Instructional Blog

How to Simplify Expressions with Decimals

Simplifying expressions is such a broad demand. If someone walked up to me and asked, “How do you simplify expressions in math?”

I’m going to tilt my head to one side and volley, “It depends on what’s in the expression.” Depending on where you are in your math studies, you could be doing simple addition, order of operations, factoring, logarithms, and even bigger, wilder words than that!”

Today’s problem is: What is the difference between the sum of the following set of numbers estimated to the nearest tenth and the exact sum?

How to Estimate Decimal Values

The first thing I did to answer this problem is estimate all the decimal values to the nearest tenth place. The tenth place is the first number on the right hand side of the decimal. To round it, I have to look at the number to the right of that!

If the number is 4 or less, then it becomes 0. The number in the tenth place stays the exact same. So, I rounded each of those numbers that way.

How to Find the Sum of a Group of Numbers

The next step was to find the sum of the estimated values. You can find the sum by adding up all of the numerical values listed. If you are at a level to use the calculator, you can do so. If not, just vertically line up all your numbers, make sure to carry numbers to accurately add everything up.

I also added all the original (unrounded) values up to find the “exact sum”.

How To Find the Difference of Numbers

Once you find both of those sums, set them up to take the difference of them, as the problem instructed. Make sure to set up the subtraction the right way. The problem specifically asked what the difference was between the sum of the estimated numbers and the sum of the exact numbers.

This means you need to put the estimated sum above the exact sum to find the difference. Subtract accurately, by making sure to borrow the 1.

And there you go! You now have yourself a double-simplified, estimated, and subtracted expression!

Thank you so much for your time!

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