2.5: Decimal Addition Using Front-End Estimation
Have you ever gone to dinner with a friend?
Jessica and Daniella went to dinner. Jessica ordered a pasta dish with shrimp and lobster for $25.25 and Daniella ordered a steak dish for $18.95.
Without adding the exact values, can you estimate the total cost of both meals?
This Concept is about front-end estimation. Pay attention and you can use it to estimate the sum of these meals.
Guidance
What is estimation?
Estimation is a method for finding an approximate solution to a problem.
For example, the sum of 22 and 51 is exactly 73. We can estimate the sum by rounding to the tens place and adding 20 + 50. Then we can say the sum of 22 and 51 is “about 70.” Before we perform an operation, an estimate gives us a rough idea of what our answer will be.
Estimation is also useful to check answers. If, after you solve a problem, you estimate to get a general idea of what an answer should be, you know if your answer is reasonable. You could say that an estimate is an “educated guess.”
By “educated guess” we don’t mean a guess that is out of nowhere. You have to have a method to figuring out the answer or estimate. Rounding numbers before adding is one way to find an estimate.
Front-end estimation is another way. Like rounding, front-end estimation uses place value; unlike rounding, it doesn’t involve any changing of values.
There are three steps to front-end estimation.
First, you add the front end—or leftmost—digits to get a general estimate of the sum. Next, to refine the first estimate, you add the digits directly to the right of the front-end digits.
Finally you add the two sums together.
Front-End Estimation for Addition:
- Add the front (leftmost) digits.
- Add the digits directly to the right of the front-end.
- Add the estimates from steps 1 and 2.
Write these steps in your notebook and then continue with the Concept.
Use front-end estimation to find the sum of 6.819 and 4.621.
We are going to use front-end estimation to add 6.819 and 4.621. Let’s begin by lining up the decimal points and taking a closer look at the numbers. Then we’ll follow the steps of front-end estimation.
6.819
4.621
1. Front-end estimation tells us to add the front or leftmost digits first, so we want to add the ones place.
\begin{align*}6 + 4 = 10\end{align*}.
2. Next, to refine that estimate, we’ll add the digits directly to the right of the front-end digits, or the tenths place.
\begin{align*}.8 + .6 = 1.4\end{align*}
3. Finally, we add our two estimates together.
\begin{align*}10 + 1.4 = 11.4\end{align*}.
Note: The original numbers extended to the thousandth place, but we don’t need to show this by adding unnecessary zeros to our answer. Where decimals end, it is assumed that zeros extend on to infinity.
Practice using front-end estimation to find the following sums.
Example A
\begin{align*}3.5 + 2.34 = \underline{\;\;\;\;\;\;\;\;}\end{align*}
Solution: \begin{align*}5.84\end{align*}
Example B
\begin{align*}12.671 + 8.123 = \underline{\;\;\;\;\;\;\;\;}\end{align*}
Solution: \begin{align*}20.7\end{align*}
Example C
\begin{align*}15.67 + 9.345 = \underline{\;\;\;\;\;\;\;\;}\end{align*}
Solution: \begin{align*}25.9\end{align*}
Here is the original problem once again.
Jessica and Daniella went to dinner. Jessica ordered a pasta dish with shrimp and lobster for $25.25 and Daniella ordered a steak dish for $18.95.
Without adding the exact values, can you estimate the total cost of both meals?
To estimate this sum, we simply add the front-ends of each price.
\begin{align*}18 + 25 = 43\end{align*}
The total cost of the two dinners is approximately $43.00.
Vocabulary
Here are the vocabulary words in this Concept.
- Decimal
- a part of a whole represented by digits to the right of a decimal point.
- Estimate
- to find an approximate solution to a problem.
- Rounding
- a method of estimating where you rewrite a decimal or whole number according to the place value that it is closest to.
- Front-End Estimation
- a method of estimating where you only add the front’s of the numbers. You add the whole numbers in the ones place if there are any, and the tenths place of the decimal digits. Then you combine the sums for the final estimate.
Guided Practice
Here is one for you to try on your own.
Use front - end estimation to find the following sum.
2.93474 + 9.72155
First, we add the front - ends of the whole numbers and decimals.
\begin{align*}.7 + .9 = 1.6\end{align*}
\begin{align*}2 + 9 = 11\end{align*}
Now put these two sums together.
Our answer is \begin{align*}12.6\end{align*}.
Video Review
Here is a video for review.
- This is a supporting video on estimating with decimals.
Practice
Directions: Use front-end estimation to find the following sums.
1. \begin{align*}4.57 + 2.34\end{align*}
2. \begin{align*}2.123 + 4.136\end{align*}
3. \begin{align*}8.913 + 2.047\end{align*}
4. \begin{align*}8.7651 + 2.345\end{align*}
5. \begin{align*}2.436 + 4.567\end{align*}
6. \begin{align*}8.127 + 9.431\end{align*}
7. \begin{align*}8.214 + 7.3214\end{align*}
8. \begin{align*}12.137 + 2.456\end{align*}
9. \begin{align*}18.671 + 20.41\end{align*}
10. \begin{align*}21.643 + 22.123\end{align*}
11. \begin{align*}18.012 + 19.367\end{align*}
12. \begin{align*}21.456 + 18.023\end{align*}
13. \begin{align*}.48218 + .61927\end{align*}
14. \begin{align*}6.7765 + 6.421192\end{align*}
15. \begin{align*}.5075412 + .859931 + .373462\end{align*}
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 one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Estimate
To estimate is to find an approximate answer that is reasonable or makes sense given the problem.Front-End Estimation
Front-end estimation is a method of estimating where you only add the digits in the greatest place value.Rounding
Rounding is reducing the number of non-zero digits in a number while keeping the overall value of the number similar.Image Attributions
Description
Learning Objectives
Here you'll learn to estimate decimal sums using front-end estimation.