Lesson 6 Homework Practice Estimate Quotients

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How to Estimate Quotients Using Compatible Numbers

Estimating quotients is a useful skill that can help you check your answers when you divide large numbers. One way to estimate quotients is to use compatible numbers, which are numbers that are easy to divide mentally. Compatible numbers are close to the original numbers, but they have factors in common.

For example, suppose you want to estimate the quotient of 121.6 Ã 43.5. You can use compatible numbers by rounding both numbers to the nearest multiple of 10: 120 Ã 40. Then you can divide easily and get an estimate of 3.

To estimate quotients using compatible numbers, follow these steps:

Round the dividend and the divisor to numbers that are easy to divide mentally.

Divide the rounded numbers and write the quotient.

Check if your estimate is reasonable by comparing it with the original numbers.

Let's try another example: Estimate 769.5 Ã 142.5 using compatible numbers.

Round the dividend and the divisor to numbers that are easy to divide mentally. A possible choice is 800 Ã 150.

Divide the rounded numbers and write the quotient: 800 Ã 150 = 5.33

Check if your estimate is reasonable by comparing it with the original numbers. The estimate is close to the actual quotient of 769.5 Ã 142.5 = 5.4, so it is reasonable.

Estimating quotients using compatible numbers can help you solve division problems quickly and accurately. You can practice this skill by using online resources such as IXL[^1^] or YouTube videos[^3^]. You can also find more examples and exercises in your textbook or homework worksheets[^2^]. Remember to always check your estimates with the original numbers and adjust them if needed.

Another way to estimate quotients is to use rounding and place value. This method involves rounding the dividend and the divisor to the same place value, such as tens, hundreds, or thousands. Then you can divide the rounded numbers and get an estimate of the quotient.

For example, suppose you want to estimate the quotient of 316.9 Ã 327.5. You can use rounding and place value by rounding both numbers to the nearest hundred: 300 Ã 300. Then you can divide easily and get an estimate of 1.

To estimate quotients using rounding and place value, follow these steps:

Identify the smallest place value of the dividend and the divisor.

Round the dividend and the divisor to that place value.

Divide the rounded numbers and write the quotient.

Check if your estimate is reasonable by comparing it with the original numbers.

Let's try another example: Estimate 511.1 Ã 247.3 using rounding and place value.

Identify the smallest place value of the dividend and the divisor. The smallest place value is tenths.

Round the dividend and the divisor to that place value: 511.1 â 510 and 247.3 â 250

Divide the rounded numbers and write the quotient: 510 Ã 250 = 2.04

Check if your estimate is reasonable by comparing it with the original numbers. The estimate is close to the actual quotient of 511.1 Ã 247.3 = 2.07, so it is reasonable.

Estimating quotients using rounding and place value can help you simplify division problems and get a rough idea of the answer. You can practice this skill by using online resources such as IXL or YouTube videos. You can also find more examples and exercises in your textbook or homework worksheets. Remember to always check your estimates with the original numbers and adjust them if needed. aa16f39245