Mathematics Standard • Year 12 • Ratios and rates • Lesson 2

Ratios, Skill Drill

Build fluency in the three core ratio mechanics: simplest form, the ratio of two quantities given in different units, and dividing a quantity in a given ratio.

Build · Skill Drill

1. Quick recall

Answer in the space provided. 1 mark each

Q1.1 A ratio compares quantities measured in the ____________ unit.

Q1.2 To divide a quantity in the ratio a:b, the number of parts is ____________.

Q1.3 In the ratio 3:4, the first share is ____________ of the whole, as a fraction.

Stuck? Revisit lesson section 04, "A ratio is a fraction wearing different clothes".

2. Worked example, dividing a quantity

Follow each line. Every step has its reason.

Problem. Share $480 in the ratio 5:3.

Step 1, count the parts.

parts = 5 + 3 = 8

Reason: the ratio terms count equal shares of the whole.

Step 2, find one part.

one part = 480 ÷ 8 = 60

Step 3, multiply out and check.

5 × 60 = $300 and 3 × 60 = $180, and 300 + 180 = 480

Reason: the shares must add back to the original amount. This catches almost every slip.

3. Simplest form

Express each ratio in simplest form. 1 mark each

Q3.1 12:18

Q3.2 25:100

Q3.3 36:48

4. Same unit first

Convert to a common unit, then simplify. 2 marks each

Q4.1 500 g to 2 kg

Q4.2 45 minutes to 2 hours

5. Dividing a quantity

Show the parts, then one part, then the shares. 2 marks each

Q5.1 Divide 40 in the ratio 3:5.

Q5.2 Divide $96 in the ratio 1:3.

Q5.3 Divide 150 kg in the ratio 2:3.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers, Do not peek before attempting

Q1.1, Same unit

A ratio compares quantities in the same unit, so the units cancel and the comparison is a pure number.

Q1.2, Number of parts

a + b. Add the terms of the ratio.

Q1.3, Ratio to fraction

3/7. There are 3 + 4 = 7 parts in total.

Q3.1, Simplify 12:18

HCF is 6, so 12:18 = 2:3. Check: 2 × 6 = 12 and 3 × 6 = 18.

Q3.2, Simplify 25:100

HCF is 25, so 25:100 = 1:4.

Q3.3, Simplify 36:48

HCF is 12, so 36:48 = 3:4.

Q4.1, 500 g to 2 kg

2 kg = 2000 g, so 500:2000 = 1:4. Convert before simplifying, never after.

Q4.2, 45 min to 2 h

2 h = 120 min, so 45:120 = 3:8 (HCF 15).

Q5.1, Divide 40 as 3:5

parts = 8, one part = 5, shares 15 and 25. Check: 15 + 25 = 40.

Q5.2, Divide $96 as 1:3

parts = 4, one part = $24, shares $24 and $72. Check: 24 + 72 = 96.

Q5.3, Divide 150 kg as 2:3

parts = 5, one part = 30 kg, shares 60 kg and 90 kg. Check: 60 + 90 = 150.