Equations and inequalities · Ages 12–13
Fractions and decimals in equations worksheet
Part of: Linear equations in one unknown
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
Fractions and decimals in equations worksheet
Equations and inequalities · Ages 12–13
Numsprite
numsprite.com
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.x5 + 9 = 16: times 5 on both sides, x + = , so x = .
Fill in each blank
Answer:
2.x + 82 = x + 265, x =
Answer:
3.x2 + x5 = −42, x =
Answer:
4.76 x = 11, x =
Answer in simplest form
Answer:
5.38 x = 4, x =
Answer in simplest form
Answer:
6.x + 112 = x + 145, x =
Answer:
7.0.9x + 3 = 16.5, x =
Answer:
8.x − 43 − x − 45 = −6, x =
Answer:
9.x − 74 − x − 35 = 5, x =
Answer:
Part B: Choose, or true or false (2 marks each)
10.x8 + 3 = 6 times 8 on both sides is x + 3 = 48.
True or false?
Answer:
11.To clear the denominators of x12 + x10 = 9, what is the handiest number to multiply both sides by?
- A. 22
- B. 120
- C. 60
- D. 12
Choose the right answer
Answer:
12.x9 + 4 = 15 times 9 on both sides is x + 4 = 135.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Members pay 0.6 times the price, less a $20 voucher: $100. What is the full price?
Working:
Answer:
14.A takes 7 hours to clear up alone and B takes 8. How many hours do they take together?
Answer in simplest form
Working:
Answer:
15.Three rides average 66 km. Two were 71 and 81 km. How long was the third?
Working:
Answer:
16.50c and 20c coins, 18 in all, worth $6. Times 10: 5x + 2(18 − x) = , x = .
Fill in each blank
Working:
Answer:
17.13 of a book on day 1, 18 on day 2, 78 pages left. How many pages?
Working:
Answer:
18.Out at 60 km/h, back at 40 km/h, 10 hours in all. How far is it each way?
Working:
Answer:
Show the answers and working
Fractions and decimals in equations worksheet: Answers and working
Part A: Working out and filling in
1. 45, 80, 35
Every term is multiplied by 5: 9 × 5 = 45, 16 × 5 = 80, x = 80 − 45 = 35.
2. 4
Cross-multiply: 5(x + 8) = 2(x + 26), which gives x = 4. Check: both sides are 6.
3. −60
Times 10: 5x + 2x = −420, 7x = −420, x = −60.
4. 667
Multiply both sides by the reciprocal, 67: x = 11 × 67 = 667. Or times 6 first, 7x = 66, then divide by 7.
5. 323
Multiply both sides by the reciprocal, 83: x = 4 × 83 = 323. Or times 8 first, 3x = 32, then divide by 3.
6. −9
Cross-multiply: 5(x + 11) = 2(x + 14), which gives x = −9. Check: both sides are 1.
7. 15
Times 10: 9x + 30 = 165, 9x = 165 − 30, x = 15.
8. −41
Times 15: 5(x − 4) − 3(x − 4) = −90. The second numerator has a minus in front, so it is a bracket and every term flips. This gives x = −41.
9. 123
Times 20: 5(x − 7) − 4(x − 3) = 100. The second numerator has a minus in front, so it is a bracket and every term flips. This gives x = 123.
Part B: Choose, or true or false
10. False
Every term is multiplied, even 3 with no denominator: 3 × 8 = 24.
11. C. 60
The L.C.M. of 12 and 10 is 60; times 60 clears both denominators.
12. False
Every term is multiplied, even 4 with no denominator: 4 × 9 = 36.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 200 dollars
0.6x − 20 = 100. Times 10: 6x − 200 = 1000, x = 200.
14. 5615 hours
Each hour they do 17 and 18: x7 + x8 = 1, 15x = 56, x = 5615. It isn't the mean of 7 and 8.
15. 46 km
71 + 81 + x3 = 66. Times 3: 71 + 81 + x = 198, x = 46.
16. 60, 8
0.5x + 0.2(18 − x) = 6, and 6 × 10 = 60. 3x + 2 × 18 = 60, 3x = 24, x = 8.
17. 144 pages
x − x3 − x8 = 78. Times 24, x = 144. Both fractions are of the whole book, not of what is left.
18. 240 km
Time = distance ÷ speed: x60 + x40 = 10, x = 240. Going takes 4 h, coming back 6 h.
Numsprite · numsprite.com/en/worksheets/linear-equations-in-one-unknown/equations-with-fractions-and-decimals
Practise it in the gameFractions and decimals in equations · Unlimited questions, no download