Algebraic expressions · Ages 13–14
Multiplying and dividing algebraic fractions worksheet
Part of: Formulae & algebraic fractions
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Multiplying and dividing algebraic fractions worksheet
Algebraic expressions · Ages 13–14
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)
1.2xx + 8 × x + 88x2 = x (simplest form)
Fill in each blank
Answer:
2.6xx + 3 × x + 37x2 = x (simplest form)
Fill in each blank
Answer:
3.5x5 ÷ (9x23) = x (simplest form)
Fill in each blank
Answer:
4.24x × 3x7 =
Answer in simplest form
Answer:
5.8x2 ÷ (4x26) = x (simplest form)
Fill in each blank
Answer:
6.43x × 9x3 =
Answer in simplest form
Answer:
7.9x + 545 ÷ x + 64 =
Answer in simplest form
Answer:
Part B: Choose, or true or false (2 marks each)
8.x9 × 9x2 = 910x.
True or false?
Answer:
9.x2 × 2x2 = 24x.
True or false?
Answer:
10.What is 5x − 2 ÷ 4(x − 2)2?
- A. 20(x − 2)3
- B. 5x − 24
- C. 54
- D. 45(x − 2)
Choose the right answer
Answer:
11.What is x2 − 815x × 2x2x + 9?
- A. 2x − 95
- B. 2xx − 95
- C. 2xx − 95(x + 9)
- D. 2xx + 95
Choose the right answer
Answer:
12.What is x2 − 497x × 3x2x + 7?
- A. 3xx − 77
- B. 3xx − 77(x + 7)
- C. 3x − 77
- D. 3xx + 77
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.Put the steps of working out 9x + 4 ÷ 5x2 − 16 in order.
- A. 9x + 4 × (x + 4)x − 45 = 9x − 45
- B. 9x + 4 × x2 − 165 = 9x + 4 × (x + 4)x − 45
- C. 9x + 4 ÷ 5x2 − 16 = 9x + 4 × x2 − 165
Write the letters in the right order
Working:
Answer:
14.A rectangular plot is x2 − 16x m long and 6xx + 4 m wide. When x = 12, what is its area, in m²?
Working:
Answer:
15.A boat sails at 2x + 14x km/h for 6xx + 7 hours. Whatever x is, how far does it go, in km?
Working:
Answer:
16.A rectangle's area is 6xx + 4 cm² and its length 7x2x + 4 cm. How wide is it, in cm?
- A. 67x
- B. 42x3(x + 4)2
- C. 7x6
- D. 67
Choose the right answer
Working:
Answer:
17.A 4x2 m roll of ribbon is cut into pieces 4x7 m long. Pieces = 4x2 ÷ (4x7) = x; when x = 4, there are pieces.
Fill in each blank
Working:
Answer:
18.A rectangle is 3xx + 3 cm long and x + 310 cm wide. Area = 3xx + 3 × x + 310 = x cm² (simplest form).
Fill in each blank
Working:
Answer:
Show the answers and working
Multiplying and dividing algebraic fractions worksheet: Answers and working
Part A: Working out and filling in
1. 1, 4
x + 8 cancels above and below, and one x cancels: 28x = 14x.
2. 6, 7
x + 3 cancels above and below, and one x cancels: 67x = 67x.
3. 1, 3
Dividing by 9x23 is multiplying by 39x2: 5x × 35 × 9x2 = 1545x = 13x.
4. 314
x cancels above and below, leaving 2 × 34 × 7 = 314.
5. 6, 1
Dividing by 4x26 is multiplying by 64x2: 8x × 62 × 4x2 = 488x = 6x.
6. 4
x cancels above and below, leaving 4 × 93 × 3 = 4.
7. 365
Dividing by x + 64 is multiplying by 4x + 6: 9x + 65 × 4x + 6; x + 6 cancels, leaving 9 × 45 = 365.
Part B: Choose, or true or false
8. False
x9 × 9x2 = 9x9x2; one x cancels, giving 99x.
9. False
x2 × 2x2 = 2x2x2; one x cancels, giving 22x.
10. B. 5x − 24
5x − 2 × (x − 2)24; one x − 2 cancels: 5x − 24.
11. B. 2xx − 95
x2 − 81 = (x + 9)(x − 9). Cancel x + 9 and one x: 2xx − 95.
12. A. 3xx − 77
x2 − 49 = (x + 7)(x − 7). Cancel x + 7 and one x: 3xx − 77.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. C → B → A
Turn the divisor over to multiply, factorise x2 − 16, then cancel x + 4.
14. 48 m²
Area = (x + 4)x − 4x × 6xx + 4 = 6(x − 4); at x = 12 it is 6 × (12 − 4) = 48 m².
15. 12 km
Distance = speed × time = 2x + 7x × 6xx + 7; x and x + 7 both cancel, leaving 2 × 6 = 12 km.
16. A. 67x
Width = 6xx + 4 ÷ 7x2x + 4 = 6xx + 4 × x + 47x2 = 67x.
17. 7, 28
Dividing by 4x7 is multiplying by 74x: 4x2 × 74x = 7x, which is 28 when x = 4.
18. 3, 10
x + 3 cancels above and below: 3x10 = 3x10.
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