frac{15}{27}$$ and $$\frac{7}{9}$$
$$\frac{8}{3}$$ and $$\frac{64}{25}$$
Q3.
The smaller the denominator, the the parts.
Correct Answer: larger
Q4.
Which statements need the symbol < inserted to make them true?
Correct answer: $$\frac{5}{1917}\ \square \ \frac{5}{1916} $$
$$\frac{17}{6}\ \square \ \frac{17}{9} $$
$$\frac{987}{988}\ \square \ \frac{987}{998} $$
Correct answer: $$\frac{11}{22}\ \square \ \frac{11}{20} $$
Q5.
Write the following in order from smallest to largest.
1 - $$\frac{193}{217}$$
2 - $$\frac{193}{216}$$
3 - $$\frac{193}{215}$$
4 - $$\frac{193}{194}$$
5 - $$\frac{193}{193}$$
6 - $$\frac{193}{192}$$
Q6.
Order these fractions from smallest to largest.
1 - $$\frac{17}{24}$$
2 - $$\frac{17}{23}$$
3 - $$\frac{18}{23}$$
4 - $$\frac{23}{24}$$

Exit quiz

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6 Questions

Q1.
The value of a number is its distance from zero.
Correct Answer: absolute
Q2.
Order the values from smallest to largest.
1 - $$(-0.682)$$
2 - $$(-0.68)$$
3 - $$(-0.628)$$
4 - $$(-0.62)$$
5 - $$(-0.068)$$
Q3.
Order the values from smallest to largest.
1 - $$(-4.731)$$
2 - $$(-4.371)$$
3 - $$(-4.137)$$
4 - $$4.137$$
5 - $$4.371$$
6 - $$4.731$$
Q4.
Order these fractions from smallest to largest.
1 - $$\left(-2\frac{1}{4}\right)$$
2 - $$\left(-1\frac{3}{4}\right)$$
3 - $$\left(-1\frac{1}{2}\right)$$
4 - $$1\frac{1}{5}$$
5 - $$1\frac{1}{4}$$
6 - $$2\frac{1}{2}$$
Q5.
Order these fractions from smallest to largest.
1 - $$\left(-\frac{12}{15}\right)$$
2 - $$\left(-\frac{7}{10}\right)$$
3 - $$\left(-\frac{3}{5}\right)$$
4 - $$\left(-\frac{16}{30}\right)$$
Q6.
Order these values from smallest to largest.
1 - $$(-0.33)$$
2 - $$\left(-\frac{8}{25}\right)$$
3 - $$\left(-\frac{3}{10}\right)$$
4 - $$\left(-\frac{15}{100}\right)$$
5 - $$0.26$$
6 - $$\frac{28}{100}$$
7 - $$\frac{7}{20}$$