How to Add or Subtract Numbers of Different Units?

廣東珠海市斗門區(qū)第二實驗小學(xué) 黃美健

Everybody knows that it is not so difficult to do addition and subtraction in primary school Maths. For example, if there were 23 students in a classroom and now another 19 students come into the classroom, there must be 42 students in the classroom in total, as none of them goes out of the classroom. We may write the equation sentence as the below.

If there were 31 boys on the bank of a swiming pool and now 14 of them jump into the pool and swim, how many boys are left on the bank of the pool?

It’s also easy. As we know there were 31 boys on the bank of the pool in total, we may regard the number 31 as the whole, and 14 boys who jump into the pool and swim as one part. We know the whole and one part of the whole, we need to find out the other part of the whole. This time we can subtract one part from the whole. Then we can get the answer. We may write an equation sentence as the below.

But if Tom spent 1 hour and 45 minutes doing his English homework and 35 minutes doing his Maths homework, how much time did Tom spend doing his homework in total? What will you do to solve this problem? Will you directly add up 1 hour and 45 minutes and 35 minutes to find the sum? You cannot do like this!

Then, what can we do?

You know that “hour” and “minute” are different units of numbers. When we come across the different units of numbers, we need to convert them to the same units.

What does “convert” mean then? The word “convert” means “change”. For example, it is known that “1 hour is equal to 60 minutes”. So “1 hour 45 minutes” can be converted to “60 minutes + 45 minutes = 105 minutes”. Then we may add up 105 minutes and 35 minutes as the below.

After that, 140 minutes can be converted to “… hours … minutes”. In 1 hour, there are 60 minutes. What about in 140 minutes? Yes, in the number 140, there are 2 hours, because 120 minutes mean 2 hours . So there are 2 hours and 20 minutes in 140 minutes. We may write as the below.

The answer is that Tom spent 2 hours and 20 minutes doing his homework.

Actually, first we also need to convert the different units to the same one when we add or subtract the length or weight of different units. For example, what about “2kg– 1kg350g”?

As “kg” and “g” are different units of weight, we need to convert them to the same unit “g” first. Then, we can follow the following steps.

Step 1 Convert the unit “kg” to “g” to get the same unit “g”.

2kgcan be converted to 2,000g, as 1kgis equal to 1,000g.

1kg350gcan be converted to 1,350g, as 1,000gplus 350gequals 1,350g.

Step 2 Subtract 1,350 g from 2 kg.

2kg– 1kg350g= 2,000g– 1,350g= 650g

Things are the same with the calculation of the addition and subtraction of lengths with different units.

For example:

Kate’s pencil is 1 dm 4 cm long, and Lucy’s pencil is 9 cm long. How much is Kate’s pencil longer than Lucy’s pencil?

We know that “cm” is short for centimetre and “dm” is short for decimetre. We also know that 1dmis equal to 10cm. Then we can do the subtraction as the above.

Step 1 Convert the unit “dm” to “cm” to get the same unit “cm”.

Step 2 Subtract 9 cm from 14 cm.

The answer is that Kate’s pencil is 5cmlonger than Lucy’s.

Now we can draw a conclusion that we can convert the different units of the numbers to the same one before doing the calculations of addition and subtraction.

Try the following exercises.

I. Fill in the blanks.

1. 3kg720gis ___kg___gheavier than 2kg980g.

2. 9:15 is ___ hour(s) ___ minute(s) later than 6:45.

3. 18:05 is ___ hour(s) ___ minute(s) earlier than 21:55.

4. 3m4dmis ___m___dmshorter than 72dm.

5. 94cmis ___dm___cmlonger than 60cm.

II. Calculate the following.

8km– 5km25m= ___km___m

90cm– 6dm3cm= ___dm___cm

116cm– 7dm2cm= ___cm

32kg+ 8kg50g= ___kg___g

3 hours 25 minutes + 4 hours 45 minutes = ___ hours ___ minutes

6 hours 5 minutes – 3 hours 55 minutes = ___ hours ___ minutes

60g+ 7kg140g= ___kg___g

12kg40g– 8kg800g= ___kg___g

（答案見本期第47頁）