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Estimating Sums and Differences

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Estimating Sums and Differences

Amanda Hobson

The students will:

1. Give the definition of Estimation.

2. Explain the differences in rounding and front-end estimation.

3. Estimate the sums or differences using the two methods.

Finding the value that is close enough to the right answer, usually with some thought or calculation.

Methods:

- Rounding
- Front-End Estimation

Rounding means reducing the digits in a number while trying to keep its value similar. The result is less accurate, but easier to use.

Example:

73 rounded to the nearest ten is 70 because the 3 is less than 5; therefore the number 73 will be rounded down.

- Decide which is the last digit to keep
- Leave it the same if the next digit is less than 5 (this is called rounding down)
- Increase it by 1 if the next digit is 5 or more (this is called rounding up)

Example: (round to the nearest ten) 26 + 14

2630

+ 14 + 10

40

Example: (round to the nearest thousand) 5,976 - 2,687

5,976 6,000

-2,687 - 3,000

3,000

A method in which the front digits in the given numbers are added or subtracted

Front end estimation mostly produces a closer estimate of sums or differences than the answer produced by adding or subtracting rounded numbers.

- Add the digits of the highest place values
- Insert zeros for the other place values

Example: 44,859 + 25,789

44,85940,000

+ 25,789 + 20,000

60,000

- Subtract the digits of the highest place values
- Insert zeros for the other place values

Example: 57,658 - 24,125

57,65850,000

- 24,125 - 20,000

30,000

Rounding

Front-End Estimation

Estimate 4,892-1,431

Subtract the values of the front digits.

4,892 4,000

1,431 - 1,000

3,000

- Estimate 86,017-35,572
Round to the nearest ten thousand.

86,017 90,000

-35,572 -40,000

50,000

Rounding

Front-End Estimation

Estimate 4,254+2,415

Add the values of the front digits.

4,254 4,000

+ 2,415 + 2,000

6,000

- Estimate 2,578+1,452
Round to the nearest thousand.

2,578 3,000

+ 1,452 + 1,000

4,000

- What is estimation?
- Estimation is the value that is close enough to the right answer. (Guess)

- What is the difference in rounding and front-end estimation?
- When you round , the result will be less accurate .

- Will you be able to estimate using the two methods you have learned?http://www.aaamath.com/g4_73ax1.htm