Algebraic expressions · Ages 12–13

Words into algebra worksheet

Part of: Algebraic expressions & sequences

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Algebraic expressions · Ages 12–13

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

1.'The sum of 9 times n and 11' as an algebraic expression is n + .
Fill in each blank
Answer:
2.'The sum of 10 times n and 17' as an algebraic expression is n + .
Fill in each blank
Answer:
3.Without the × signs: 9 × x × 7 × x × x = x^□
Fill in each blank
Answer:
4.Take 14 from y, then multiply by 6. With y = 9, the value is .
Answer:
5.Take 7 from y, then multiply by 3. With y = 1, the value is .
Answer:

13.A two-digit number has tens digit x and units digit y: it is x + y. With x = 4 and y = 1, the number with its digits swapped, minus the number, is .
Fill in each blank
Working:
Answer:
14.Build '9 times the sum of x and 2, then minus 5' step by step. Put the steps in order.
- A. Result = x
- B. Result = 9(x + 2)
- C. Result = 9(x + 2) − 5
- D. Result = x + 2
Write the letters in the right order
Working:
Answer:
15.May plays a guessing game: think of a number x, add 4, then multiply by 9. The result is 9(x + 4), that is x + .
Fill in each blank
Working:
Answer:
16.A tour group has x people, and 34 of them are children. How many are children?
- A. 3x4
- B. 4x3
- C. x + 34
- D. x − 34
Choose the right answer
Working:
Answer:
17.Ming thinks of a number n, multiplies by 4, takes away 7, then divides the result by 2. What is the final number?
- A. 4n − 72
- B. 4n − 72
- C. 4n − 72
- D. 2n − 74
Choose the right answer
Working:
Answer:
18.An older sister has x stickers and a younger sister y. The older has 8 more than 4 times the younger's. Which is right?
- A. x = 4(y + 8)
- B. y = 4x + 8
- C. x = 4y + 8
- D. x + 8 = 4y
Choose the right answer
Working:
Answer:

Show the answers and working

Words into algebra worksheet: Answers and working

1. 9, 11
9 times n is 9n; then add 11: 9n + 11.
2. 10, 17
10 times n is 10n; then add 17: 10n + 17.
3. 63, 3
Numbers together: 9 × 7 = 63; x multiplied 3 times is x³. So it is 63x³.
4. −30
The expression is 6(y − 14). Put in the number: 9 − 14 = −5, −5 × 6 = −30.
5. −18
The expression is 3(y − 7). Put in the number: 1 − 7 = −6, −6 × 3 = −18.

6. A. 9 − y
Start from 9 and take y away: 9 − y.
7. B. 4(x + 6)
The sum x + 6 first, then times 4: 4(x + 6). Check with x = 10: (10 + 6) × 4.
8. False
Both x and 7 are multiplied by 3: 3(x + 7) = 3x + 21.
9. False
Both x and 7 are multiplied by 6: 6(x + 7) = 6x + 42.
10. B. 5(x + 5)
The sum x + 5 first, then times 5: 5(x + 5). Check with x = 10: (10 + 5) × 5.
11. A. y9 − 4
Share first: y9; then take away: y9 − 4.
12. D. y9 − 5
Share first: y9; then take away: y9 − 5.

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

13. 10, −27
The tens digit counts tens. The number is 41, swapped 14: 14 − 41 = −27, which is 9 × (1 − 4).
14. A → D → B → C
Each step takes the whole of the step before: sum, then times 9, then minus 5.
15. 9, 36
Both x and 4 are multiplied by 9: 9 × x + 9 × 4 = 9x + 36.
16. A. 3x4
34 of x is x × 34 = 3x4.
17. C. 4n − 72
Step by step: 4n, then 4n − 7, then all of it divided by 2: 4n − 72.
18. C. x = 4y + 8
4 times the younger's is 4y, and 8 more makes the older's: x = 4y + 8.

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