Estimating quotients

In this lesson, we will learn:

• How to estimate the answer to division statements
• The three methods for estimating quotients: estimation by rounding, estimation with compatible numbers, estimation with long division
• How to check and compare your estimated quotients with the exact answer

• An estimation is a rough calculation of what the exact answer could be around. It is less exact but easier (faster) to calculate!


• When estimating, it is helpful to remember the rules for rounding numbers:
• If the number to the right of the digit you are rounding to is $\geq$ 5, round UP; if the number is < 5, round DOWN
• For mixed fractions, round to the nearest whole number: if the fraction part is $\geq$ $\frac{1}{2}$, round UP. If the fraction part is < $\frac{1}{2}$, round OWN.


• Three methods to estimate quotients are: estimation by rounding, estimation with compatible numbers, and estimation with long division.



• Estimation by Rounding:
1. Round
• Round each number to its greatest place value
• For mixed fractions, round to the nearest whole number
2. Divide the rounded numbers
• If there are more place values in the dividend compared to the divisor, you can try rounding smaller place values to have more precise estimates


• Estimation with Compatible Numbers:
1. Use compatible numbers
• Think of numbers that are close to the dividend and divisor that are “compatible” (easier to compute using your times tables)
2. Divide using the compatible numbers
• If dividing mixed fractions, remember to convert back into improper fractions first
• Then, change the division to multiplication by flipping the second fraction (multiplying the reciprocal)


• Estimation with Long Division:
1. Line up the decimal point
• Write the decimal point in the quotient (answer on top of the long division bracket)
2. Calculate the first non-zero digit
• When is the first time you will write a number in your answer (quotient)?
• Where you can you first start dividing the dividend by the divisor?
3. Write zeroes for the rest of the quotient (answer)


• You can compare the exact quotient and the estimated quotient to see how close they are
• For the dividend: rounding DOWN the dividend will give an underestimate
• Rounding UP the dividend will give an overestimate
• For the divisor: rounding DOWN the divisor will give an overestimate
• Rounding UP the divisor will give an underestimate