Learn It
Comparing across two measurement systems
Kilometers and miles both measure distance, but they come from different measurement systems, so the numbers cannot be compared directly. A conversion factor links the two systems, and a ratio table scales it up to the amount you need.
Picture itSee what the math looks like before you read about it
Watch me solve itI do — read one step at a time
- Evelyn sees a Canadian highway sign reading 100 kilometers per hour and wonders whether that is faster or slower than 100 miles per hour.
- Kilometers are metric and miles are customary, so 100 and 100 cannot be compared as they stand. Both measure distance, so a links them: 1 kilometer ≈ 0.6 mile, or the ratio 1 : 0.6.
- I build a from that unit ratio. Kilometers 1, 10, 100 pair with miles 0.6, 6, 60 — each column multiplies both numbers by the same factor.
- So 100 kilometers ≈ 60 miles, which means 100 kilometers per hour ≈ 60 miles per hour.
- Now the comparison is fair: 100 miles per hour is faster, because in one hour you would travel 100 miles instead of only about 60.
Watch out — mistakes students make here
- Equal numbers with different units are not equal amounts — that is exactly why you convert.
- 4–10 kg would be about 9–22 pounds, lighter than this dog.
- 25–40 kg would be about 55–88 pounds, far heavier than this dog.
Try it with meWe do — you answer first, then check
Same steps, new numbers.
- Terrance needs flea medicine for a dog weighing 31 pounds, but the packages are labeled in kilograms.
- The is 1 pound ≈ 0.45 kilogram, so the ratio is 1 : 0.45.
- Scale it with a : 10 lb ≈ 4.5 kg, 20 lb ≈ 9 kg, 30 lb ≈ 13.5 kg, 40 lb ≈ 18 kg.
- 31 pounds is just past 30, so the dog is a little more than 13.5 kilograms. That falls inside the package for dogs between 10 and 25 kilograms.
On your ownYou do — solve this one by yourself
Before you start, remember:
- A supplier lists a sack of flour as 5 kilograms. The recipe is written in pounds.
- Use the 1 kilogram ≈ 2.2 pounds and write it as a ratio.
- Scale it up to 5 kilograms with a .
- About how many pounds is the sack? Write your answer with ≈ and say why the answer is not exact.
Solve: 1 pound ≈ 0.45 kilogram. Complete the , then use it to place a 31-pound dog.
| Pounds | Kilograms |
|---|---|
| 1 | 0.45 |
| 10 | |
| 30 | |
| 40 |
Stuck? Open one hint at a time.
Hint 1
Row 1 is the conversion factor, 1 : 0.45.
Hint 2
For 10 pounds multiply both parts by 10; for 30 pounds, by 30.
Hint 3
0.45 × 30 = ?
Check my answer
- 10 → Kilograms: 4.5
- 30 → Kilograms: 13.5
- 40 → Kilograms: 18
Turn & TalkSay it out loud with a partner
A 5-kilometer race and a 5-mile race have the same number — 5. Before converting anything: which race is longer, and how do you know?
Try starting with:
- The ___ race is longer because one ___ is bigger than one ___.La carrera de ___ es más larga porque un(a) ___ es más grande que un(a) ___.
- The numbers match, but the units ___.Los números coinciden, pero las unidades ___.