Ratios That Make Sense
8:12 simplified.
2:3
3:5 =6:__?
10
Write “5 more than x”
x+5
3.4 × 2
6.8
-5 + 3
-2
A class has 8 boys and 12 girls. What is the ratio of boys to girls?
2:3
5:8 = 15:24?
Yes (×3)
Simplify: 3(x + 4)
3x + 12
0.6 ÷ 0.2
3
Which is greater: -2 or -7?
-2
2:3 → 6:?
9
Scale 4:7 to a ratio with 21 as the second number.
12:21
Simplify: 4x + 3x
7x
1.25 + 0.75
2
A temperature starts at -3 and rises 9 degrees. Where does it end?
6
Create a ratio for 10 red and 5 blue marbles. Simplify it.
10:5 → 2:1
Find the missing value: 7:9 = ___:27
21
Write an expression for “twice a number minus 7”
2x − 7
3/4 ÷ 1/2
3/2 or 1.5
A submarine is at -12 meters below sea level. It rises 5 meters, then descends 9 meters.
Where is it now?
-16 meters
Is 8:11 equivalent to 4:5? Explain.
No — 4×2=8, but 5×2=10 ≠ 11
Explain how you know two ratios are equivalent without dividing.
Multiply (or divide) both parts by the same number / use scaling
A student says 2(x + 6) = 2x + 6. What’s the mistake?
They didn’t distribute to both terms (should be 2x + 12)
Explain why 3/4 ÷ 1/2 = 3/2
Dividing by 1/2 asks “how many halves are in 3/4” → 1.5 groups
Explain why subtracting a negative becomes addition.
Opposite of a negative = positive (distance increases)