Chapter 4: Decimals, Percentages, Ratio, and Proportion
Decimals, Percentages, Ratio and Proportion
Connect decimals, percentages and ratios so the same relationship can be written in different useful ways.
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Step-by-step teaching, practice and checkpoint.
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Workbook pages
Fun Maths Book 3 pages 34-48
Simplify ratios, calculate decimals and percentages, and connect fractions, decimals and percentages.
Think first
Good mathematicians decide what the question is asking before they calculate.
- 1Is the number showing parts of one whole, parts out of 100, or a comparison?
- 2Can we rewrite the values in a friendlier form first?
- 3Are all ratio parts being scaled by the same amount?
- 4Does the answer fit the size of the original amount?
Visual teaching
See the method
A hundred square shades a percentage, then stretches into a ratio bar where each part scales up and down together.
1 : 2 : 3
Worked examples
Write 0.75 as a percentage.
Step 1: First, what does the decimal mean?
0.75 means 75 hundredths, or 75 out of 100.
Why: A percentage is a number out of 100.
Step 2: Now write the hundredths as a percent.
75 out of 100 is 75%.
Why: The percent sign means out of 100.
Be careful: Do not write 7.5%. 0.75 is close to one whole, so it should be close to 100%.
Step 3: Check whether the size makes sense.
0.75 is three quarters of one whole, and 75% is three quarters of 100%.
Why: The decimal and percentage describe the same value.
Common mistake: Moving the decimal point the wrong number of places.
Simplify 1.5 : 3 : 4.5.
Step 1: What makes this ratio awkward?
Two parts are decimals, so first make all parts whole numbers.
Why: Ratios are easier to simplify when every part is a whole number.
Step 2: How can we remove the decimals fairly?
Multiply every part by 2: 1.5 : 3 : 4.5 becomes 3 : 6 : 9.
Why: Every ratio part must be scaled by the same amount.
Be careful: Changing only one part changes the comparison.
Step 3: Now what common factor can we divide by?
3, 6 and 9 can all be divided by 3.
Why: Dividing every part by the same number keeps the ratio equivalent.
Step 4: Write the simplified ratio.
3 : 6 : 9 becomes 1 : 2 : 3.
Why: The parts are now as small as possible while keeping the same comparison.
Common mistake: Dividing only the largest number and leaving the other parts unchanged.
Find 35% of 240.
Step 1: What are we trying to find?
We need 35 out of every 100 parts of 240.
Why: Percentages describe parts out of 100.
Step 2: Is there a friendlier way than multiplying by 0.35 straight away?
Break 35% into 30% + 5%.
Why: Using friendly percentages reduces calculation load.
Step 3: Find the friendly parts.
10% of 240 is 24, so 30% is 72. 5% is half of 10%, so 5% is 12.
Why: 10% and 5% are useful building blocks.
Step 4: Combine the parts.
72 + 12 = 84.
Why: 30% plus 5% gives the full 35%.
Common mistake: Finding 30% correctly but forgetting to add the extra 5%.
Guided practice
In a class, 18 students walk and 12 students cycle. Simplify the ratio walk : cycle.
Independent practice
Your turn
Write 0.75 as a percentage.
Simplify 6 : 9 : 15.
Find 20% of 350.
Mini checkpoint
Check your thinking
Find 12.5% of 160.
Fruit : yoghurt = 2 : 5. If yoghurt is 250 g, how much fruit is needed?
Which statement is true?
Key idea
Decimals, percentages and ratios are different ways to describe size or comparison. Convert with meaning, scale every ratio part equally, and use friendly percentages to make calculations easier to check.
Parent signal
Check whether the child keeps ratio parts in the correct order; many errors are order errors, not arithmetic errors.