Lesson Guide
Explanation
Mass runs grams, kilograms, tonnes, with a thousand between each step — the same ladder as millilitres and litres. Mixed units are the trap: two tonnes four hundred kilograms is two thousand four hundred kilograms, and a truck carrying one thousand eight hundred kilograms of cargo then weighs four thousand two hundred, which is eight hundred under a five-tonne bridge limit. Write everything in one unit before adding or comparing, and keep a few sizes in mind: a bag of sugar is a kilogram, a small car about a tonne.
Your Turn
Write 1 kg 250 g in grams and 3 500 g in kilograms. Check: 1 250 g; 3.5 kg.
Watch Out
2 t 400 kg is 2 400 kg. The 400 is kilograms, not a decimal of a tonne to be read as 2.4 kg.
Explanation
A balance that sits level says the two sides have the same mass. Three apples against a three-hundred-gram weight means each apple is a hundred grams. If three apples balance a pear and a hundred-gram weight, and the pear is two hundred, then the three apples are three hundred again. Taking the same thing off both pans keeps it level, which is exactly the both-sides rule from the number-sentence chapter, with fruit instead of boxes.
Your Turn
4 equal blocks balance 600 g. One block? Check: 150 g.
Watch Out
Read what is on EACH pan. "A pear and a 100 g weight" is 300 g altogether if the pear is 200.
Explanation
Three boxes weighed two at a time: A and B twenty-eight, B and C thirty-two, A and C thirty-eight. Add the three weighings, ninety-eight, and notice that every box was on the scale twice, so the three together weigh half of that, forty-nine. When the question only wants the total, that is the whole answer in one line, and it is the way the test disguises find the total. Add and halve.
Your Turn
A + B = 20, B + C = 26, A + C = 30. Total of the three? Check: 76 ÷ 2 = 38.
Watch Out
Halve the SUM of the weighings, not each weighing. 98 ÷ 2 = 49; 14 + 16 + 19 is a different, wrong 49 — by coincidence here, not in general.
Explanation
Once the total is known, each box is the total minus the pair it was not in. A is forty-nine minus the B-and-C weighing, seventeen; B is forty-nine minus thirty-eight, eleven; C is forty-nine minus twenty-eight, twenty-one. Check every pair, and then C is the heaviest and B the lightest. Comparing two weighings works as well — A and C is six more than B and C, so A is six more than B — but the subtraction from the total is quicker, and the three pair checks at the end catch any slip.
Your Turn
A + B = 20, B + C = 26, A + C = 30 (total 38). Find B. Check: 38 − 30 = 8.
Watch Out
Subtract the pair WITHOUT the box. A = 49 − (B + C). Subtracting a pair that contains A gives a different box.
Explanation
In a story, convert to one unit, do the arithmetic, then answer in the unit the question names. A truck of two tonnes four hundred with eighteen hundred kilograms of cargo is four thousand two hundred kilograms, eight hundred under a five-tonne limit. Eight bags of three hundred and fifty grams and a two-kilogram bag are four thousand eight hundred grams, which is four point eight kilograms if kilograms are asked for. Quiz and exercises now.
Your Turn
8 bags of 350 g and one 2 kg bag. Total in kg? Check: 2 800 + 2 000 = 4 800 g = 4.8 kg.
Watch Out
"In kg" means the decimal, 4.8. Writing 4 800 with kg after it is wrong by a thousand.
📌 Key Points — this lesson in a nutshell
- 1 kg = 1 000 g, 1 t = 1 000 kg. Convert to the small unit before adding or comparing: 2 kg 400 g is 2 400 g.
- A balanced scale says the two sides are equal. Take the same thing off both sides and it stays balanced.
- Three things weighed in pairs: add the three weighings and halve — every item was weighed twice.
- Then each item is the total minus the pair it was not in.
Step 1: Introduction
Step 1 of 5
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