Estimating with compatible numbers
Estimating with Compatible Numbers in Grade 4 Saxon Math Intermediate 4 Chapter 8 teaches a mental-math strategy for division: replace the dividend with a nearby number that the divisor divides evenly. To estimate 254 divided by 5, change 254 to the compatible number 250 and compute 250 / 5 = 50. To estimate 483 / 7, find that 7 x 70 = 490 is close to 483, so use 490 / 7 = 70. Students learn to pick the closest compatible number for the best estimate and also handle a zero in the quotient (such as 513 / 5 = 102 R3) by remembering to write 0 for any step where the brought-down digit is smaller than the divisor.
Key Concepts
Property To find 'about how many,' we can use compatible numbers to estimate. Find a number close to the dividend that is easily divisible by the divisor.
Example 1: To estimate $254 \div 5$, change $254$ to the nearby compatible number $250$. Now solve $250 \div 5 = 50$. Example 2: To estimate how many boxes are in 6 railcars with 538 boxes total, change $538$ to $540$. Now solve $540 \div 6 = 90$. It's about $90$ boxes per car.
Why wrestle with tricky numbers when you can estimate? The secret is using 'compatible numbers'—numbers that are close to the originals but play nicely together. Swap the dividend for a nearby number that the divisor can divide cleanly. This gives you a sensible, quick answer that's perfect for figuring out 'about how many' miles per hour or boxes per car.
Common Questions
What is the compatible numbers strategy for estimating division?
Replace the dividend with a nearby number that the divisor divides evenly. For 254 / 5, use 250 / 5 = 50.
How do you estimate 483 / 7?
Find a multiple of 7 close to 483: 7 x 70 = 490. Use 490 / 7 = 70. There are about 70 per group.
How do you estimate 538 / 6?
540 is a multiple of 6 close to 538: 540 / 6 = 90. About 90 per group.
When does a zero appear in the middle of a quotient?
When you bring down a digit and the new partial dividend is still smaller than the divisor, you cannot divide yet, so write 0 in the quotient before bringing down the next digit.
How do you solve 513 / 5?
Divide 5 by 5 = 1 (hundreds). Bring down 1; 1 < 5, write 0 (tens). Bring down 3 to make 13; 13 / 5 = 2 R3. Answer: 102 R3.