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# Estimating Sums and Differences - PowerPoint PPT Presentation

Estimating Sums and Differences. Amanda Hobson. Objectives:. 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. Estimation.

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Estimating Sums and Differences

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## Estimating Sums and Differences

Amanda Hobson

### Objectives:

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.

### Estimation

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

### Estimation

Methods:

• Rounding

• Front-End Estimation

### Rounding

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

### Rounding

Example:

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

### How to Round Numbers

• 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)

### Estimate the Sum by Rounding

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

2630

+ 14 + 10

40

### Estimate the Difference by Rounding

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

5,976 6,000

-2,687 - 3,000

3,000

### Front-End Estimation

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

### Front-End Estimation

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

### How to estimate the sum using Front-End Estimation

• Add the digits of the highest place values

• Insert zeros for the other place values

### How to estimate the sum using Front-End Estimation

Example: 44,859 + 25,789

44,85940,000

+ 25,789 + 20,000

60,000

### How to estimate the difference using Front-End Estimation

• Subtract the digits of the highest place values

• Insert zeros for the other place values

### How estimate the difference using Front-End Estimation

Example: 57,658 - 24,125

57,65850,000

- 24,125 - 20,000

30,000

### Estimate Differences

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

### EstimateSums

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

### Review:

• 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