Question

The ratio of solid beads to clear beads in a vase is 820
. Select all the correct statements that tell if the operations will give an equivalent ratio.

Add 2 solid and 2 clear beads.


Subtract 8 solid and 6 clear beads.


Multiply the number of solid and clear beads by 2.


Divide the number of solid and clear beads by 4.


Multiply the number of solid and clear beads by 18
.

Answer 1

Initial ratio = 8:20 = 8/20 = 2/5.

Compute each operation:

- Add 2 and 2: (8+2)/(20+2) = 10/22 = 5/11 ≠ 2/5 — not equivalent.
- Subtract 8 and 6: (8−8)/(20−6) = 0/14 = 0 ≠ 2/5 — not equivalent.
- Multiply both by 2: (8·2)/(20·2) = 16/40 = 2/5 — equivalent.
- Divide both by 4: (8/4)/(20/4) = 2/5 — equivalent.
- Multiply both by 18: (8·18)/(20·18) = 144/360 = 2/5 — equivalent.

Correct statements: multiply by 2; divide by 4; multiply by 18.