Concept 7 of 8
Compound-Unit Arithmetic: km+m, kg+g, L+mL
Today's big idea
Compound units carry at 1000, so 1200 m becomes 1 km 200 m and moves across.
Same column rule as ordinary addition, with a bigger number to carry at.
How it works
👀 What's going on?
Write 2 km 400 m above 1 km 800 m and it looks like an ordinary column sum. It very nearly is. The only thing that changes is when you carry, and that feels wrong the first few times.
💡 Here's the trick
Look at the sum above. The metres column gives 400 + 800 = 1200, which is past 1000. So 1000 of those metres turn into 1 km and move across, leaving 200 m behind. The kilometres column then reads 2 + 1 + 1 = 4. You carry at 1000 here, not at 10, and the same boundary works for kg with g and L with mL.
🪄 How to do it
- 1.Stack the amounts as in the sum above, big unit under big unit.
- 2.Do the small column first, carrying 1000 across if it overflows.
- 3.Do the big column, adding on any carry you made.
✍️ Try it
- 1.Add 3 kg 650 g and 2 kg 500 g.
- 2.Take 2 L 700 mL away from 6 L 300 mL.
Grams first: 650 + 500 = 1150, so write 150 g and carry 1 kg. Then 3 + 2 + 1 = 6 kg, giving 6 kg 150 g. For the litres, 300 is under 700, so borrow 1 L as 1000 mL. Now 1300 − 700 = 600 mL, and 5 − 2 = 3 L, giving 3 L 600 mL.
⚠️ Watch out
You might be thinking you carry once the small column passes 100, the way tens do. You do not. 950 g + 80 g is 1030 g, so that one carries. But 400 g + 300 g is only 700 g, and it stays exactly where it is.
🌟 Why this matters
Road signs, packets, and kitchen jugs all give you an amount in two parts. Walk 1 km 400 m and then 900 m and you have walked 2 km 300 m, not 1 km 1300 m. One carry rule covers length, weight, and capacity together.
Exam tip: Rewrite both amounts in the small unit if the carry confuses you; the answer comes out the same.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“4 L 600 mL + 2 L 700 mL = ?”
- 1
Small unit first
Millilitres: 600 + 700 = 1300 mL.
- 2
Carry at 1000
1300 mL = 1 L + 300 mL. Carry 1 L to the L column.
- 3
Add L (including carry)
4 + 2 + 1 = 7 L
- 4
Answer ✓
= 7 L 300 mL
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Add the m column first. If it reaches 1,000, carry 1 km.
COMPOUND UNITS · ROUND 1 OF 3
Quick check
✅ VERIFICATION
A bottle holds 1 L 400 mL. How much more juice is needed to make 3 L?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Balance Scales & Container Ratios
Reach the smallest unit, then multiply your way up.