Algebra and equations · Ages 11–12
Equations with brackets, decimals and fractions worksheet
Covers: Equations with brackets and like terms, Equations with decimals, fractions and percentages, Finding the original, Solving word problems with equations
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Equations with brackets, decimals and fractions worksheet
Algebra and equations · Ages 11–12
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.
Part A: Working out and filling in (2 marks each)
1.Solve 9x − 5x = 7. x =
Answer:
2.Solve 2(x − 2) = 5. x =
Answer:
3.Solve 5x + 4x + 3 = 84. x =
Answer:
4.Solve (13)x = 3. x =
Answer:
5.Solve 50% × x + 10 = 12. x =
Answer:
6.Solve (25)x − 1 = 23. x =
Answer:
7.70% of ? = 28
Answer:
8.35% of ? = 105
Answer:
9.25% off is $225: was $?
Answer:
10.A triangle has an area of 21.25 cm² and a base of 5 cm. How tall is it, in cm?
Answer:
Part B: Choose, or true or false (2 marks each)
11.Ming buys 5 notebooks at the same price and a pencil case for 25 dollars, paying 45 dollars in all. With x dollars for one notebook, which equation is right?
- A. 5x = 45 + 25
- B. 5x + 25 = 45
- C. x + 25 = 45
- D. 5(x + 25) = 45
Choose the right answer
Answer:
12.10% of a number is 2. Let the number be x. Which equation is right?
- A. x ÷ 10% = 2
- B. x − 10% = 2
- C. 10% × x = 2
- D. 2 × 10% = x
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.Ka-lok and Ka-yan have 77 stickers between them. Ka-lok has 32 more than 4 times as many as Ka-yan. How many stickers does Ka-yan have?
Working:
Answer:
14.8 children each buy a meal of a $21 burger and a drink, paying $288 in all. How much is each drink?
Working:
Answer:
15.Ka-yan spends 34 of her pocket money on books, which is $45. How much pocket money did Ka-yan have?
Working:
Answer:
16.apples cost $18.4 a kilogram. Tsz-hin buys some and pays $25 for delivery, $71 in all. How many kilograms of apples does Tsz-hin buy?
Working:
Answer:
17.5 pupils in a class wear glasses. That is 20% of the class. How many pupils are in the class?
Working:
Answer:
18.Ka-lok gives 20% of his savings to charity, then spends $12 on a book, leaving $340. How much were his savings?
Working:
Answer:
Show the answers and working
Equations with brackets, decimals and fractions worksheet: Answers and working
Part A: Working out and filling in
1. 1.75
9x − 5x are like terms, so first work out how many x are left.
Join the like terms: 4x = 7, so x = 7 ÷ 4 = 1.75.
2. 4.5
2 multiplies the whole bracket, so divide both sides by 2 first and see what x − 2 is.
Divide both sides by 2: x − 2 = 2.5; add 2 to both sides: x = 4.5.
3. 9
Join 5x and 4x first, then take 3 from both sides.
Join: 9x + 3 = 84; take 3 from both sides: 9x = 81; x = 9.
4. 9
13 of x is 3, so 1 parts make 3. Find one part first.
13 of x is 3: one part is 3 ÷ 1 = 3, and 3 parts are 3 × 3 = 9.
5. 4
Take 10 from both sides first to see what 50% × x is, then divide by 50%.
Take 10 from both sides: 50% × x = 2; x = 2 ÷ 50% = 4.
6. 60
Add 1 to both sides first and see what (25)x is.
That is 2 parts: find one part, then 5 parts.
Add 1 to both sides: (25)x = 24; one part is 24 ÷ 2 = 12, so x = 12 × 5 = 60.
7. 70% of 40 = 28
28 is 70% of the number, so the number = 28 ÷ 70%: 28 × 100 = 2800, 2800 ÷ 70 = 40
8. 35% of 300 = 105
105 is 35% of the number, so the number = 105 ÷ 35%: 105 × 100 = 10500, 10500 ÷ 35 = 300
9. 25% off is $225: was $300
25% off leaves 75% of the price, so the price = 225 ÷ 75%: 225 × 100 = 22500, 22500 ÷ 75 = 300
10. 8.5 cm
Triangle area = base × height ÷ 2. Let the height be x: 5 × x ÷ 2 = 21.25.
Let the height be x cm: 5 × x ÷ 2 = 21.25; 5x = 42.5; x = 8.5.
Part B: Choose, or true or false
11. B. 5x + 25 = 45
5 notebooks cost 5x dollars. Add the pencil case: what should the total be?
5 notebooks cost 5x dollars; with the 25-dollar case that is 45: 5x + 25 = 45.
12. C. 10% × x = 2
“10% of the number” means 10% × x. Which equation says that equals 2?
“10% of the number” is 10% × x, and it equals 2: 10% × x = 2, x = 20.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 9 stickers
Let Ka-yan have x, so Ka-lok has 4x + 32. Together they make 77.
Let Ka-yan have x, so Ka-lok has 4x + 32: x + 4x + 32 = 77, 5x = 45, x = 9.
14. 15 dollars
Let a drink be $x: each meal is x + 21, and 8 of them make 288: 8(x + 21) = 288.
Let a drink be $x: 8(x + 21) = 288; x + 21 = 36; x = 15.
15. 60 dollars
34 of the pocket money is $45, so 3 parts make 45 dollars. Find one part first.
Let it be $x: (34)x = 45; one part is 45 ÷ 3 = 15, so x = 15 × 4 = 60.
16. 2.5 kg
Let it be x kg: the apples cost 18.4x dollars, plus 25 delivery, 71 in all.
Let it be x kg: 18.4x + 25 = 71; 18.4x = 46; x = 2.5.
17. 5 pupils in a class wear glasses. That is 20% of the class. How many pupils are in the class? (Answer: 25 pupils)
5 ÷ 20 × 100 = 25
18. 440 dollars
Let the savings be $x. After giving 20% away, what percentage of x is left?
Then think: how much was left before the book?
Let it be $x: x − 20% × x − 12 = 340; 80% × x = 352; x = 352 ÷ 80% = 440.
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