Interconcept — Class 5 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 5 Mathematics. Linking the ideas of the year together: fractions and decimals, measurement and money, and time and distance.
1. Why a chapter about connections
Every unit so far taught one idea at a time. Real problems are not so tidy. Buying cloth involves measurement and money. Planning a journey involves time and distance.
This chapter is about carrying one idea into another.
2. Fractions and decimals are the same thing
A fraction and a decimal are two ways of writing the same amount.
To turn a fraction into a decimal, divide the numerator by the denominator.
| Fraction | Division | Decimal |
|---|---|---|
| 1/2 | 1 ÷ 2 | 0.5 |
| 1/4 | 1 ÷ 4 | 0.25 |
| 3/4 | 3 ÷ 4 | 0.75 |
| 1/5 | 1 ÷ 5 | 0.2 |
| 1/10 | 1 ÷ 10 | 0.1 |
| 1/100 | 1 ÷ 100 | 0.01 |
Going the other way, read the decimal aloud and write what you hear. 0.5 is "five tenths", which is 5/10 = 1/2. 0.25 is "twenty five hundredths", which is 25/100 = 1/4.
The place after the decimal point is tenths, and the next is hundredths.
3. Decimals in money and measurement
You have been using decimals all year without calling them that.
Money. ₹45.75 is 45 rupees and 75 paise. Because 100 paise make a rupee, 75 paise is 75/100 of a rupee, which is 0.75. So ₹45.75 means 45 and three-quarter rupees.
Length. 1.5 m is 1 metre and 5 tenths of a metre. A tenth of 100 cm is 10 cm, so 5 tenths is 50 cm. That is why 1.5 m = 1 m 50 cm, and never 1 m 5 cm.
Weight. 2.25 kg is 2 kg and 25 hundredths of a kilogram, which is 250 g.
The same fraction keeps reappearing: half is 0.5, which is 50 paise, 50 cm, or 500 g depending on what you are measuring.
4. Linking measurement and money
Problems often give a rate — a price for one unit — and ask for the cost of several.
Total cost = rate × quantity
Cloth costs ₹120 per metre. What do 3 m 50 cm cost?
First make the quantity a single number: 3 m 50 cm = 3.5 m.
Cost = 120 × 3.5 = ₹420
Turning it round, if 4 m of ribbon cost ₹100, then one metre costs 100 ÷ 4 = ₹25. That is the rate.
5. Linking time and distance
Distance = speed × time, and speed = distance ÷ time
A bus covers 120 km in 3 hours. Its speed is 120 ÷ 3 = 40 km per hour.
Travelling at that speed for 5 hours, it would cover 40 × 5 = 200 km.
Keep the units consistent. If the speed is in kilometres per hour, the time must be in hours. Half an hour is 0.5 hours, not 30.
6. Multi-step problems
The real skill is deciding the order of the steps. Write down what you know, work out what is missing, and only then answer the question asked.
A worked problem. Kavitha buys 2 kg 500 g of rice at ₹60 per kg and 1 kg 250 g of dal at ₹80 per kg. She pays with a ₹500 note. What change does she get?
- Rice: 2 kg 500 g = 2.5 kg, so 60 × 2.5 = ₹150
- Dal: 1 kg 250 g = 1.25 kg, so 80 × 1.25 = ₹100
- Total = 150 + 100 = ₹250
- Change = 500 − 250 = ₹250
Four steps, each one simple. The difficulty was never the arithmetic; it was seeing the order.
7. Worked examples
Example 1. Write 3/4 as a decimal.
Solution: 3 ÷ 4 = 0.75.
Example 2. Write 0.2 as a fraction in its simplest form.
Solution: 0.2 is two tenths, 2/10, which simplifies to 1/5.
Example 3. How many centimetres are there in 2.5 m?
Solution: 2.5 × 100 = 250 cm, that is 2 m 50 cm.
Example 4. Sugar costs ₹45 per kg. What do 2.5 kg cost?
Solution: 45 × 2.5 = ₹112.50.
Example 5. A train covers 240 km in 4 hours. Find its speed.
Solution: 240 ÷ 4 = 60 km per hour.
Example 6. A car travels at 50 km per hour for 2 hours 30 minutes. How far does it go?
Solution: 2 hours 30 minutes is 2.5 hours, so 50 × 2.5 = 125 km.
Example 7. Ribbon costs ₹15 per metre. Find the cost of 4 m 20 cm.
Solution: 4 m 20 cm = 4.2 m, so 15 × 4.2 = ₹63.
8. Practice
- Write 1/4 as a decimal.
- Write 0.5 as a fraction in its simplest form.
- How many grams are there in 1.75 kg?
- Write 1.5 m in metres and centimetres.
- Oil costs ₹180 per litre. What do 2.5 litres cost?
- A bus covers 150 km in 3 hours. Find its speed.
- A cyclist rides at 12 km per hour for 1 hour 30 minutes. How far does she go?
- Rice costs ₹55 per kg. Find the cost of 3 kg 200 g, then the change from ₹200.
9. Answers
- 1 ÷ 4 = 0.25.
- Five tenths, 5/10, which simplifies to 1/2.
- 1.75 × 1000 = 1750 g.
- 1 m 50 cm, because five tenths of a metre is 50 cm.
- 180 × 2.5 = ₹450.
- 150 ÷ 3 = 50 km per hour.
- 1 hour 30 minutes is 1.5 hours, so 12 × 1.5 = 18 km.
- 3 kg 200 g = 3.2 kg, so 55 × 3.2 = ₹176. Change = 200 − 176 = ₹24.
10. Summary
- A fraction becomes a decimal when you divide the numerator by the denominator.
- 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/10 = 0.1.
- The first place after the point is tenths and the second is hundredths.
- Half is 0.5, whether that means 50 paise, 50 cm or 500 g.
- 1.5 m is 1 m 50 cm, never 1 m 5 cm.
- Total cost = rate × quantity; rate = total cost ÷ quantity.
- Speed = distance ÷ time, and distance = speed × time.
- Keep units consistent: half an hour is 0.5 hours.
- In a multi-step problem, list what you know, then decide the order before calculating.
