Your child can calculate a percentage when the question is straightforward. But ask them to compare two shopping deals, adjust a recipe or share an amount in a ratio, and they become unsure.

The difficulty may be recognising how the quantities relate.

Ratios, rates and percentages help learners compare amounts and reason proportionally. Understanding those connections makes it easier to choose a method rather than guess an operation.

This guide explains the ideas using everyday examples and original practice questions for British Columbia Grade 8 learners.

How Does This Connect With the BC Grade 8 Curriculum?

British Columbia’s Mathematics 8 curriculum includes proportional reasoning involving ratios, rates, proportions and percentages. It also includes percentages below 1% and above 100%, alongside practical applications such as unit pricing.

The examples below introduce and practise selected skills. Follow your child’s school guidance on the sequence and depth of learning.

What Is the Difference Between a Ratio, Rate and Percentage?

ConceptWhat it expressesExampleRatioA comparison between quantitiesRed to blue beads = 2:3RateA comparison involving different units60 kilometres per hourPercentageA proportion expressed per hundred25% = 25/100

These ideas connect, but they are not interchangeable.

For example, a red-to-blue ratio of 2:3 does not mean that two-thirds of all the beads are red. There are five parts altogether, so two-fifths are red.

1. Understanding Ratios

A ratio compares quantities in a stated order.

Suppose a bowl contains 8 red beads and 12 blue beads.

The ratio of red beads to blue beads is:

8:12

Divide both quantities by 4:

8:12 = 2:3

This means there are two red beads for every three blue beads.

Why Order Matters

Red to blue is 2:3.

Blue to red is 3:2.

Ask your child to label the quantities before writing the numbers.

2. Finding Equivalent Ratios

Equivalent ratios express the same relationship.

For example:

2:3 = 4:6 = 8:12

Both quantities must be multiplied or divided by the same non-zero factor.

Worked Example: Adjusting a Drink Recipe

A drink uses juice and water in the ratio 2:5.

If you use 6 cups of juice, how much water is needed?

The juice amount increases from 2 to 6:

2 × 3 = 6

Apply the same scale factor to the water:

5 × 3 = 15

Answer: 15 cups of water.

Adding the same number to both quantities would not preserve the ratio.

3. Sharing an Amount in a Ratio

Worked Example: Sharing $60

Two children share $60 in the ratio 2:3.

Step 1: Find the total number of parts.

2 + 3 = 5 parts

Step 2: Find the value of one part.

$60 ÷ 5 = $12

Step 3: Calculate each share.

First share: 2 × $12 = $24

Second share: 3 × $12 = $36

Check:

$24 + $36 = $60

Also:

24:36 simplifies to 2:3.

Common Mistake

Dividing $60 by 2 and then by 3 does not divide the money in the required ratio.

The total amount represents all five parts.

4. Understanding Three-Term Ratios

A ratio can compare three quantities.

Worked Example: Three Pieces of Ribbon

A ribbon is 90 cm long and is cut into pieces in the ratio 2:3:4.

Total parts:

2 + 3 + 4 = 9

Length of one part:

90 ÷ 9 = 10 cm

The pieces measure:

• 2 × 10 = 20 cm
• 3 × 10 = 30 cm
• 4 × 10 = 40 cm

Check:

20 + 30 + 40 = 90 cm.

5. Understanding Rates and Unit Rates

A rate compares quantities with different units.

Examples include dollars per kilogram, kilometres per hour and litres per minute.

A unit rate expresses the amount for one unit.

Worked Example: Comparing Rice Prices

Two bags of the same rice are available:

• Bag A: 2 kg for $7.80
• Bag B: 5 kg for $18.50

Find the price per kilogram.

Bag A:

$7.80 ÷ 2 = $3.90/kg

Bag B:

$18.50 ÷ 5 = $3.70/kg

Bag B has the lower unit price.

However, the buying decision may also depend on the amount needed, available storage and budget.

Checking Question

“Am I comparing both products using the same unit?”

Comparing one price per kilogram with another price per 100 g would require conversion first.

6. Calculating Percentages

Percent means “per hundred.”

For example:

25% = 25/100 = 1/4 = 0.25

Worked Example: Finding a Discount

A jacket costs $80 and is reduced by 25%.

Discount:

0.25 × $80 = $20

Sale price:

$80 − $20 = $60

Answer: $60 before any applicable tax.

Notice the difference between the discount amount and the final price.

7. Expressing One Quantity as a Percentage of Another

Worked Example: A Quiz Result

A learner answers 18 out of 24 questions correctly.

Fraction correct:

18/24

Convert to a percentage:

18 ÷ 24 × 100 = 75%

The denominator represents the total possible number of correct answers.

This calculation expresses the quiz result as a percentage; it does not establish a report card proficiency level.

8. Percentages Greater Than 100%

A percentage greater than 100% represents more than the reference amount.

Worked Example

Find 150% of 40.

150% = 1.5

1.5 × 40 = 60

Therefore:

150% of 40 = 60

This is reasonable because 150% means one whole amount plus half of that amount:

40 + 20 = 60.

9. Percentages Below 1%

A percentage below 1% represents less than one-hundredth of the reference amount.

Worked Example

Find 0.5% of $200.

Convert the percentage to a decimal:

0.5 ÷ 100 = 0.005

Calculate:

0.005 × $200 = $1

Answer: $1.

Common Mistake

Using 0.5 as the multiplier calculates 50%, not 0.5%.

Keep the percentage sign in mind when converting.

10. Percentage Increase and Decrease

The original amount is the reference when calculating a percentage change.

Worked Example: Increase

A club’s membership rises from 40 to 50.

Increase:

50 − 40 = 10

Percentage increase:

10 ÷ 40 × 100 = 25%

Worked Example: Decrease

Membership later falls from 50 to 40.

Decrease:

50 − 40 = 10

Percentage decrease:

10 ÷ 50 × 100 = 20%

The changes involve the same number of members but different starting amounts.

A 25% increase followed by a 20% decrease returns to the original value in this example.

Common Mistakes to Watch For

MistakeWhat to checkReversing a ratioLabel the quantities in the requested orderTreating 2:3 as two-thirds of the totalAdd the parts before finding a part-to-whole fractionScaling only one side of a ratioApply the same factor to every termComparing incompatible unit pricesConvert to a common unitGiving the discount instead of the sale priceReread what the question requestsUsing the final amount for percentage changeIdentify the original reference amountConfusing 0.5% with 50%Divide the percentage number by 100

BC Grade 8 Maths Practice Questions

Show your working and explain your reasoning where requested.

Question 1: Simplifying Ratios

Simplify:

18:30

Question 2: Equivalent Ratios

A recipe uses flour and sugar in the ratio 3:2.

How much sugar is needed for 12 cups of flour?

Question 3: Sharing

Share $84 in the ratio 3:4.

Question 4: Three-Term Ratio

Share 72 counters in the ratio 1:3:5.

Question 5: Unit Price

Which has the lower price per kilogram?

• 3 kg for $12.60.
• 5 kg for $20.00.

Question 6: Discount

A bag costs $120. It has a 15% discount.

Find the sale price before any applicable tax.

Question 7: Percentage Change

A plant grows from 20 cm to 26 cm.

Find the percentage increase in height.

Question 8: Below 1%

Find 0.25% of 800.

Question 9: Above 100%

Find 125% of 64.

Question 10: Explain the Mistake

A learner says:

“The ratio of red to blue counters is 2:3, so two-thirds of all the counters are red.”

Explain why this is incorrect.

Answers and Working

QuestionAnswer1Divide both terms by 6: 3:52Scale factor = 12 ÷ 3 = 4. Sugar = 2 × 4 = 8 cups3Seven parts; $84 ÷ 7 = $12 per part. Shares: $36 and $484Nine parts; 72 ÷ 9 = 8 per part. Shares: 8, 24 and 405$12.60 ÷ 3 = $4.20/kg; $20 ÷ 5 = $4.00/kg. The 5 kg option6Discount = $18. Sale price = $1027Increase = 6 cm. 6 ÷ 20 × 100 = 30%80.0025 × 800 = 291.25 × 64 = 8010There are five parts altogether. Red counters represent 2/5, or 40%, of the total.

How Parents Can Help at Home

Use manageable everyday comparisons.

Ask your child to:

• Adjust a recipe for a different number of servings.
• Compare prices using the same unit.
• Calculate a discount and the final price.
• Explain which amount represents the whole.
• Estimate an answer before calculating.

Ask “Why does that method work?” as well as “What is the answer?”

If your child struggles, return to a simple example, a ratio table or a drawing before increasing the difficulty.

Grade 8 Maths Support With Glareminds

Glareminds provides one-to-one online Maths tutoring, including support for learners following the British Columbia curriculum.

Lessons can focus on proportional reasoning, fractions, percentages, problem-solving and explaining methods clearly.

Share your child’s current schoolwork and teacher feedback when making an enquiry.

A free 30–40-minute consultation and diagnostic session provides an opportunity to discuss learning priorities and a suitable support plan.

Frequently Asked Questions

What is proportional reasoning?

It involves understanding multiplicative relationships between quantities—for example, scaling every ingredient in a recipe by the same factor.

Is a ratio the same as a fraction?

A ratio compares quantities. It can be written in fraction form, but you must identify what is being compared. A red-to-blue ratio of 2:3 gives a red-to-total fraction of 2/5.

Can a percentage exceed 100%?

Yes. For example, 150% of an amount is one and a half times that amount.

Does a bigger package always offer better value?

No. Compare unit prices first, then consider whether the quantity suits your needs.

Build Understanding Through Everyday Maths

Help your child identify the quantities, choose a reference amount and explain the relationship before calculating.

To discuss personalised BC Grade 8 Maths support, book a free consultation with Glareminds.

Call or WhatsApp: +2347039472179

Website: https://glareminds.com/