Addition with decimals is the the same as addition of whole numbers. Remember that decimal means of a power of ten. For example: .7 = 7/10 therefore .7 + .2 = 7/10 + 2/10 = 9/10 or .9
Adding decimals together with pencil and paper algorithm
Subtraction
Subtraction with decimals is the same as subtractions of whole numbers. The secret with both addition and subtraction of decimals is to line up the decimal points. Remember that you can add a zero or multiple zeros to a decimal number to representing the digits to the right. For example: .7 = .70000000
Subtracting decimals with pencil and paper algorithm
Multiplication
Multiplication with decimals is the same as multiplication of whole numbers. Decimal points are not lined up as are in addition and subtraction. The secret to multiplying decimals is after you work the problem, add up the number of digits to the right of the decimal point(s) and place a decimal point in your product to the left of that same number of digits. For example: 45 x 8 = 360 .45 x .8 = .360 or .36
This video can be helpful in teaching by pencil and paper algorithm.
Using Base ten blocks can be helpful in teaching multiplication with decimals.
Division
Division with decimals is closely related to division with whole numbers. The secret to dividing with decimals it to know that we can never divide by a decimal. We adjust the problem by making the divisor a whole. Seen in this illustration
Do you remember these properties for rational numbers?
- Closure Properties: the set of rational numbers is closed under addition and multiplication. [a + b and a x b are unique rational numbers]
- Commutative Properties: for addition and multiplication are both commutative. [a + b = b + a and a x b = b x a]
- Associative Properties: for addition and multiplication are both associative. [(a + b) + c = a + (b + c) and (a x b) x c = a x (b x c)]
- Identity Properties: for addition it is 0 and for multiplication it is 1. [0 + b = b and 1 x b = b]
- Distributive Properties: for multiplication is distributive over addition. [a x( b + c) = a x b + a x c]
- Inverse Properties:
- for addition there is a unique inverse for every nonzero number. [b + -b = 0]
- for multiplication there is a unique inverse number. [c not equal to 0, c x 1/c = 1]
Jodi, you explained things really well in this post. The links that go with each topic are great! Also the "Practice your skills" link is helpful too. Things like this are what make your blog stick out from all the others. Great job =)
ReplyDeleteI really liked your post. You have some great examples in each of your addition, subtraction, multiplication, and division. Also, the end... Properties of Rational Numbers is a great reminder.
ReplyDeleteThe explanation of how to do operations was really easy to understand how we are to do problems with decimals.
ReplyDeleteWow great posts! All of your visuals are great! And you did a great job explaining all of the properties, When I was younger I had trouble multiplying decimals and whole numbers, I liked you video for this. Looking back I don't know why I had such trouble, it really isn't much different from a whole number multiplied by a whole number
ReplyDeleteJodi Thank you! I watched these videos after the lesson we went over and it actually really helped me! Now that I have a better understanding of operations with decimals i will be able to teach my class better!! I have to say that your entire blog has been very helpful!!
ReplyDeleteI really like the decimal video with the base ten blocks. I never learned how to use these blocks till now and your video is a good reference for me to go back and see how it is done.
ReplyDelete-Margaret