Grade: Grade 6 Subject: Mathematics Unit: Ratios & Rates Lesson: 6 of 6 SAT: Algebra ACT: Math

Unit Checkpoint

Unit Review

This checkpoint assesses your mastery of ratios and rates. Review the key concepts before completing the assessment.

Key Concepts

Ratios

  • A ratio compares two quantities
  • Written as a:b, a/b, or "a to b"
  • Equivalent ratios have the same value when simplified

Rates and Unit Rates

  • A rate compares quantities with different units
  • A unit rate has 1 in the denominator
  • Unit rate = total / number of units

Proportions

  • Two equal ratios form a proportion
  • Cross multiply to solve: a/b = c/d means ad = bc
  • Use proportions to find missing values

Unit Assessment

Question 1

Write the ratio 15:25 in simplest form.

Question 2

A package of 6 muffins costs $4.50. What is the cost per muffin?

Question 3

Are 4/6 and 10/15 equivalent ratios? Explain how you know.

Question 4

Solve for x: 3/8 = x/24

Question 5

A car travels 225 miles in 5 hours. What is the speed in miles per hour?

Question 6

Complete the ratio table:

Red Paint24?10
Blue Paint5?15?

Question 7

Brand A juice costs $3.60 for 48 ounces. Brand B costs $2.70 for 32 ounces. Which is the better buy?

Question 8

The ratio of teachers to students in a school is 1:18. If there are 450 students, how many teachers are there?

Question 9

A recipe uses 3 cups of flour for every 2 cups of sugar. If you use 9 cups of flour, how much sugar do you need?

Question 10

A machine fills 150 bottles in 10 minutes. At this rate, how many bottles will it fill in 1 hour?

Answer Key

Click to reveal answers

1. 15:25 = 3:5 (divide both by 5)

2. $4.50 / 6 = $0.75 per muffin

3. Yes. 4/6 = 2/3 and 10/15 = 2/3. Both simplify to the same ratio.

4. 3/8 = x/24. Cross multiply: 3 x 24 = 8x. 72 = 8x. x = 9

5. 225 / 5 = 45 miles per hour

6. Red: 2, 4, 6, 10. Blue: 5, 10, 15, 25. (Ratio is 2:5)

7. Brand A: $3.60/48 = $0.075/oz. Brand B: $2.70/32 = $0.084/oz. Brand A is the better buy.

8. 1/18 = x/450. x = 450/18 = 25 teachers

9. 3/2 = 9/x. 3x = 18. x = 6 cups of sugar

10. 150 bottles/10 min = 15 bottles/min. 15 x 60 = 900 bottles per hour

Self-Assessment

ScoreMastery LevelNext Steps
9-10AdvancedMove on to the next unit!
7-8ProficientReview missed concepts, then proceed.
5-6DevelopingReview lessons 3-5 before moving on.
0-4BeginningRestart the unit from Lesson 1.