Year 6 Arithmetic (SATs): Formulae in words and letters
Part of the Year 6 Arithmetic (SATs) algebra and formulae chapter. Chapter overview · whole chapter on one page
Formulae in words and letters
Rule
A formula shows how one quantity depends on others. Write it in words first, then replace the words with letters: cost = 3 + 2 × miles becomes C = 3 + 2m.
A letter next to a number means multiply: 2m is 2 × m. For the full work on formulae, read Year 6 maths, chapter 6.
Key ideas
- Replace each word with a letter, and keep the number in front of it.
- 2m means 2 × m; the letter is never written as a number.
- A formula with a total often uses the number of items times the price, plus any extra fixed amount.
Method. Write the cost in words, then replace the words with letters.
- Write it in words. Cost = £3 plus £2 for each mile.cost = 3 + 2 × miles
- Replace the words with letters. Cost becomes C and miles becomes m.C = 3 + 2 × m
- Tidy the formula. We do not write the multiplication sign with a letter.C = 3 + 2m
- Write the answer. C = 3 + 2m
Check. When m = 1, C = 5, which is £3 + £2. ✓
Method. The perimeter is two lengths and two widths.
- Add the four sides. Two sides are l and two sides are w.l + w + l + w
- Group the same letters. l + l is 2l and w + w is 2w.2l + 2w
- Write the formula. Perimeter P is 2l + 2w.P = 2l + 2w
- Write the answer. P = 2l + 2w
Check. A 3 by 2 rectangle has P = 2 × 3 + 2 × 2 = 10. ✓
Method. Start with 40 and take away the number given away.
- Write it in words. Left = 40 minus the number given away.left = 40 - given
- Replace with letters. Left is N and given away is s.N = 40 - s
- Write the answer. N = 40 - s
Check. If s = 15, N = 25. ✓
Exercise 6A Practice: formulae in words and letters
Non-calculatorMethod. Cost is the number of pens times the price.
- Write it in words. Cost = pens × 3p.cost = pens × 3
- Use letters. T = 3 × n.T = 3n
- Write the answer. T = 3n
Check. If n = 4, T = 12p. ✓
Method. Five bags, each with b sweets.
- Write it in words. Sweets = 5 × sweets in one bag.5 × b
- Write the formula. S = 5b.S = 5b
- Write the answer. S = 5b
Check. If b = 6, S = 30. ✓
Method. Add the cost of the adults and the cost of the children.
- Adults. Cost for adults is 5 × a.5a
- Children. Cost for children is 3 × c.3c
- Add them. C = 5a + 3c.C = 5a + 3c
- Write the answer. C = 5a + 3c
Check. 2 adults and 1 child: C = 13. ✓
Method. Boxes times 12, plus the loose sweets.
- Write it in words. Sweets = 12 × boxes + 5.12 × b + 5
- Use letters. S = 12b + 5.S = 12b + 5
- Write the answer. S = 12b + 5
Check. If b = 2, S = 29. ✓
Method. Cost = price per metre times metres, plus delivery.
- Write it in words. Cost = 4 × metres + 2.4m + 2
- Use letters. C = 4m + 2.C = 4m + 2
- Write the answer. C = 4m + 2
Check. If m = 3, C = 14. ✓
Method. There are 7 days in a week.
- Days in the weeks. Each week has 7 days.7w
- Add the extra days. Add the 3 extra days.D = 7w + 3
- Write the answer. D = 7w + 3
Check. If w = 2, D = 17. ✓
Method. Each child needs 3 items in total.
- Items for one child. 2 pencils + 1 ruler = 3 items.3
- Items for c children. I = 3 × c.I = 3c
- Write the answer. I = 3c
Check. If c = 5, I = 15. ✓
Method. Start height plus growth each week.
- Write it in words. Height = 5 + 3 × weeks.5 + 3w
- Use letters. H = 5 + 3w.H = 5 + 3w
- Write the answer. H = 5 + 3w
Check. After 2 weeks, H = 11. ✓
Method. Each hour has 60 minutes.
- Minutes in the hours. There are 60 × h minutes in h hours.60h
- Add the minutes. Add the extra m minutes.M = 60h + m
- Write the answer. M = 60h + m
Check. 2 hours and 15 minutes: M = 135. ✓
Method. Add the three sides.
- Add the sides. Perimeter is the total of all the sides.a + b + c
- Write the answer. P = a + b + c
Check. If a = 3, b = 4 and c = 5, P = 12. ✓
Method. Look at what the number in front of the letter means.
- Look at the number. The 3 says there are three lots of n.3 lots of n
- Write it out. Three lots of n is n + n + n.n + n + n
- Write the answer. Yes, because 3n means 3 lots of n, which is n + n + n.
Check. If n = 2, 3n = 6 and 2 + 2 + 2 = 6. ✓
Method. Find the seats in all the rows, then take away the broken ones.
- Seats in the rows. r rows of 8 seats is 8r.8r
- Take away the broken seats. Subtract 3.S = 8r - 3
- Write the answer. S = 8r - 3
Check. If r = 4, S = 29. ✓