Did you know? A ratio can look difficult simply because it contains fractions or decimals. Yet 0.6 : 1.5 describes exactly the same relationship as 2 : 5. Learning to clear the decimal places or denominators can turn a confusing question into ordinary whole-number parts.
Quick answer for Bukit Timah parents: Secondary 4 G1 Mathematics includes ratios involving fractions and decimals, equivalent ratios, simplifying ratios and sharing a quantity in a given ratio. Before doing any calculation, make sure both quantities use compatible units and both parts of the ratio are multiplied by the same positive factor.
What is a ratio actually comparing?
A ratio describes a relationship between quantities in a particular order. If the ratio of red to blue counters is 2 : 5, there are two red parts for every five blue parts. It does not mean two red counters out of five total. A set following this ratio has seven parts altogether, so the red fraction of the combined set is 2/7.
A ratio can be scaled without changing the relationship: 2 : 5, 4 : 10 and 6 : 15 are equivalent. Multiplying or dividing both terms by the same non-zero positive number preserves the relationship.
Example 1: simplify decimal ratios
Simplify 0.6 : 1.5. Multiply both terms by 10 to remove the decimal point: 6 : 15. Divide both by 3: 2 : 5. Never multiply just one term by ten; doing so changes the ratio.
Try 1.25 : 0.75. Multiply both parts by 100: 125 : 75. Divide both by 25: 5 : 3. A student who swaps the terms to 3 : 5 has described the inverse ordering, not the original comparison.
Example 2: a ratio containing fractions
Simplify 1/2 : 3/4. Multiply both terms by the lowest common denominator, 4: (1/2 × 4) : (3/4 × 4) = 2 : 3. The simplified result is 2 : 3.
Now try 3/4 : 1/2. Multiplying both by 4 gives 3 : 2. Order matters: the two expressions compare the same fractional quantities but in opposite directions.
Example 3: fractions and decimals together
Simplify 0.75 : 1/2. Write 0.75 as 3/4, giving 3/4 : 1/2. Multiply both parts by 4 to obtain 3 : 2. You could instead convert 1/2 to 0.5, then simplify 0.75 : 0.5 to 75 : 50 = 3 : 2.
Both methods are valid. A tutor should help the learner choose the representation they can handle accurately, not insist that every ratio be solved with the same unnecessary steps.
Example 4: units must agree before simplifying
Find the ratio of 1.2 m to 80 cm. First convert 1.2 m into 120 cm. The ratio is 120 cm : 80 cm, which simplifies to 3 : 2.
Using 1.2 : 80 directly ignores that metres and centimetres are different units. When quantities are the same kind, convert them to the same unit before removing their units in the final numerical ratio.
Example 5: sharing money using a decimal ratio
A fictional group splits $96 between two materials in the ratio 0.75 : 1.25. Multiplying both terms by 100 gives 75 : 125, which simplifies to 3 : 5.
There are 3 + 5 = 8 parts. Each part is $96 ÷ 8 = $12. The first share is 3 × $12 = $36, and the second is 5 × $12 = $60. Check that $36 + $60 = $96.
If a pupil divides $96 by 3 and by 5 separately, the resulting values are not a valid sharing of one total. The parts share the same whole, which is why we add the ratio numbers before dividing.
A five-step routine for G1 ratios
- Label the order: which quantity is the first term and which is second?
- Match units: turn centimetres and metres into a single unit, for example.
- Clear decimals or denominators: scale both ratio terms equally.
- Simplify: divide both terms by a common factor to obtain small whole numbers.
- Answer the right question: distinguish comparing, sharing and finding a missing corresponding amount.
A quick reverse-ratio problem
Suppose A : B = 2 : 5 and A = 18. Since two parts represent 18, one part represents 9. B has five parts, so B = 45. Ask the student why multiplying 18 by 5/2 works here: it converts the known two-part share into the corresponding five-part share.
The official G1 K110 syllabus boundary
The SEAB 2027 Mathematics syllabus K110 lists ratios involving fractions and decimals, equivalent ratios, simplifying ratios, comparing quantities and dividing a quantity in a given ratio under N2, Ratio and proportion. These Number and Algebra skills are relevant to both Mathematics papers.
The SEAB 2027 G1 school-candidate list identifies K110 and shows 4046 as the reference code for 2026 and earlier. Families preparing for an examination in 2026 should use the student’s registered syllabus, not assume the 2027 code applies.
How to check learning in a small group
Ask each student to solve 0.4 : 1.0, 1/3 : 1/2 and 1.5 m : 50 cm, then explain their methods. The answers are 2 : 5, 2 : 3 and 3 : 1. A wrong response can reveal a unit-conversion mistake, an incorrectly cleared denominator or a reversed ratio.
The unchanged eduKateSG Clementi three-pupil Mathematics reference illustrates close individual feedback at a separate Secondary 1 level. Parents should verify current Secondary 4 G1 availability and class details directly.
Frequently asked questions
Can a ratio contain decimals? Yes, although simplifying it to equivalent whole-number terms is often more convenient. Is 2 : 5 the same as 2/5 of the total? No. In a two-part sharing ratio, the first share is 2/7 of the total. Does the order matter? Yes.
Continue the ratio pathway
Read ratio, map scales and proportion, percentages and everyday bills, and the K110 paper plan.