Reveal Math · Unit 3 · Supplemental

Ratios & Rates

Grade 6 · Standards 6.RP.A.1, 6.RP.A.2, 6.RP.A.3 — ratios, unit rates & equivalent ratios

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⚖️Ratio — compares two amounts, like 3 to 4 (3:4).

🏃Rate — a ratio of two different units, like miles per hour.

1️⃣Unit rate — a rate for exactly 1 unit, like $3 per 1 pound.

🟰Equivalent ratios — ratios that show the same comparison (2:3 = 4:6).

📋Ratio table — a table of equal ratios that grow by the same multiplier.

🔄Conversion factor — a rate used to change units, like 12 in = 1 ft.

Worked Example

Step 1: Write the rate: 12 dollars / 4 pounds.

Step 2: Divide to get "per 1 pound": 12 ÷ 4 = 3.

Step 3: Write the unit rate with units: $3 per pound.

Answer: $3 per pound.

The ratio of to is .

The unit rate is per .

These ratios are equivalent because I multiplied both parts by .

Directions: Solve each problem. Show your work and use the hint cue if you need it.

A class has 12 boys and 16 girls. Write the ratio of boys to girls in simplest form.
Hint: divide both numbers by the largest number that fits both (4).
Write a ratio equivalent to 2 : 3 by multiplying both parts by 4.
Hint: 2 × 4 and 3 × 4.
Find the unit rate: 150 miles in 3 hours.
Hint: divide miles by hours to get miles per 1 hour.
Find the unit price: $6.00 for 3 candy bars.
Hint: 6.00 ÷ 3 gives the price per 1 bar.
Fill in the ratio table — cups of flour : cookies. 1:6, 2:12, 3:______
Hint: each row multiplies 1:6 by the same number.
A recipe uses 2 cups of sugar for 5 cups of flour. How much sugar for 15 cups of flour?
Hint: 15 is 5 × 3, so multiply the sugar by 3 too.
Are 4 : 6 and 6 : 9 equivalent ratios? (Yes / No)
Hint: simplify both. Do they reduce to the same ratio?
Convert 3 feet to inches using 1 foot = 12 inches.
Hint: multiply 3 by 12.
A car travels 240 miles on 8 gallons. Find the unit rate (miles per gallon).
Hint: 240 ÷ 8.
The ratio of red to blue marbles is 3 : 5. If there are 9 red marbles, how many blue?
Hint: 9 is 3 × 3, so multiply the blue part by 3.