Compatible Numbers

By Chandrajeet K


• The word "compatible" means "well-matched". Compatible numbers are numbers that are friendly with each other.

For example:

15 and 5 are compatible numbers, because, 5 goes into 15 evenly ---- 15/5=3
So are 15 and 3, because, 3 goes into 15 evenly ---- 15/3=5

• Compatible numbers make estimation or mental calculation easier. They are useful in estimating the sum, difference, product, or quotient. Compatible numbers are close in value to the actual numbers given in the problem. They often end in 0 or 5.

Let’s look at a few examples.

Example 1

Estimate 33 + 28.

Look for close numbers that are easier to work with. Multiples of 10 are easier to work with.

28 is closer to 30.

Adding 33 and 30 is easy.

So,

33 + 28 is approximately equal to 33 + 30 = 63.


Example 2

Estimate 12 + 59 + 38.

Now, look for numbers that can be added together to make a 10 or multiples of 10.

12 + 59 + 38

= 12 + 38 + 59 ----- Swap the positions of 59 and 38

= 50 + 59 ------------ The 2 and the 8 are compatible. They add to make a 10.

= 109


Example 3

Estimate 52 – 37.

Look for close numbers that are easier to work with. Multiples of 10 are easier to work with.

37 is closer to 40.

Subtracting 40 from 52 is easy.

So,

52 – 37 is approximately equal to 52 – 40 = 12.


Example 4

Estimate the value of 61 × 5.8.

Compatible numbers for 61 and 5.8 are 60 and 6 respectively.

So, 61 × 5.8 is approximately equal to 60 × 6 = 360.


Example 5

Estimate 33/8.

To get a good estimate, round the dividend to the nearest multiple of the divisor.

Look for a number ‘close to 33 and at the same time is divisible by 8’. In other words, try to find a multiple of 8 that is close to 33.

32 is the right choice.

So,

33/8 is approximately equal to 32/8 = 4.


Example 6

Estimate 29/6.5.

29 and 6.5 are not friendly with each other. Try to find a pair of compatible numbers one of which is close to 29 and the other is near 6.5.

Round the numbers 29 and 6.5.

30, 6 is the ideal pair of compatible numbers with 30 close to 29 and 6 close to 6.5.

Therefore, 29 ÷ 6.5 is approximately equal to 30 ÷ 6 = 5.

Our estimate is 5. The actual quotient is 4.46. We are not for away from the actual answer.


Sometimes we should be careful about our choice of compatible numbers. It is important to choose compatible numbers that are appropriate to a given situation.

Let’s look at an example.

83 apples have to be packed in boxes. Each box holds 10 apples. About how many boxes will you need?

In order to find the number of boxes needed to pack ALL the apples, we have to divide 83 by 10. But…83 and 10 do not go well together.

Can you think of a number that goes well with 10 and at the same time is closer to 83?

Let’s try 80.

Well…80 is indeed friendly with 10, since 10 goes into 80 evenly.
But REMEMBER! We have to pack ALL 83 apples. 83 is greater than 80. If we consider 80, then we’ll have 3 apples left unpacked.

Think of another number…90?

Hooray!

90 is close to 83 and is friendly with 10 since 90 is a multiple of 10.

83/10 is approximately equal to 90/10 = 9.

Therefore you’ll need about 9 boxes.