Websink Prep UKKS2 Arithmetic (SATs)Year 6 chaptersArithmetic (SATs) textbooksYear 6Browse allPast papersFind a tutorBecome a tutor
SATs practice · Year 6Chapter 6 · Algebra and formulae
Year 6 Arithmetic (SATs) · Algebra and formulae · Lesson 6.2

Year 6 Arithmetic (SATs): Substituting values into formulae

Part of the Year 6 Arithmetic (SATs) algebra and formulae chapter. Chapter overview · whole chapter on one page

6.2

Substituting values into formulae

Year 6
Use simple formulae written in words and in letters, and substitute values into them (Year 5-6)
Story. Ruby uses the taxi formula C = 3 + 2m to work out the cost of a 6 mile journey. She replaces m with 6, then works out the answer.

Rule

Substitute means replace each letter with its value. Then work out the calculation, using the order of operations: multiply before you add or subtract.

Key ideas

  • Replace every letter with its value before you calculate.
  • 2m with m = 6 is 2 × 6 = 12.
  • Multiply before you add or subtract.
Worked example 6.2.1
Use C = 3 + 2m to find C when m = 6.

Method. Replace m with 6, then work out the calculation.

  1. Substitute. Replace m with 6: C = 3 + 2 × 6.
    C = 3 + 2 × 6
  2. Multiply first. 2 × 6 = 12.
    C = 3 + 12
  3. Add. 3 + 12 = 15.
    C = 15
  4. Write the answer.
    15

Check. The cost for 6 miles is £15. ✓

Worked example 6.2.2
Use a = 3b - 4 to find a when b = 9.

Method. Replace b with 9, then multiply, then subtract.

  1. Substitute. a = 3 × 9 - 4.
    a = 3 × 9 - 4
  2. Multiply. 3 × 9 = 27.
    a = 27 - 4
  3. Subtract. 27 - 4 = 23.
    a = 23
  4. Write the answer.
    23

Check. 27 - 4 = 23, so a = 23 when b = 9. ✓

Worked example 6.2.3
Find the value of 2x + 3y when x = 4 and y = 5.

Method. Replace x with 4 and y with 5, then work out each part.

  1. Substitute. 2 × 4 + 3 × 5.
    2 × 4 + 3 × 5
  2. Work out each part. 2 × 4 = 8 and 3 × 5 = 15.
    8 + 15
  3. Add. 8 + 15 = 23.
    23
  4. Write the answer.
    23

Check. 8 + 15 = 23. ✓

Exercise 6B  Practice: substituting values into formulae

Non-calculator
1
FWork out 4a + 1 when a = 3.
2
FWork out 10 - 2n when n = 3.
3
FWork out 3p + q when p = 2 and q = 7.
4
FWork out pq when p = 3 and q = 8.
5
FWork out (a + b) × 2 when a = 5 and b = 4.
6
FWork out 5x - y when x = 4 and y = 6.
7
PSUse P = 2l + 2w to find P when l = 7 and w = 3.
8
PSUse M = 60h + m to find M when h = 2 and m = 15.
9
PSUse C = 5a + 3c to find C when a = 2 adults and c = 4 children.
10
PSUse S = 12b + 5 to find S when b = 3.
11
RThe formula is T = 4x + 3. Find the value of x that makes T equal 19.
12
RFind the value of x that makes 2x + 5 = 17.
13
RAli says that if a = 2 and b = 3, then 2a + b = 7. Is he right? Explain.

Websink Prep UK is an independent site. It is not affiliated with, endorsed by or sponsored by AQA, Pearson Edexcel, OCR, WJEC, Eduqas, CCEA, SQA, GL Assessment, CEM or the Department for Education. All exam board names and trademarks belong to their owners. Past papers are linked from the exam boards' own websites and are not hosted here.

About Websink Prep UK · Find a tutor · Privacy · Terms · Cookie settings