“Make the Same” – The Secret to Solving Primary Math Questions Efficiently

When solving Math problems involving fractions, ratios, and unit conversions, there’s one simple trick that can help:

🔑 “Make the Same.”

By aligning denominators, numerators, or total values, we can simplify calculations and avoid mistakes. Let’s go through some examples to see this method in action.

Example 1: Boys and Girls in a School

The ratio of boys to girls in a school is 3:4.
After 3/8 of the girls left, there were 48 more boys than girls.
How many boys were there?

Step 1: Make the Denominators the Same

• The given ratio is 3:4.
• The fraction 3/8 tells us that the total number of girls should be divisible by 8.
• But in the ratio, the number of girls is 4 units, not 8.

To “make the same,” we adjust the ratio so that the number of girls is expressed in eighths.
Since 4 × 2 = 8, we multiply both parts of the ratio by 2 to maintain the same relationship:

• Boys: 3 × 2 = 6 units
• Girls: 4 × 2 = 8 units

Now, since 3/8 of the girls left, that means:

• 3/8 × 8u = 3u girls left.
• Remaining girls: 8u – 3u = 5u.

Since the boys outnumbered the remaining girls by 48, we set up the equation:

$$6u-5u=48$$ $$1u=48$$ $$6u=6\times 48=288$$

🔹 There were 288 boys in the school.

Example 2: Decorating Tables and Chairs with Ribbons

7m of ribbon is needed for every 3 tables.
3m of ribbon is needed for every 5 chairs.
Students from Class 6A decorated 30 tables and 30 chairs.
How many more metres of ribbon did they use for tables than for chairs?

Step 1: Make the Number of Tables and Chairs the Same

• Tables are grouped in 3s, chairs in 5s.
• LCM of 3 and 5 is 15.

Now, for 30 tables and 30 chairs (twice 15 tables and chairs):

• Tables: 35m × 2 = 70m
• Chairs: 9m × 2 = 18m

Difference in ribbon used = 70m – 18m = 52m

🔹 They used 52m more ribbon for tables than chairs.

Example 3: Shading a Fraction of a Figure

The figure is made up of 16 similar triangles.
How many more triangles must be shaded so that 3/4 of the figure is shaded?

Step 1: Make the Denominators the Same

We need 3/4 of the total figure to be shaded.
The figure consists of 16 triangles, but the denominator is 4.

To make them the same, convert 3/4 to a fraction out of 16:

$$3/4=12/16$$

This means 12 triangles need to be shaded.

Step 2: Find How Many More Need to be Shaded

From the image, we count that 6 triangles are already shaded.

So, the number of additional shaded triangles required is:

$$12-6=6$$

🔹 6 more triangles must be shaded.

Why “Make the Same” Works Every Time

• Fractions become whole numbers → Easier to compare.
• Ratios align with the problem → Prevents miscalculations.
• Units match up correctly → No confusion in word problems.

Whenever you’re stuck on a Math question, ask yourself:
❓ What do I need to make the same?

This strategy makes problems easier and faster to solve. 🚀

Would you like more worked examples? Let me know in the comments! 😊