Numbers in daily and work situations
Numbers hide in many places: prices, discounts, bus times, recipes, phone data, medicine doses and temperatures. To use them well you need a few tools.
- Unit price: price ÷ amount. It lets you compare a big pack and a small pack fairly.
- Percent: "per hundred". 25% off ₹800 means you save 25 out of every 100, so you save ₹200.
- Speed: distance ÷ time. 150 km in 2.5 h is 60 km/h.
- Estimate and round: a quick rough answer (about ₹600) tells you if your exact answer is sensible.
Always write the unit with the number: ₹, g, km, h. A number without a unit can mislead.
Making decisions with maths
Maths does not decide for you, it shows the facts. A good method has five small steps:
- Write down what you know.
- Put everything in the same unit.
- Calculate.
- Compare and choose.
- Check: does the answer make sense? Do you really need that much?
Example: the bigger pack is cheaper per 100 g, but if you only need a little and the rest will spoil, the small pack can still be the better choice. Maths gives the number; you add the common sense.
Messages in graphs
A graph is a picture of numbers. A picture can be honest or tricky. Read it in this order:
- Read the title and what each axis shows.
- Look at where the axis starts. If a bar chart does not start at 0, small gaps look big.
- Look at the scale: are the steps even?
- Read the actual numbers, then say the message in one sentence.
A line that rises steeply may only be rising from 100 to 103. Pictures of different sizes for the same value also fool the eye, because we notice area, not height.
Maths in the media
News, ads and social media love big numbers. Ask these questions.
- Out of how many? "Up 100%" can mean from 1 case to 2 cases.
- Percent or real number? Both are needed. 50% of 10 people is 5; 50% of 10 million is 5 million.
- Who was asked? A survey of 10 friends does not speak for a whole city.
- Which average? One very rich person pulls the mean up. The middle value (median) can tell a fairer story.
- Percent up then down: +20% then −20% does not bring you back. ₹500 → ₹600 → ₹480.
Maths in professions
Every job uses a few maths tools again and again.
- Nurse: dose = amount for each kg × body weight (ratio).
- Builder: area and volume to order tiles and cement.
- Farmer: seed and water per hectare, price per quintal, profit and loss.
- Shopkeeper: percent profit, discount, tax (GST), stock counting.
- Programmer or game maker: coordinates, angles, probability.
- Cricket analyst: average, strike rate, graphs.
Try it: the three-price test
Next time you go to a shop (or look at an online shop), pick one product sold in two pack sizes. Write down the weight and price of each. Work out the price per 100 g (or per litre). First guess which is cheaper, then check. Were you right? Slide the B sliders in the 3D above to make a pack where the small one wins.
Key formulas and definitions
- Unit price = price ÷ amount (then × 100 for "per 100 g")
- Percent of a number = (percent ÷ 100) × number
- Price after a discount of d% = price × (100 − d) ÷ 100
- Speed = distance ÷ time
- Percent change = (new − old) ÷ old × 100
- Key term: axis = the number line of a graph; check where it starts
Worked examples
1. Pack A: 500 g for ₹60. Pack B: 800 g for ₹88. Which is the better buy?
A: 60 ÷ 500 × 100 = ₹12.0 per 100 g. B: 88 ÷ 800 × 100 = ₹11.0 per 100 g. B is cheaper by ₹1 per 100 g.
2. Shop X sells a ₹800 shirt at 25% off. Shop Y sells it at ₹700 with 10% off. Which is cheaper?
X: 800 × 0.75 = ₹600. Y: 700 × 0.90 = ₹630. Shop X is cheaper by ₹30.
3. Plan 1: 1.5 GB a day for 28 days costs ₹299. Plan 2: 2 GB a day for 56 days costs ₹579. Which is cheaper per GB?
Plan 1 gives 1.5 × 28 = 42 GB, so 299 ÷ 42 ≈ ₹7.12 per GB. Plan 2 gives 2 × 56 = 112 GB, so 579 ÷ 112 ≈ ₹5.17 per GB. Plan 2 is cheaper per GB.
4. A bar chart starts its axis at 45. The bars are 50 and 55. The second bar looks twice as tall. What is the real change?
Heights on screen: 50 − 45 = 5 and 55 − 45 = 10, so it looks double. Real change: (55 − 50) ÷ 50 × 100 = 10%. The cut axis made 10% look like 100%.
5. A headline says "Accidents up 100%". Last year there was 1 accident at a junction, this year 2. Is the headline wrong?
The percent is correct: (2 − 1) ÷ 1 × 100 = 100%. But it hides the real number: just one more accident. Always ask "out of how many?".
6. A bus travels 150 km in 2.5 hours. At the same speed, how long will 210 km take?
Speed = 150 ÷ 2.5 = 60 km/h. Time = 210 ÷ 60 = 3.5 hours (3 h 30 min).
Common mistakes
- Comparing only the total prices of packs of different sizes. Compare the price for the same amount.
- Reading a graph without checking where the axis starts.
- Thinking +20% then −20% gives back the start. The second 20% is taken from a bigger number.
- Believing a percent without asking "out of how many?". Small totals give big-sounding percents.