Compatible numbers are numbers that are close to the actual numbers in a problem but are easier to add, subtract, multiply, or divide in your head. Examples include pairs like \(25\) and \(75\), or \(40\) and \(60\).
How is using compatible numbers different from rounding?
Rounding follows a strict rule (5 or more, round up). Using compatible numbers is more flexible; you choose nearby numbers that work well together, even if it's not the closest ten or hundred.
Estimate the sum \(24 + 77\) using compatible numbers.
You can change the numbers to \(25 + 75\). The estimated sum is \(100\). (Rounding would give \(20 + 80 = 100\)).
Estimate the sum \(163 + 38\) using compatible numbers.
You might change the numbers to \(160 + 40\) because they are easy to add. The estimated sum is \(200\).
Estimate the difference \(98 - 24\) using compatible numbers.
You can change the numbers to \(100 - 25\), which is easy to solve. The estimated difference is \(75\).
Estimate the difference \(412 - 209\) using compatible numbers.
You might choose \(400 - 200 = 200\) or, for a closer estimate, \(410 - 210 = 200\).
Why are numbers ending in \(25\), \(50\), and \(75\) often used as compatible numbers?
They are like coins (quarters) and are very easy for most people to add and subtract mentally to make friendly hundreds.
Estimate the sum of \(346 + 54\) using compatible numbers.
A good choice would be \(350 + 50\). These numbers are close to the originals and easy to add. The estimated sum is \(400\).
Can two people use different compatible numbers for the same problem and both be correct?
Yes! As long as the numbers are close to the original numbers and the math is correct, different compatible pairs can be used. One person might use \(125 + 50\) and another might use \(120 + 50\) for the problem \(123 + 48\).
