Algebra and equations · Ages 11–12

Equations with decimals, fractions and percentages worksheet

Part of: Equations with brackets, decimals and fractions

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

Algebra and equations · Ages 11–12

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.May spends 15 of her pocket money on books, which is $14. How much pocket money did May have?
Working:
Answer:
14.kiwis cost $18.4 a kilogram. Ming buys some and pays $30 for delivery, $57.6 in all. How many kilograms of kiwis does Ming buy?
Working:
Answer:
15.35 of a number, subtract 15, is 15. What is the number?
Working:
Answer:
16.Ka-lok is 1.02 m tall, which is 0.6 times his dad's height. How tall is his dad, in metres?
Working:
Answer:
17.A eraser is 15% off, which takes $66 off its price. What was the price before?
Working:
Answer:
18.kiwis cost $18.4 a kilogram. Tsz-ching buys some and pays $29 for delivery, $102.6 in all. How many kilograms of kiwis does Tsz-ching buy?
Working:
Answer:

Show the answers and working

Equations with decimals, fractions and percentages worksheet: Answers and working

1. 8
34 of x is 6, so 3 parts make 6. Find one part first.
34 of x is 6: one part is 6 ÷ 3 = 2, and 4 parts are 2 × 4 = 8.
2. 9
To find x, divide both sides by 0.6: 5.4 ÷ 0.6. The divisor is a decimal, so move both points together first.
Divide both sides by 0.6: x = 5.4 ÷ 0.6 = 9.
3. 8
To find x, divide both sides by 0.2: 1.6 ÷ 0.2. The divisor is a decimal, so move both points together first.
Divide both sides by 0.2: x = 1.6 ÷ 0.2 = 8.
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. 8
Take 5 from both sides first to see what 75% × x is, then divide by 75%.
Take 5 from both sides: 75% × x = 6; x = 6 ÷ 75% = 8.
6. 20
Take 9.4 from both sides first and see what 0.8x is.
Take 9.4 from both sides: 0.8x = 16; divide by 0.8: x = 20.
7. 18
Take 2 from both sides first and see what 0.8x is.
Take 2 from both sides: 0.8x = 14.4; divide by 0.8: x = 18.
8. 24
Take 2 from both sides first to see what 25% × x is, then divide by 25%.
Take 2 from both sides: 25% × x = 6; x = 6 ÷ 25% = 24.
9. 55
Add 9 to both sides first and see what (15)x is.
That is 1 parts: find one part, then 5 parts.
Add 9 to both sides: (15)x = 11; one part is 11 ÷ 1 = 11, so x = 11 × 5 = 55.
10. 2
x and 0.8x are like terms, so add 1 and 0.8 first.
Join: 1.8x = 3.6, x = 3.6 ÷ 1.8 = 2.

11. A. 6
x = 4.8 ÷ 0.8. Move both points right together until the divisor is whole.
x = 4.8 ÷ 0.8: move both points right together, giving 6.
12. C. 12
x = 2.4 ÷ 0.2. Move both points right together until the divisor is whole.
x = 2.4 ÷ 0.2: move both points right together, giving 12.

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

13. 70 dollars
15 of the pocket money is $14, so 1 parts make 14 dollars. Find one part first.
Let it be $x: (15)x = 14; one part is 14 ÷ 1 = 14, so x = 14 × 5 = 70.
14. 1.5 kg
Let it be x kg: the kiwis cost 18.4x dollars, plus 30 delivery, 57.6 in all.
Let it be x kg: 18.4x + 30 = 57.6; 18.4x = 27.6; x = 1.5.
15. 50
Let it be x: (35)x − 15 = 15. Add 15 to both sides first.
Let it be x: (35)x − 15 = 15; (35)x = 30; x = 50.
16. 1.7 m
Let Dad be x m, so Ka-lok is 0.6x m: 0.6x = 1.02. Divide both sides by 0.6.
Let Dad be x m: 0.6x = 1.02, x = 1.02 ÷ 0.6 = 1.7.
17. 440 dollars
Let the old price be $x: the saving is 15% of x, so 15% × x = 66.
Let it be $x: 15% × x = 66, x = 66 ÷ 15% = 440.
18. 4 kg
Let it be x kg: the kiwis cost 18.4x dollars, plus 29 delivery, 102.6 in all.
Let it be x kg: 18.4x + 29 = 102.6; 18.4x = 73.6; x = 4.

Numsprite · numsprite.com/en/worksheets/equations-with-brackets-decimals-and-fractions/equations-with-fractions-and-decimals