Grade 8 Unit Mastery Quiz: Solving Proportions with Unknown Values

This record is a dedicated assessment for the skill of solving proportions with one unknown value. It assumes prior instruction on equivalent ratios and scaling. For broader end-of-unit coverage, see rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz; for narrower practice on generating equivalent ratios by scaling, see rea.m08.number.ratios-rates-proportions.equivalent-ratios.scaling-ratios.unit-mastery-quiz; for equivalent-ratio simplification and missing-value basics inside ratio concepts, see rea.m08.number.ratios-rates-proportions.ratio-concepts.equivalent-ratios.unit-mastery-quiz.

Quiz Instructions

• Total: 20 marks
• Suggested time: 25 to 35 minutes
• Show ratio reasoning clearly.
• A correct answer with no valid method may earn reduced credit on multi-step items.
• Unless stated otherwise, write answers as whole numbers, fractions, or decimals in simplest useful form.

Questions

1. Solve the proportion. (2 marks)

3/5 = x/20

2. Solve the proportion. (2 marks)

7/9 = 21/y

3. Fill in the missing value to make the ratios equivalent. (2 marks)

4 : 11 = 12 : x

4. Fill in the missing value. (2 marks)

x : 18 = 5 : 30

5. A recipe uses 2 cups of rice for 5 people. If the recipe is scaled for 20 people, how many cups of rice are needed? (2 marks)

6. Six notebooks cost $15. At the same rate, how much do 14 notebooks cost? (2 marks)

7. A map scale is 3 cm : 24 km. If two towns are 15 cm apart on the map, what is the actual distance? (2 marks)

8. Complete the table, then state the missing value. (2 marks)

Red paint	Blue paint
2	3
6	9
10	x

9. A class survey found that 8 out of 12 students prefer basketball to soccer. If another class has the same preference ratio and 18 students prefer basketball, how many students were surveyed in that class? (3 marks)

10. Decide whether the value given makes a true proportion. Show your check. (3 marks)

5/8 = 15/x, where x = 24

If it is true, say so. If it is false, give the correct value of x.

Full Marking Solutions

1. 3/5 = x/20 (2 marks)

Scale the denominator from 5 to 20.

5 x 4 = 20, so multiply the numerator by 4 as well.

3 x 4 = 12

So x = 12.

Answer: 12

Marking:

• 1 mark for identifying the scale factor or equivalent setup
• 1 mark for correct value x = 12

2. 7/9 = 21/y (2 marks)

Compare numerators: 7 x 3 = 21.

So the denominator must also be multiplied by 3:

9 x 3 = 27

So y = 27.

Answer: 27

Marking:

• 1 mark for correct proportional reasoning
• 1 mark for correct value y = 27

3. 4 : 11 = 12 : x (2 marks)

The first term is multiplied by 3 because 4 x 3 = 12.

Multiply the second term by 3 as well:

11 x 3 = 33

So x = 33.

Answer: 33

Marking:

• 1 mark for using the same scale factor on both parts
• 1 mark for correct value x = 33

4. x : 18 = 5 : 30 (2 marks)

Write as fractions:

x/18 = 5/30

Simplify 5/30 = 1/6.

So x/18 = 1/6.

Since 18 / 6 = 3, we get x = 3.

Answer: 3

Marking:

• 1 mark for equivalent fraction or scaling method
• 1 mark for correct value x = 3

5. Rice for 20 people (2 marks)

2 cups / 5 people = x cups / 20 people

The number of people is multiplied by 4 because 5 x 4 = 20.

So cups of rice are also multiplied by 4:

2 x 4 = 8

So x = 8 cups.

Answer: 8 cups

Marking:

• 1 mark for correct proportion or scale factor
• 1 mark for correct answer 8 cups

6. Cost of 14 notebooks (2 marks)

6 notebooks : $15 = 14 notebooks : x

Use unit rate or scaling.

Unit rate:

15 / 6 = 2.5

Each notebook costs $2.50.

For 14 notebooks:

14 x 2.5 = 35

So the cost is $35.

Answer: $35

Marking:

• 1 mark for correct proportional setup or valid rate reasoning
• 1 mark for correct answer $35

7. Map distance (2 marks)

3 cm : 24 km = 15 cm : x km

The map distance is multiplied by 5 because 3 x 5 = 15.

Multiply the actual distance by 5:

24 x 5 = 120

So the towns are 120 km apart.

Answer: 120 km

Marking:

• 1 mark for correct scale factor or equivalent proportion
• 1 mark for correct answer 120 km

8. Paint table (2 marks)

The ratio of red to blue is 2 : 3.

From 2 red to 10 red is multiplying by 5.

So blue must also be multiplied by 5:

3 x 5 = 15

So x = 15.

Completed table row: 10 : 15

Answer: 15

Marking:

• 1 mark for identifying the common scale factor
• 1 mark for correct value x = 15

9. Survey problem (3 marks)

First class ratio:

8 prefer basketball out of 12 surveyed

Second class has the same ratio, with 18 preferring basketball.

Set up the proportion:

8/12 = 18/x

Simplify 8/12 = 2/3.

So:

2/3 = 18/x

Since 2 x 9 = 18, multiply 3 by 9:

x = 27

So 27 students were surveyed.

Answer: 27 students

Marking:

• 1 mark for correct proportion
• 1 mark for valid solving steps
• 1 mark for correct answer 27 students

10. Check the proposed value (3 marks)

Given:

5/8 = 15/x, with x = 24

Check by substitution:

15/24

Simplify 15/24 by dividing by 3:

15/24 = 5/8

So the proportion is true when x = 24.

If solving directly:

5 x 3 = 15, so 8 x 3 = 24

Therefore the correct value is 24, and the given value is correct.

Answer: True; x = 24 is correct.

Marking:

• 1 mark for checking by simplification or equivalent scaling
• 1 mark for valid justification
• 1 mark for correct conclusion that the proportion is true

Answer Key Summary

1. 12
2. 27
3. 33
4. 3
5. 8 cups
6. $35
7. 120 km
8. 15
9. 27 students
10. True; x = 24

Recommended Mastery Threshold

Recommended mastery threshold: 16/20 (80%), with at least:

• success on 8 of 10 questions, and
• correct solutions on at least 3 of Questions 5 to 10, since these require proportion solving in context rather than only bare-number scaling.

Interpretation

• 18 to 20 marks: Strong mastery. The learner solves unknowns accurately and transfers the skill to tables and applications.
• 16 to 17 marks: Secure mastery. Minor slips may remain, but the learner is ready to move on.
• 12 to 15 marks: Partial mastery. Review is needed, especially on identifying the common scale factor and keeping ratios in the same order.
• 0 to 11 marks: Not yet secure. Re-teach equivalent-ratio structure, then return to solving missing values.

Common Error Checks for the Marker

Watch for these recurring errors:

• Using different scale factors on the two parts of a ratio
• Reversing the ratio order, such as treating a:b as b:a
• Adding instead of multiplying when building equivalent ratios
• Solving context questions with the wrong unit attached
• Checking a proposed value incompletely without showing equivalence

For repair work before reassessment, use the linked equivalent-ratio quiz records rather than repeating this quiz immediately.