What are compatible numbers? Definition and examples
What are compatible numbers? Compatible numbers are numbers that look nice or friendly with each other when we do mental calculation to estimate a product, an addition, a subtraction, but especially a division.
Using the figure above, we can make the following conclusions about compatible numbers:
Estimating sums
- Fives are compatible: 75 + 25 = 100
- Any numbers that make tens are compatible. 32 + 48 = 80
Estimating differences
- Numbers with the same final digit or digits are compatible: 72 - 52.
- Numbers that end with 1 or more zeros are compatible. For example, use 200 - 100 to estimate 198 - 99.
Estimating products and quotients.
- Numbers that end with 1 or more zeros are compatible.
- Numbers in the multiplication table assuming that we know the table by heart.
Some examples of compatible numbers when doing division are 400 and 10, 36 and 6, 2400 and 12, and 64 and 8.
2400 and 12 are compatible because when doing this division (2400/12), we can quickly divide 24 by 12 to get 2 and put two zeros at the end to get 200.
Some examples of compatible numbers when doing multiplication are 200 and 40, 1100 and 40, 25 and 4.
1100 and 40 are compatible because we can quickly do this multiplication by multiplying 11 and 4 to get 44 and add three zeros at the end to get 44000.
Some examples of compatible numbers when doing addition are 225 and 75, 298 and 2, and 540 and 60.
Some examples of compatible numbers when doing subtraction are 435 and 25, 800 and 600, and 5986 and 2986.
When estimating, keep in mind that we are not claiming the answer will be exact. we are just looking for a reasonable estimate.
When estimating with division, if you decrease the value of one number, you should also decrease the value of the other. If you increase the value of one number, you should increase the value of the other.
This helps to keep the estimate as close as possible to the exact answer.
Estimate the following division using compatible numbers
1. 232 ÷ 11 2. 3421 ÷ 9 3. 25889 ÷ 52
1. Compatible numbers for 232 and 11 are 240 and 12. Notice that both numbers were increased!
24 can be divided by 12 to get 2. Then, add a zero at the end to get 20
2. Compatible numbers for 3421 and 9 are 3200 and 8.
32 can be divided by 8 to get 4. Then add one zero at the end to get 400
400 is a reasonable estimate. 3321 ÷ 9 = 369 and 369 can be rounded to the nearest hundred to 400
3. Compatible numbers for 25889 and 52 are 25000 and 50
When dividing 25000 by 50, the zero next to 50 cancels out with one zero of 25000, so the problem becomes 2500 ÷ 5
25 ÷ 5 = 5. Then, add two zeros at the end and the answer is 500
500 is a reasonable estimate because 25889 ÷ 52 = 497.86 and 497.86 is close to 500
Estimate the following multiplication using compatible numbers
1.72 × 78 2. 288 × 415
1. Compatible numbers for 72 and 78 are 70 and 80. Note that one number was decreased while the other was increased!
Multiply 7 by 8 and add two zeros at the end to get 5600
2.Compatible numbers for 288 and 415 are 300 and 400
Multiply 3 by 4 and add four zeros at the end to get 120000.
Now, if I ask the question again, what are compatible numbers, would you be able to answer with confidence? If not, just study again! So, what are compatible numbers? Just kidding!