GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1

CONVERT — Fractions, decimals and percentages

Think first. Use AI purposefully. Verify always.

DISCOVER

Begin with a prediction.

Can 0.25, one quarter and 25% describe the same amount? Sketch evidence.

Sketch or write an independent attempt before reading on. Test your idea using the model.

Understand

Fractions, decimals and percentages are different representations of a number. A recurring decimal may need an approximation; a fraction can preserve the exact value.

Key Ideas

24 % = \frac{24}{100} = \frac{6}{25} = 0.24

0.5 means 50%, not 0.5%. One third is exactly $\frac{100}{3}$ %, approximately 33.33%.

Visualise

One value, three representations

Predict first. Change the controls, then compare your reasoning.

Numerator: 3Denominator: 4

1234

Method

Fraction to decimal: divide numerator by denominator. Decimal to percentage: multiply by 100 and attach %. Percentage to decimal: divide by 100.

Worked Example

Given

A share of 24%.

To Find

The equivalent simplified fraction and decimal

Reasoning

Percent means divided by 100.

Solution

24% = $\frac{24}{100}$ .
Divide numerator and denominator by 4: $\frac{6}{25}$ .
24 ÷ 100 = 0.24.

Result

24% = $\frac{6}{25}$ = 0.24.

AIMS Method

A — Attempt independently
Estimate and predict first.
I — Investigate the idea
Identify the whole and the percentage base.
M — Make connections
Connect fractions, decimals, bars and multipliers.
S — Scrutinise your reasoning
Check units, bases and the reasonableness of the result.

Think first. Use AI purposefully. Verify always.

Focused Practice

Convert $\frac{9}{20}$ to a percentage and a decimal. Check using an equivalent fraction.

Your reasoning

Continue with CONVERT →

Check & Feedback

Name the whole, explain the method and give one check that would catch a wrong percentage base.

Explain your conclusion

Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 8