Secondary 1 G1 Mathematics Tutor Bukit Timah. Learn to simplify G1 Maths ratios containing fractions and decimals while keeping both sides in the same proportion. This quick-read guide gives parents and students a clear worked example, one common mistake to watch for, and a short home check.
Start with the idea. Then see if your child can explain the method without looking at an answer key. A useful lesson is one that leaves the learner more independent than before.
Did you know? A ratio may compare fractions rather than whole numbers
Did you know? The ratio 1/2 : 3/4 can be written as 2 : 3 without changing the relationship. This is an important Secondary 1 G1 Mathematics idea: ratios compare quantities, and both parts can be scaled together.
The symbols look more complicated when they contain fractions or decimals. But the core idea is familiar. If one quantity is half a unit and another is three quarters of a unit, doubling or multiplying the two quantities by the same number preserves the comparison.
Why scaling both parts works
Consider 2 : 3. If both quantities double, the ratio becomes 4 : 6. If both triple, it becomes 6 : 9. In every case, the first quantity is two-thirds of the second. That is what an equivalent ratio means.
Now compare 2 : 3 with 2 : 6. Only the second part changed; the original relationship was not preserved. A tutor can use that small counterexample to help students stop altering one side of a ratio while leaving the other untouched.
Simplify a ratio containing fractions
For 1/2 : 3/4, choose a number that removes the denominators. Multiplying both parts by 4 gives 2 : 3. The ratio is now in whole-number form and already in its simplest form.
Take a different example: 2/3 : 1/6. Multiplying both parts by 6 gives 4 : 1. You can check the relationship another way: two thirds divided by one sixth is 4, so the first amount is four times the second.
The essential step is writing the multiplier beside both entries. When children skip that explanation, they may accidentally multiply the first fraction’s numerator but forget to scale the other quantity.
Simplify a decimal ratio
Consider 0.6 : 1.2. Multiply both entries by 10 to make 6 : 12. Divide both by 6 to obtain 1 : 2. Alternatively, divide both original quantities by 0.6 and reach the same result.
A quick visual check: 0.6 is exactly half of 1.2, so 1 : 2 makes sense. A pupil who writes 6 : 2 has removed the decimal points without treating both quantities fairly. The mistake is about place value as well as ratios.
Three-part ratios still follow the same rule
Imagine an invented recipe using 0.25 L of one ingredient, 0.5 L of another and 1 L of a third. The ratio is 0.25 : 0.5 : 1. Multiply every entry by 4 to get 1 : 2 : 4.
Why can’t we divide only the first two entries? Because the third quantity belongs to the same comparison. Each part must be transformed using the same scale factor. If the relationship has three or four parts, all of them are included.
Using a ratio to share a quantity
Suppose a group shares 30 counters in the ratio 2 : 3. There are 2 + 3 = 5 equal parts. Each part represents 30 ÷ 5 = 6 counters. The shares are 12 counters and 18 counters.
Now connect it to fractions: since 2 out of the five parts belong to the first group, the first group receives 2/5 of the total, or 12. Ratio and fraction are closely related, but they answer slightly different questions. The ratio compares the groups; the fraction 2/5 compares one group to the whole.
Check the work in two ways: 12 + 18 = 30 and 12 : 18 simplifies to 2 : 3. The total and the relationship must both agree.
Where small-group tutoring can help
One student may understand sharing but freeze when a ratio contains decimals. Another may multiply each entry by a different number. A third may simplify 1 : 2 correctly but choose the wrong total number of parts in a word problem.
The published eduKateSG Secondary 1 Mathematics tutorial approach near Sixth Avenue MRT uses three students per group and weekly 1.5-hour lessons. A tutor can ask each pupil to explain the scaling choice, then give a changed ratio to see if the principle has transferred.
Five-minute ratio practice
A. Simplify 0.4 : 0.8. Answer: 1 : 2. B. Simplify 1/3 : 1/6. Answer: 2 : 1. C. Divide 25 in the ratio 2 : 3. Answer: 10 and 15.
Ask your child to show the identical scale factor in both parts. For the sharing question, ask what one part represents before they calculate either share. This tells you whether the ratio is being understood or merely manipulated.
Frequently asked questions
Are fractional and decimal ratios part of Secondary 1 G1 Mathematics? Yes. The MOE G1 syllabus covers ratios involving fractions and decimals, equivalent ratios and ratios in simplest form.
Can I simplify 0.5 : 1 by deleting the decimal point? No. Both quantities must be scaled consistently. Multiplying both by 2 gives 1 : 2.
What should I check after sharing in a ratio? Check that the amounts add to the stated total and simplify back to the requested ratio.
More Secondary 1 G1 Mathematics guides
- Number Patterns: Finding the Nth Term
- Percentage Increase and Decrease Explained
- Turning Word Problems into Algebraic Expressions
- Ratios You Can Draw Before You Calculate
Read the original eduKateSG Secondary 1 Mathematics small-group tutorial guide for details of the existing teaching model. The source guide is unchanged. The published programme describes three-student tutorials near Sixth Avenue MRT, using 1.5-hour weekly lessons and focused, guided correction.
For Singapore’s official topic boundaries, refer to the Ministry of Education G1 Mathematics syllabus. G1 is a subject level under Full Subject-Based Banding and is not a permanent label for a child’s ability. Schools may arrange topics and assessments in different sequences.
For parents in Bukit Timah: bring a recent marked question when exploring tuition. Ask which first decision needs correcting and whether the weekly three-pupil Mathematics format would suit your child’s current G1 work. Enquire with eduKate Singapore about current classes and availability.