Algebraic expressions · Ages 13–14

Simplifying algebraic fractions worksheet

Part of: Formulae & algebraic fractions

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Algebraic expressions · Ages 13–14

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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 pile of (4x + 36) stickers is split into (x + 9) equal shares. Whatever x is, how many stickers are in each share?
Working:
Answer:
14.A cuboid's volume is (x³ + 11x² + 24x) cm³; its base is (x + 3) cm by x cm. When x = 4, how tall is it, in cm?
Working:
Answer:
15.x friends share (6x² + 30x) dollars equally. How many dollars does each get?
- A. 6 + 30
- B. 6x + 30x
- C. 6x + 30
- D. 6x² + 30
Choose the right answer
Working:
Answer:
16.A rectangle's area is (3x² + 9x) cm² and its width 3x cm. Length = 3x² + 9x3x = x + cm; when x = 5, the length is cm.
Fill in each blank
Working:
Answer:
17.A rectangle's area is (x² + 7x + 12) cm² and one side is (x + 3) cm. The other side = x² + 7x + 12x + 3 = (x + ) cm; when x = 5, it is cm.
Fill in each blank
Working:
Answer:
18.A coach covers (6x² + 36x) km in (x + 6) hours. Average speed = 6x² + 36xx + 6 = x km/h; when x = 8, it is km/h.
Fill in each blank
Working:
Answer:

Show the answers and working

Simplifying algebraic fractions worksheet: Answers and working

1. 3, 2
Divide the top and the bottom by 6xy: x²y ÷ xy = x, xy² ÷ xy = y, 18 ÷ 6 = 3, 12 ÷ 6 = 2.
2. 5
Top = −5(x − 2), and 2 − x = −(x − 2). Cancel x − 2: −5 ÷ (−1) = 5.
3. 1, 8
Top = 2(x + 4), bottom = 16(x + 4). Cancel x + 4: 216 = 18.
4. 5, 8
Top = 10(x + 3), bottom = 16(x + 3). Cancel x + 3: 1016 = 58.
5. −4
Top = 4(x − 9), and 9 − x = −(x − 9). Cancel x − 9: 4 ÷ (−1) = −4.
6. 2
7 × 2 = 14 and 7 + 2 = 9, so x² + 9x + 14 = (x + 7)(x + 2). Cancel x + 7: x + 2.
7. 6
7 × 6 = 42 and 7 + 6 = 13, so x² + 13x + 42 = (x + 7)(x + 6). Cancel x + 7: x + 6.

8. True
Divide the top and the bottom by their common factor 4x: 16x20x² = 45x.
9. D. 54x
Top = 5(x + 8), bottom = 4x(x + 8); cancel x + 8: 54x.
10. A. 53x
Top = 5(x + 4), bottom = 3x(x + 4); cancel x + 4: 53x.
11. C. −1x
Top = 1(x − 3), bottom = x(3 − x) = −x(x − 3). Cancel x − 3: −1x.
12. B. −6x
Top = 6(x − 6), bottom = x(6 − x) = −x(x − 6). Cancel x − 6: −6x.

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

13. 4 stickers
4x + 36x + 9 = 4x + 9x + 9 = 4: x + 9 cancels, so x doesn't matter.
14. 12 cm
x³ + 11x² + 24x = x(x + 3)(x + 8); divided by the base area x(x + 3), the height is x + 8 = 12 cm.
15. C. 6x + 30
6x² + 30xx = x6x + 30x = 6x + 30.
16. 3, 8
3x² + 9x = 3x(x + 3); cancel 3x and the length is x + 3, which is 8 cm when x = 5.
17. 4, 9
3 × 4 = 12 and 3 + 4 = 7: x² + 7x + 12 = (x + 3)(x + 4); cancel x + 3, and the other side is x + 4 = 9 cm.
18. 6, 48
6x² + 36x = 6x(x + 6); x + 6 cancels, leaving 6x, which is 6 × 8 = 48 km/h when x = 8.

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