UA · Unit 1 review

1. 1.

   Complete the equivalent ratio: 6 : 4 = 24 : ?

   A	B
   6	4
   24	?

   Answer. 16

   Multiply both parts by 4: 4 × 4 = 16.

2. 2.

   A scale drawing uses a scale factor of 4. The original is 4 cm by 2 cm. What are the drawing’s dimensions?

   Answer. 16 cm by 8 cm

   Multiply each length by 4: 16 by 8.

3. 3.

   A recipe uses 34 cup of oil for 15 cup of flour. How many cups of oil per 1 cup of flour?

   Answer. 334 cup per cup

   34 ÷ 15 = 334.

4. 4.

   The table shows x and y. What is the constant of proportionality k if y = kx?

   x	y
   1	5
   2	10
   3	15
   4	20

   Answer. 5

   Each y ÷ x equals 5, so k = 5.

5. 5.

   A proportional relationship has constant of proportionality 5. Write an equation for y in terms of x. Write a complete answer — Theo will compare with a partner.

   Answer. y = 5x

   y = kx with k = 5 gives y = 5x.

6. 6.

   Solve: 6/x = 714. Find x. Then Owen needs 5 of that amount. What is the total they need?

   Answer. 60

   Cross multiply: 6 × 14 = 7x → 84 = 7x → x = 12. Then multiply by 5: 60.

7. 7.

   A circle has radius 10 cm. Find the circumference in terms of π. Write a complete answer — Theo will compare with a partner.

   Answer. 20π cm

   C = 2πr = 2π(10) = 20π cm.

8. 8.

   In Malik’s class, 7 students walk and 5 students bike. What is the part-to-whole ratio of walkers to the class, in simplest form? Write a complete answer — Priya will compare with a partner.

   Answer. 7 : 12

   Walkers : class = 7 : 12 = 7 : 12.

9. 9.

   A scale drawing uses a scale factor of 3. The original is 3 cm by 4 cm. What are the drawing’s dimensions? Then Grace needs 3 of that amount. What is the total they need?

   Answer. 27 cm by 12 cm

   Multiply each length by 3: 9 by 12. Then multiply by 3: 27 cm by 12 cm.

10. 10.

    A recipe uses 34 cup of oil for 13 cup of flour. How many cups of oil per 1 cup of flour? Then Theo needs 4 of that amount. What is the total they need?

    Answer. 9 cup per cup

    34 ÷ 13 = 214. Then multiply by 4: 9 cup per cup.

11. 11.

    Think

    Sam tried this problem:
    The table shows x and y. What is the constant of proportionality k if y = kx?
    Sam wrote 3. That is not correct. What is the right answer?

    x	y
    1	2
    2	4
    3	6
    4	8

    Answer. 2

    Sam’s answer 3 is off. Each y ÷ x equals 2, so k = 2.

12. 12.

    Think

    Sam tried this problem:
    A proportional relationship has constant of proportionality 4. Write an equation for y in terms of x.
    Sam wrote y = 5x. That is not correct. What is the right answer?

    Answer. y = 4x

    Sam’s answer y = 5x is off. y = kx with k = 4 gives y = 4x.

Original extra practice. Keys are computed from the items, not guessed.