Operations & Word Problems

Depth · one concept from first principles · step 2 of 4

Find the unit amount first

An iron bar of even thickness weighs 1451\frac{4}{5} kg for 34\frac{3}{4} m. We need the weight of 2 m of the bar, in kilograms.
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
2STEP 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
3STEP 3

Scale up to two meters

Twice the length weighs twice as much.

12/5 × 2 = 24/5
Answer
4454\frac{4}{5} 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
Where next?
Level upsuggested
Unit distance is total distance divided by timeSet the whole job to 1 and write a day's work as a fraction
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3 reasoning problems grow out of this type — the bridge toward competition →

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▶ Practice — 12 problems

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