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Home / Practice / Maths
Putting numbers in place of letters, and reading a formula as an instruction.
Question 1 of 12
If a = 9 and b = 12, what is the value of 7a + 2b − 11?
7a means 7 × a, not 7 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 9, 7a = 7 × 9 = 63. 2b = 2 × 12 = 24, so the expression is 63 + 24 − 11 = 76. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. Substitute first, calculate second. Doing both at once is where errors creep in.
The answer is D. 7a means 7 × a, not 7 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 9, 7a = 7 × 9 = 63. 2b = 2 × 12 = 24, so the expression is 63 + 24 − 11 = 76. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. Substitute first, calculate second. Doing both at once is where errors creep in.
If a = 5 and b = 6, what is the value of 5a − b + 14?
5a means 5 × a, not 5 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 5, 5a = 5 × 5 = 25. b = 6, so the expression is 25 − 6 + 14 = 33. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. A number written against a letter always means multiply. 3a is three lots of a.
The answer is C. 5a means 5 × a, not 5 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 5, 5a = 5 × 5 = 25. b = 6, so the expression is 25 − 6 + 14 = 33. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. A number written against a letter always means multiply. 3a is three lots of a.
If a = 5 and b = 11, what is the value of 3a − b + 7?
3a means 3 × a, not 3 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 5, 3a = 3 × 5 = 15. b = 11, so the expression is 15 − 11 + 7 = 11. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. Write the numbers in brackets as you replace the letters: it keeps negatives and multiplications straight.
The answer is B. 3a means 3 × a, not 3 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 5, 3a = 3 × 5 = 15. b = 11, so the expression is 15 − 11 + 7 = 11. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. Write the numbers in brackets as you replace the letters: it keeps negatives and multiplications straight.
If a = 3 and b = 4, what is the value of 3a + 2b − 11?
3a means 3 × a, not 3 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 3, 3a = 3 × 3 = 9. 2b = 2 × 4 = 8, so the expression is 9 + 8 − 11 = 6. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. Write the numbers in brackets as you replace the letters: it keeps negatives and multiplications straight.
The answer is C. 3a means 3 × a, not 3 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 3, 3a = 3 × 3 = 9. 2b = 2 × 4 = 8, so the expression is 9 + 8 − 11 = 6. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. Write the numbers in brackets as you replace the letters: it keeps negatives and multiplications straight.
A minibus firm charges a booking fee of £5 plus £2 for each mile. The cost in pounds, C, for n miles is C = 5 + 2n. What is the cost for 6 miles?
The formula has two parts and both are needed. 2n means £2 for each of the 6 miles: £2 × 6 = £12. The £5 is charged once whatever happens, so it is added on rather than multiplied: £5 + £12 = £17. Multiplying the whole thing by 6 would charge the booking fee 6 times over. Substitute the number for n and the formula does the rest. The words are there to be turned into arithmetic.
The answer is B. The formula has two parts and both are needed. 2n means £2 for each of the 6 miles: £2 × 6 = £12. The £5 is charged once whatever happens, so it is added on rather than multiplied: £5 + £12 = £17. Multiplying the whole thing by 6 would charge the booking fee 6 times over. Substitute the number for n and the formula does the rest. The words are there to be turned into arithmetic.
If a = 8 and b = 4, what is the value of 5a + 2b − 6?
5a means 5 × a, not 5 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 8, 5a = 5 × 8 = 40. 2b = 2 × 4 = 8, so the expression is 40 + 8 − 6 = 42. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. A number written against a letter always means multiply. 3a is three lots of a.
The answer is B. 5a means 5 × a, not 5 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 8, 5a = 5 × 8 = 40. 2b = 2 × 4 = 8, so the expression is 40 + 8 − 6 = 42. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. A number written against a letter always means multiply. 3a is three lots of a.
If a = 3 and b = 8, what is the value of 6a + 2b − 14?
6a means 6 × a, not 6 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 3, 6a = 6 × 3 = 18. 2b = 2 × 8 = 16, so the expression is 18 + 16 − 14 = 20. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. Write the numbers in brackets as you replace the letters: it keeps negatives and multiplications straight.
The answer is B. 6a means 6 × a, not 6 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 3, 6a = 6 × 3 = 18. 2b = 2 × 8 = 16, so the expression is 18 + 16 − 14 = 20. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. Write the numbers in brackets as you replace the letters: it keeps negatives and multiplications straight.
If a = 8 and b = 5, what is the value of 7a + 2b − 10?
7a means 7 × a, not 7 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 8, 7a = 7 × 8 = 56. 2b = 2 × 5 = 10, so the expression is 56 + 10 − 10 = 56. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. A number written against a letter always means multiply. 3a is three lots of a.
The answer is C. 7a means 7 × a, not 7 next to a — the multiplication sign is left out to save writing, and forgetting it is the commonest mistake in the whole topic. With a = 8, 7a = 7 × 8 = 56. 2b = 2 × 5 = 10, so the expression is 56 + 10 − 10 = 56. Replacing each letter with its number, in brackets, before doing any arithmetic keeps it honest. A number written against a letter always means multiply. 3a is three lots of a.
A printer charges a set-up charge of £1.50 plus £1 for each poster. The cost in pounds, C, for n posters is C = 1.5 + 1n. What is the cost for 7 posters?
The formula has two parts and both are needed. 1n means £1 for each of the 7 posters: £1 × 7 = £7. The £1.50 is charged once whatever happens, so it is added on rather than multiplied: £1.50 + £7 = £8.50. Multiplying the whole thing by 7 would charge the set-up charge 7 times over. Substitute the number for n and the formula does the rest. The words are there to be turned into arithmetic.
The answer is D. The formula has two parts and both are needed. 1n means £1 for each of the 7 posters: £1 × 7 = £7. The £1.50 is charged once whatever happens, so it is added on rather than multiplied: £1.50 + £7 = £8.50. Multiplying the whole thing by 7 would charge the set-up charge 7 times over. Substitute the number for n and the formula does the rest. The words are there to be turned into arithmetic.
A minibus firm charges a booking fee of £6 plus £2.25 for each mile. The cost in pounds, C, for n miles is C = 6 + 2.25n. What is the cost for 11 miles?
The formula has two parts and both are needed. 2.25n means £2.25 for each of the 11 miles: £2.25 × 11 = £24.75. The £6 is charged once whatever happens, so it is added on rather than multiplied: £6 + £24.75 = £30.75. Multiplying the whole thing by 11 would charge the booking fee 11 times over. Check the answer is bigger than the per-item cost alone, since the fixed charge is still to come.
The answer is A. The formula has two parts and both are needed. 2.25n means £2.25 for each of the 11 miles: £2.25 × 11 = £24.75. The £6 is charged once whatever happens, so it is added on rather than multiplied: £6 + £24.75 = £30.75. Multiplying the whole thing by 11 would charge the booking fee 11 times over. Check the answer is bigger than the per-item cost alone, since the fixed charge is still to come.
A minibus firm charges a booking fee of £2.50 plus £1.50 for each mile. The cost in pounds, C, for n miles is C = 2.5 + 1.5n. What is the cost for 6 miles?
The formula has two parts and both are needed. 1.5n means £1.50 for each of the 6 miles: £1.50 × 6 = £9. The £2.50 is charged once whatever happens, so it is added on rather than multiplied: £2.50 + £9 = £11.50. Multiplying the whole thing by 6 would charge the booking fee 6 times over. Check the answer is bigger than the per-item cost alone, since the fixed charge is still to come.
The answer is A. The formula has two parts and both are needed. 1.5n means £1.50 for each of the 6 miles: £1.50 × 6 = £9. The £2.50 is charged once whatever happens, so it is added on rather than multiplied: £2.50 + £9 = £11.50. Multiplying the whole thing by 6 would charge the booking fee 6 times over. Check the answer is bigger than the per-item cost alone, since the fixed charge is still to come.
A printer charges a set-up charge of £6 plus £1.50 for each poster. The cost in pounds, C, for n posters is C = 6 + 1.5n. What is the cost for 7 posters?
The formula has two parts and both are needed. 1.5n means £1.50 for each of the 7 posters: £1.50 × 7 = £10.50. The £6 is charged once whatever happens, so it is added on rather than multiplied: £6 + £10.50 = £16.50. Multiplying the whole thing by 7 would charge the set-up charge 7 times over. Substitute the number for n and the formula does the rest. The words are there to be turned into arithmetic.
The answer is C. The formula has two parts and both are needed. 1.5n means £1.50 for each of the 7 posters: £1.50 × 7 = £10.50. The £6 is charged once whatever happens, so it is added on rather than multiplied: £6 + £10.50 = £16.50. Multiplying the whole thing by 7 would charge the set-up charge 7 times over. Substitute the number for n and the formula does the rest. The words are there to be turned into arithmetic.
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