2.2: Estimate Decimal Sums and Differences Using FrontEnd Estimation
Have you ever tried to figure out a restaurant bill? Take a look at this situation.
Carmen and her friend went out for lunch. When they received the bill, they saw the following figures written down.
Carmen wants to add this up quickly in her head so that she can estimate the bill.
Do you know how she can do this? In this Concept, you will learn how to use frontend estimation in situations just like this one.
Guidance
Did you know that you can estimate decimal sums and differences using frontend estimation? Let's take a look at frontend estimation. What is it?
Frontend estimation is a particular way of rounding numbers to estimate sums and differences. To use frontend estimation, add or subtract only the numbers in the greatest place value.
Take a look at this estimation problem.
Estimate the sum using frontend estimation:
First add the digits in the ones places:
Now look at the digits in the tenths places:
A good estimate for the sum is 15. This is our answer.
Here is a problem using subtraction. We can use frontend estimation for this one too.
Estimate the difference using frontend estimation:
First subtract the digits in the ones places:
Now look at the digits in the tenths places. Since the difference of 5 and 3 is 2, it will not affect your first estimate.
A good estimate for the difference is 6. This is our answer.
Use frontend estimation to find each sum or difference.
Example A
Solution:
Example B
Solution:
Example C
Solution:
Now let's go back to the dilemma from the beginning of the Concept.
Here is the list of costs that was on Carmen's bill.
We use frontend estimation by taking the first value from each price. Then we add.
The estimated cost of lunch is
Vocabulary
 Decimal
 a part of a whole. The numbers to the left of the decimal point represent whole quantities. The numbers to the right of the decimal point represent parts.
 Estimate
 to find an approximate answer that is reasonable or makes sense given the problem.
 FrontEnd Estimation
 a method of estimating where you only add the digits in the greatest place value.
Guided Practice
Here is one for you to try on your own.
Estimate the following sum.
Solution
To complete this task using frontend estimation, we take the leading value from each number.
Now we add these values.
Our estimate is
Video Review
Practice
Directions: Find each estimate by using frontend estimation.

45.67+3.04=−−−−− 
55.10+5.6=−−−−− 
88.99−2.10=−−−−− 
80.09−12.78=−−−−− 
34.75−3.05=−−−−− 
5.67+3.87=−−−−− 
235.56−120.45=−−−−− 
17.8+12.3+5.3=−−−−− 
33.1+11.4+2.8=−−−−− 
18.11+25.4+2.1=−−−−− 
34.1−10.123=−−−−− 
301.1−10.2345=−−−−− 
12.234+15.1004=−−−−− 
2.00987+5.0123+8.118=−−−−− 
3.0045−1.0008=−−−−−
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Decimal
In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of onetenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).FrontEnd Estimation
Frontend estimation is a method of estimating where you only add the digits in the greatest place value.Image Attributions
Here you'll learn to estimate decimal sums and differences using frontend estimation.