Algebra and equations · Ages 10–11

Terms, coefficients and simplifying worksheet

Part of: First algebra and simple equations

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Algebra and equations · Ages 10–11

Numsprite
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Name:Date:Score:／48

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

13.A triangle's three sides are 4x cm, 3x cm and 8x cm long. Its perimeter (the three sides added) is x cm.
Working:
Answer:
14.A box holds b sweets. May has 5 boxes and 7 loose sweets; Ming has 2 boxes and 4 loose. Together they have (b + ) sweets.
Fill in each blank
Working:
Answer:
15.A rectangle is 5a cm long and 2a cm wide. Its perimeter (all four sides added) is a cm.
Working:
Answer:
16.Ka-yee buys 8 ballpoint pens at y dollars each, then 7 more of the same pens. Altogether Ka-yee pays y dollars for the pens.
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Answer:
17.Ming has 12m dollars and spends 7m dollars on stationery. Ming has m dollars left.
Working:
Answer:
18.May buys 7 ballpoint pens at y dollars each, then 8 more of the same pens. Altogether May pays y dollars for the pens.
Working:
Answer:

Show the answers and working

Terms, coefficients and simplifying worksheet: Answers and working

1. 9
The coefficient is the number right in front of the letter. Look at what is in front of m.
The number in front of the letter is its coefficient: in 9m it is 9. 14 is a number term.
2. 11
y on its own has coefficient 1. Adding 11 y's is like adding 11 ones.
Each y has coefficient 1; 11 lots of y is 11 × y, written 11y.
3. 4
y on its own has coefficient 1. Adding 4 y's is like adding 4 ones.
Each y has coefficient 1; 4 lots of y is 4 × y, written 4y.
4. 9, 12
Group the like terms first: the x terms together and the number terms together.
The x terms: 2x + 7x = 9x. The number terms: 11 + 1 = 12.
5. 9
13b and 4b are like terms: keep the letter and work with the coefficients only.
Like terms: subtract the coefficients, 13 − 4 = 9, and keep the letter: 9b.
6. 9
What is the coefficient of m on its own? Write it in, then subtract.
m on its own has coefficient 1: 10m − 1m = 9m.
7. 6, 15
Group the like terms first: the x terms together and the number terms together.
The x terms: 2x + 4x = 6x. The number terms: 9 + 6 = 15.
8. 12
No need to substitute term by term. Simplify 4a + 2a − 3a first, then put 4 in for a.
Simplify first: 4a + 2a − 3a = 3a. Then substitute: 3 × 4 = 12.
9. 10
No need to substitute term by term. Simplify 6a + 7a − 8a first, then put 2 in for a.
Simplify first: 6a + 7a − 8a = 5a. Then substitute: 5 × 2 = 10.

10. D. 9a + 2b
Check each one: only terms with the same letter combine. Which has no like terms left?
9a and 2b have different letters, so they are not like terms and can't be combined.
11. False
Find the like terms first: 9y and 3y combine, but what about 4?
The y terms: 9y + 3y = 12y. The number term 4 can't join them: 12y + 4.
12. True
Find the like terms first: 7y and 2y combine, but what about 7?
The y terms: 7y + 2y = 9y. The number term 7 can't join them: 9y + 7.

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

13. 15
The perimeter is the three sides added. All three carry x, so they are like terms: add the coefficients.
The perimeter is the three sides added: 4x + 3x + 8x = 15x cm.
14. 7, 11
Put both lots of boxes together (the b terms) and the loose sweets together (the numbers), and combine each lot.
5b + 7 + 2b + 4: the boxes make 7b and the loose ones 11, so 7b + 11.
15. 14
A rectangle has two lengths and two widths. Write all four sides out: 5a + 2a + …
Perimeter = length + width + length + width = 5a + 2a + 5a + 2a = 14a cm.
16. 15
8 pens cost 8y dollars and 7 pens 7y. Are those like terms?
8 pens cost 8y dollars and 7 cost 7y; like terms combine: 8y + 7y = 15y.
17. 5
Money spent is subtracted. 12m and 7m are like terms, so work with the coefficients only.
12m − 7m: subtract the coefficients, 5m dollars.
18. 15
7 pens cost 7y dollars and 8 pens 8y. Are those like terms?
7 pens cost 7y dollars and 8 cost 8y; like terms combine: 7y + 8y = 15y.

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