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N1

Order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥

Order numbers

Worked answers, methods and verified real exam appearances for N1 on Edexcel GCSE Maths 1MA1.

Explanation

  • Integers, decimals and fractions can be ordered once they are written in a comparable form.
  • Convert fractions to decimals, or use a common denominator, then place the values on a number line: values increase from left to right.
  • This is especially important for negatives, because the number with the greater distance below zero is smaller; for example, 1.7<32-1.7<-\dfrac{3}{2} since 1.7<1.5-1.7<-1.5.
  • Use == for equal values, \neq for unequal values, and read \leq or \geq as allowing equality.
  • In an exam, show the conversion that justifies each comparison.
A number line showing that 1.85-1.85 lies to the left of 1.75-1.75.

Worked example

Write 74-\dfrac{7}{4}, 1.68-1.68, 53\dfrac{5}{3} and 1.71.7 in ascending order.

  1. 1.Convert the fractions: 74=1.75-\dfrac{7}{4}=-1.75 and 53=1.666\dfrac{5}{3}=1.666\ldots.
  2. 2.Compare the negative values first: 1.75<1.68-1.75<-1.68.
  3. 3.Compare the positive values: 1.666<1.71.666\ldots<1.7, then write the complete ordered list.

Answer: 74, 1.68, 53, 1.7-\dfrac{7}{4},\ -1.68,\ \dfrac{5}{3},\ 1.7.

Common mistakes

  • Don't write 8>3-8>-3 because 8>38>3, ignoring that 8-8 lies farther left.
  • Don't treat \leq as meaning strictly less than and reject the equal endpoint.
  • Don't round a recurring decimal too early and change the intended order.

Exam tip

For a 2-mark ordering question, show decimal or common-denominator conversions before the final list.

Worked practice

Q1
Tier 1 · Easy

1

Insert either <<, >> or == between 0.62-0.62 and 35-\dfrac{3}{5}.

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
QuestionAnswerMarkMark scheme
1
  • 0.62<35-0.62<-\dfrac{3}{5}
1Convert 35-\dfrac{3}{5} to 0.6-0.6. Since 0.62-0.62 is farther left on the number line than 0.6-0.6, 0.62<35-0.62<-\dfrac{3}{5}.
Q2
Tier 2 · Standard

2

Mia says that 6>2-6>-2 because 6>26>2. Explain why Mia is wrong.

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
QuestionAnswerMarkMark scheme
2
  • 6<2-6<-2 because 6-6 lies farther to the left on a number line.
2For negative numbers, the number with the greater distance below zero is smaller. Since 6-6 is farther left than 2-2, the correct comparison is 6<2-6<-2.
Q3
Tier 3 · Hard

3

An integer kk satisfies 2.4<k31.7-2.4<\dfrac{k}{3}\leq1.7. Write down every possible value of kk.

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
QuestionAnswerMarkMark scheme
3
  • k=7,6,5,4,3,2,1,0,1,2,3,4,5k=-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5
3Multiply every part by positive 33, so the inequality signs stay unchanged: 7.2<k5.1-7.2<k\leq5.1. The integers in this interval are 7-7 through 55 inclusive.
Q4
Tier 1 · Easy

4

Write 0.47-0.47, 920-\dfrac{9}{20}, 0.52-0.52 and 12-\dfrac{1}{2} in ascending order.

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
QuestionAnswerMarkMark scheme
4
  • 0.52, 12, 0.47, 920-0.52,\ -\dfrac{1}{2},\ -0.47,\ -\dfrac{9}{20}
2920=0.45-\dfrac{9}{20}=-0.45 and 12=0.5-\dfrac{1}{2}=-0.5. From smallest to greatest, the values are 0.52,0.5,0.47,0.45-0.52,-0.5,-0.47,-0.45.
Q5
Tier 2 · Standard

5

Write 1.2-1.2, 76-\dfrac{7}{6} and 1.15-1.15 in descending order.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
QuestionAnswerMarkMark scheme
5
  • 1.15, 76, 1.2-1.15,\ -\dfrac{7}{6},\ -1.2
276=1.1666-\dfrac{7}{6}=-1.1666\ldots. For negative numbers, the value closest to zero is greatest, so the descending order is 1.15,1.1666,1.2-1.15,-1.1666\ldots,-1.2.
Q6
Tier 3 · Hard

6

Sam writes 1320<0.66<23-\dfrac{13}{20}<-0.66<-\dfrac{2}{3}. Is Sam correct? Give a reason.

(2)

(Total for Question 6 is 2 marks)

Mark scheme

Mark scheme for question 6
QuestionAnswerMarkMark scheme
6
  • No; the correct order is 23<0.66<1320-\dfrac{2}{3}<-0.66<-\dfrac{13}{20}.
2Use denominator 300300: 23=200300-\dfrac{2}{3}=-\dfrac{200}{300}, 0.66=198300-0.66=-\dfrac{198}{300} and 1320=195300-\dfrac{13}{20}=-\dfrac{195}{300}. Therefore 23<0.66<1320-\dfrac{2}{3}<-0.66<-\dfrac{13}{20}, so Sam is not correct.
Q7
Tier 2 · Standard

7

The box in 0.6-0.6\square is filled with one digit. The completed decimal is greater than 0.64-0.64 and less than 0.58-0.58. Work out all the possible digits.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
QuestionAnswerMarkMark scheme
7
  • 0,1,2,30,1,2,3
3The completed decimal must lie between 0.64-0.64 and 0.58-0.58. The values 0.60-0.60, 0.61-0.61, 0.62-0.62 and 0.63-0.63 all do this, whereas 0.64-0.64 is not greater than the lower endpoint. The possible digits are 0,1,2,30,1,2,3.
Q8
Tier 3 · Hard

8

Four cards show 1118-\dfrac{11}{18}, 0.605-0.605, 61%-61\% and 0.59-0.59. Work out the difference between the greatest value and the smallest value. Give your answer as a fraction.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
QuestionAnswerMarkMark scheme
8
  • 19900\dfrac{19}{900}
41118=0.6111-\dfrac{11}{18}=-0.6111\ldots and 61%=0.61-61\%=-0.61. The greatest value is 0.59-0.59 and the smallest is 1118-\dfrac{11}{18}. Their difference is 59100+1118=381800=19900-\dfrac{59}{100}+\dfrac{11}{18}=\dfrac{38}{1800}=\dfrac{19}{900}.
Q9
Tier 3 · Hard

9

Points PP, QQ, RR and SS have coordinates 34-\dfrac{3}{4}, 0.72-0.72, 73%-73\% and 710-\dfrac{7}{10} respectively. Which points lie in the interval 0.74<x0.71-0.74<x\leq-0.71? Write their coordinates in descending order.

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
QuestionAnswerMarkMark scheme
9
  • QQ and RR; 0.72, 73%-0.72,\ -73\% (or 0.72, 0.73-0.72,\ -0.73)
3P=0.75P=-0.75, R=0.73R=-0.73 and S=0.70S=-0.70. Only Q=0.72Q=-0.72 and R=0.73R=-0.73 lie in the stated interval. Since 0.72>0.73-0.72>-0.73, their coordinates in descending order are 0.72,0.73-0.72,-0.73.
Q10
Tier 3 · Hard

10

The integer kk satisfies 0.56<k40<0.54-0.56<-\dfrac{k}{40}<-0.54. Work out kk. You must show all your working.

(3)

(Total for Question 10 is 3 marks)

Mark scheme

Mark scheme for question 10
QuestionAnswerMarkMark scheme
10
  • k=22k=22
3Multiplying by 4040 gives 22.4<k<21.6-22.4<-k<-21.6. Multiplying by 1-1 reverses both inequality signs, so 21.6<k<22.421.6<k<22.4. The only integer in this interval is 2222.

Verified exam appearances

SeriesPaperQuestionMarksCalculatorTierLinks
2022-112FQ11AllowedFoundationQPMS
2023-063FQ51AllowedFoundationQPMS
2022-061FQ51Non-calculatorFoundationQPMS
2019-062FQ165AllowedFoundationQPMS
2021-112FQ31AllowedFoundationQPMS
2022-113HQ112AllowedHigherQPMS
2024-062FQ11AllowedFoundationQPMS
2022-112FQ124AllowedFoundationQPMS
2021-111FQ21Non-calculatorFoundationQPMS
2019-062FQ102AllowedFoundationQPMS
2021-112HQ13AllowedHigherQPMS
2023-113FQ31AllowedFoundationQPMS
2024-112FQ31AllowedFoundationQPMS
2022-113FQ11AllowedFoundationQPMS
2019-062FQ51AllowedFoundationQPMS
2019-061FQ82Non-calculatorFoundationQPMS
2021-112FQ152AllowedFoundationQPMS
2024-063FQ51AllowedFoundationQPMS
2024-061FQ41Non-calculatorFoundationQPMS
2023-061FQ31Non-calculatorFoundationQPMS
2022-113FQ21AllowedFoundationQPMS
2022-061FQ41Non-calculatorFoundationQPMS
2022-062FQ142AllowedFoundationQPMS
2022-062FQ61AllowedFoundationQPMS
2019-062FQ21AllowedFoundationQPMS
2024-113FQ41AllowedFoundationQPMS
2023-113FQ142AllowedFoundationQPMS
2019-112FQ11AllowedFoundationQPMS

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