Diag · Diagnostic set

1. 1.

   Are the ratios 2 : 5 and 8 : 20 equivalent?

   Answer. yes

   Both simplify to 2 : 5, so they are equivalent.

2. 2.

   A pack of 10 markers costs $16.1. What is the unit price per marker?

   Answer. $1.61

   $16.1 ÷ 10 = $1.61 per marker.

3. 3.

   Theo has 5 red marbles and 3 blue marbles. Write the ratio of red to blue in simplest form.

   Answer. 5 : 3

   Red : blue = 5 : 3 = 5 : 3.

4. 4.

   In Theo’s class, 7 students walk and 5 students bike. What is the part-to-whole ratio of walkers to the class, in simplest form?

   Answer. 7 : 12

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

5. 5.

   Complete the equivalent ratio: 2 : 4 = 12 : ? Then Sam needs 3 of that amount. What is the total they need?

   A	B
   2	4
   12	?

   Answer. 72

   Multiply both parts by 6: 4 × 6 = 24. Then multiply by 3: 72.

6. 6.

   A pack of 10 markers costs $21.8. Jonah needs 40 markers. How much will that cost at the same unit price?

   Answer. $87.2

   Unit price $2.18. 4 packs: $21.8 × 4 = $87.2.

7. 7.

   Malik has 3 red marbles and 9 blue marbles. Write the ratio of red to blue in simplest form. Write a complete answer — Priya will compare with a partner.

   Answer. 1 : 3

   Red : blue = 3 : 9 = 1 : 3.

8. 8.

   In Jonah’s class, 2 students walk and 3 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. 2 : 5

   Walkers : class = 2 : 5 = 2 : 5.

9. 9.

   Are the ratios 2 : 4 and 10 : 20 equivalent? Write a complete answer — Priya will compare with a partner.

   Answer. yes

   Both simplify to 1 : 2, so they are equivalent.

10. 10.

    A pack of 5 markers costs $10.9. Nora needs 25 markers. How much will that cost at the same unit price?

    Answer. $54.5

    Unit price $2.18. 5 packs: $10.9 × 5 = $54.5.

11. 11.

    Think

    Theo tried this problem:
    Elena has 5 red marbles and 8 blue marbles. Write the ratio of red to blue in simplest form.
    Theo wrote -5 : 8. That is not correct. What is the right answer?

    Answer. 5 : 8

    Theo’s answer -5 : 8 is off. Red : blue = 5 : 8 = 5 : 8.

12. 12.

    Think

    Sam tried this problem:
    In Malik’s class, 3 students walk and 7 students bike. What is the part-to-whole ratio of walkers to the class, in simplest form?
    Sam wrote 4 : 10. That is not correct. What is the right answer?

    Answer. 3 : 10

    Sam’s answer 4 : 10 is off. Walkers : class = 3 : 10 = 3 : 10.

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