Problem
Find the unit amount first
A bar of even thickness has a known weight for a known length. We need the weight of a different length.
Number systemRatios
Your answer
How to solve
Strategy Analyze the Units — Going straight from 3/4 m to 2 m needs an awkward multiplier. Passing through 1 m costs one extra step and makes both steps easy -- and the weight of one meter is worth knowing on its own.
1STEP 1
Write both numbers as improper fractions
A mixed number is hard to divide with, so turn it into a single fraction first.
1 4/5 = 9/5
9/5 kg for 3/4 m.
6.NS.A.1Analyze The Units2STEP 2
Find the weight of one meter
Divide the weight by the length, and dividing by 3/4 is multiplying by 4/3.
9/5 × 4/3 = 12/5
One meter weighs 12/5 kg.
6.RP.A.2Work BackwardsOne metre of the bar weighs .
Why?
The bar has the same thickness all along, so every metre of it weighs the same and the whole weight is a count of equal metres.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Finding one metre's weight from three quarters of a metre's is undoing that multiplication, which is what dividing by does.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
3STEP 3
Scale up to two meters
Twice the length weighs twice as much.
12/5 × 2 = 24/5
Two meters weigh 4 4/5 kg.
6.RP.A.2Draw A DiagramAnswer
kg
Sanity-check the size: 2 m is a bit more than two and a half times 3/4 m, and 4 4/5 is a bit more than two and a half times 1 4/5.
Takeaway
Find the amount for one unit first -- then any other amount is one multiplication away.
- Write both numbers as improper fractions
- Find the weight of one meter
- Scale up to two meters