MIA · Mixed set · Unit 1

1. 1.

   Complete the equivalent ratio: 6 : 7 = 24 : ?

   A	B
   6	7
   24	?

   Answer. 28

   Multiply both parts by 4: 7 × 4 = 28.

2. 2.

   A scale drawing uses a scale factor of 3. The original is 5 cm by 6 cm. What are the drawing’s dimensions?

   Answer. 15 cm by 18 cm

   Multiply each length by 3: 15 by 18.

3. 3.

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

   Answer. 5 cup per cup

   1 ÷ 15 = 5.

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 9. Write an equation for y in terms of x. Write a complete answer — Jonah will compare with a partner.

   Answer. y = 9x

   y = kx with k = 9 gives y = 9x.

6. 6.

   Solve: 7/x = 735. Find x. Then Priya needs 2 of that amount. What is the total they need?

   Answer. 70

   Cross multiply: 7 × 35 = 7x → 245 = 7x → x = 35. Then multiply by 2: 70.

7. 7.

   A circle has radius 5 cm. Find the circumference in terms of π. Write a complete answer — Sam will compare with a partner.

   Answer. 10π cm

   C = 2πr = 2π(5) = 10π cm.

8. 8.

   In Grace’s class, 5 students walk and 2 students bike. What is the part-to-whole ratio of walkers to the class, in simplest form? Write a complete answer — Mei will compare with a partner.

   Answer. 5 : 7

   Walkers : class = 5 : 7 = 5 : 7.

9. 9.

   A scale drawing uses a scale factor of 3. The original is 5 cm by 2 cm. What are the drawing’s dimensions? Then Ava needs 5 of that amount. What is the total they need?

   Answer. 75 cm by 6 cm

   Multiply each length by 3: 15 by 6. Then multiply by 5: 75 cm by 6 cm.

10. 10.

    A recipe uses 1 cup of oil for 112 cup of flour. How many cups of oil per 1 cup of flour? Then Jonah needs 4 of that amount. What is the total they need?

    Answer. 223 cup per cup

    1 ÷ 112 = 23. Then multiply by 4: 223 cup per cup.

11. 11.

    Think

    Priya tried this problem:
    The table shows x and y. What is the constant of proportionality k if y = kx?
    Priya wrote 2. That is not correct. What is the right answer?

    x	y
    1	3
    2	6
    3	9
    4	12

    Answer. 3

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

12. 12.

    Think

    Mei tried this problem:
    A proportional relationship has constant of proportionality 5. Write an equation for y in terms of x.
    Mei wrote y = 6x. That is not correct. What is the right answer?

    Answer. y = 5x

    Mei’s answer y = 6x is off. y = kx with k = 5 gives y = 5x.

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