Estimation strategies - Lesson 2

in #mathematics6 years ago

Estimation strategies:

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Estimating sums and differences of fractions:

When adding or subtracting fractions, we can also estimate an answer first before doing the correct calculations.

We are going to look at 2 strategies for adding and subtracting fractions.

Strategy 1:

First make a rough estimation considering these two facts.  Is the fraction closer to the next whole number or is the fraction closer to one half??


Examples:

1.

In the example above, the first fraction is closer to a whole, that means we can round off to the nearest whole which will give us 25.  The second fraction is closer to a half so we can round off to a half. This fraction can round off to 4 and a half.  The estimated fractions will be 25 plus 4 and a half which gives up 29 and a half.


2.  

In this example, we have to subtract the two fractions.  Again, we look to see if the fractions are closer to a whole, or closer to a half.  The first fraction is closer to a half, so we can round off to the nearest whole, the second fraction is closer to a half.  The estimated sum will be 4 - 1 and a half.  The estimated answer will then be equal to 2 and a half.

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Strategy 2:

The second strategy we are going to discuss is to look for compatible fractions with a sum or difference close to whole numbers of fractions that we can easily add or subtract mentally.


Examples:

1.  

In the example above, we first add the whole numbers together, then we put the fractions with the same denominators together and lastly we add what is left of the sum.  This is almost like filling up tens or hundreds when adding.  The whole numbers adds up to 18, plus the two fractions that makes a whole, and then lastly we add the fraction that is left.  The answer we get is 19 and a third.


2.  

In the second example, we can see that the first fraction, 12 over 25, is closer to a half, rounded off then will be 4 and a half.  The second fraction is closer to 1 whole, and the third fraction is closer to a half again.  After estimating the sum, we get 4 and a half - 1 - a half which will give us 2 wholes.  



Link to the previous estimation strategy:

Estimation strategies - Lesson 1

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