# Estimating quotients

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##### Intros

###### Lessons

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##### Examples

###### Lessons

**Estimating Quotients by Rounding**

Estimate the quotient using estimation by rounding. Then, find the exact quotient to check your answer.**Estimating Quotients using Compatible Numbers**

Estimate the quotient by rewriting the statement using compatible numbers. Then, find the exact quotient to check your answer.**Estimating Quotients with Long Division**

Estimate the quotient using estimation with long division. Then, find the exact quotient to check your answer.**Estimating Quotients Word Problem - 1**

At a local pie eating contest, the winner ate 13.136 pounds of apple pie in 8 minutes. About how many pounds did the winner eat in one minute?**Estimating Quotients Word Problem - 2**

If Laura makes a salary of $41,004 in a year from her job as a laboratory technician, about how much money does she make in 3 months?**Estimating Quotients Word Problem - 3**

Trisha was able to complete 28$\frac{1}{3}$ levels in her video game in 3$\frac{1}{5}$ hours.

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###### Topic Notes

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

__Notes:__- 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 each number to its greatest place value
- For mixed fractions, round to the nearest whole number
- 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 - Think of numbers that are close to the dividend and divisor that are “compatible” (easier to compute using your times tables)
- 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 - Write the decimal point in the quotient (answer on top of the long division bracket)
- 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?
- You can
**compare**the**exact quotient**and the**estimated quotient**to see how close they are - For the
: rounding DOWN the dividend will give an__dividend__**underestimate** - Rounding UP the dividend will give an
**overestimate** - For the
: rounding DOWN the divisor will give an__divisor__**overestimate** - Rounding UP the divisor will give an
**underestimate**

__Round__

__Divide__the rounded numbers

__compatible numbers____Divide__using the

**compatible numbers**

__decimal point__

__first non-zero digit__

__zeroes__for the rest of the quotient (answer)

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