Algebra and equations · Ages 10–11

Algebra: letters for numbers worksheet

Part of: First algebra and simple equations

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Algebra and equations · Ages 10–11

Numsprite
numsprite.com

Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

13.Each ballpoint pen costs x dollars. Ming buys 7, paying 7x dollars. When x = 25, how many dollars does Ming pay?
Working:
Answer:
14.A rectangle is a cm long and 9 cm wide, so its perimeter is (2a + 18) cm. When a = 15, what is the perimeter?
Working:
Answer:
15.Tsz-ching is n years old, and Tsz-ching's dad is (2n + 1). When n = 8, how old is the dad?
Working:
Answer:
16.A box holds m apples, shared equally among 7 people: (m ÷ 7) each. When m = 77, how many does each get?
Working:
Answer:
17.A rectangle is a cm long and 8 cm wide, so its perimeter is (2a + 16) cm. When a = 37, what is the perimeter?
Working:
Answer:
18.Ka-yee is n years old, and Ka-yee's dad is (2n + 9). When n = 8, how old is the dad?
Working:
Answer:

Show the answers and working

Algebra: letters for numbers worksheet: Answers and working

1. 18
3x means 3 × x. Put 6 in place of x, then work it out.
3x means 3 × x: 3 × 6 = 18.
2. 23
Swap y for 7 and it becomes an ordinary addition.
Put 7 in place of y: 7 + 16 = 23.
3. 94
8a means 8 × a. Work out 8 × 14 first, then subtract 18.
8 × 14 = 112, then 112 − 18 = 94.
4. 15
Put 16 in place of n. In the usual order, divide first, then add.
Divide, then add: 16 ÷ 2 = 8, 8 + 7 = 15.
5. 79
9a means 9 × a. Work out 9 × 9 first, then subtract 2.
9 × 9 = 81, then 81 − 2 = 79.
6. 33
Put 2 in place of a and 19 in place of b. Multiply first, then add.
7 × 2 + 19 = 14 + 19 = 33.
7. 62
Put 7 in place of a and 13 in place of b. Multiply first, then add.
7 × 7 + 13 = 49 + 13 = 62.

8. B. 6 × x
When a number is written right before a letter, a sign has been left out between them. Which one?
A number before a letter, with the × left out: 6x = 6 × x.
9. A. A storybook costs y dollars, so 7 of them cost 7y dollars.
Ask of each sentence: could the letter be swapped for a number? A letter in a unit, a name or a short form can't.
A letter in algebra stands for a number: y stands for a book's price. The letters in a unit (m, kg), a route's name (36A) or a short form (GPS) stand for no number.
10. C. 9 × x
When a number is written right before a letter, a sign has been left out between them. Which one?
A number before a letter, with the × left out: 9x = 9 × x.
11. False
2x doesn't mean writing 2 and the value of x side by side. Work out 2 × 3, then compare with 23.
2x = 2 × x = 2 × 3 = 6.
12. C. y5
An algebraic expression needs a letter standing for a number. In which one is the letter a number, not a unit?
An algebraic expression has a letter standing for a number: y5 is y ÷ 5. The others have only numbers, or are just an amount with a unit.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 175 dollars
7x means 7 × x. Put the price of one, 25, in place of x.
7x = 7 × 25 = 175 dollars.
14. 48 cm
Put 15 in place of a: work out 2 × 15 first, then add 18.
2 × 15 + 18 = 48 cm.
15. 17 years old
Put Tsz-ching's age, 8, in place of n: work out 2 × 8, then add 1.
Put n = 8 in: 2 × 8 + 1 = 17, so the dad is 17 years old.
16. 11 apples
Put 77 in place of m, then share it into 7 equal parts.
77 ÷ 7 = 11.
17. 90 cm
Put 37 in place of a: work out 2 × 37 first, then add 16.
2 × 37 + 16 = 90 cm.
18. 25 years old
Put Ka-yee's age, 8, in place of n: work out 2 × 8, then add 9.
Put n = 8 in: 2 × 8 + 9 = 25, so the dad is 25 years old.

Numsprite · numsprite.com/en/worksheets/algebra-and-simple-equations/letters-for-numbers