for example, 0.47x 0.18=tHow do I explain to my 5th grader how to get the answer and show the work with the new math?

Question

He is studing the beginning of Algebra. His homework says to find each unknown. I would just multiply and move the descimal point. But yesterdays homework was wrong so I am assuming that they are looking for a different way of showing the work.

example question:  0.47 x 0.18 =t

or

Tamara recycles 29.5 pounds of aluminum cans at a recycling center that pays $0.26 per pound. How much does Tamara receive for the cans?

I would multiply it to get my answer but he seems to think that it shouild look different or be done differently. Am I not using the correct way to solve this?

 

Answer 1

I taught 5th grade math last year and many students struggled with multiplying decimals. The important thing to remember is that multiplying decimals with a number in the ones place is really the same concept as multiplying whole numbers. However, multiplying decimals such as the example 0.47 x 0.18 = t  is a bit tricky because what you are actually solving is the question what fraction is 0.18 of 0.47. The "of" means multiply, but the result is a fraction that is SMALLER than 0.18 and 0.47, so it's more like dividing. The best way to understand these problems is using recipes. For instance, if I need to find 1/4 of a 1/2 cup, then I multiply 1/4 x 1/2, or in decimal form: 0.25 x 0.5. The answer, of course, will be 1/2 cup divided into 4 parts, which is 1/8 of a cup (0.125). 

That is the understanding part. Here is the solving part (which is probably what you did already):

  0.47

x 0.18

   376      (note: don't worry about the decimal point until the END)

+47  

  846 

Now go back to the original numbers and count the TOTAL number of digits to the RIGHT of the decimal point. 0.47 and 0.18, there are 4 digits, so you need to count 4 place values from right to left like this:

start           one           two           three          four

846.  --->  84.6  --->  8.46  --->   0.846  ---> 0.0846

Now there are four digits to the right of the decimal point: 0.0846, so t = 0.0846

For the word problem, you will do the same thing. Make sure you line up the numbers so that they look like this:

  29.5

x 0.26

 

Don't worry about where the decimals are. If it's easier, just write it without the decimals:

 295

x 26

Once you solve this, just remember to place the decimal in the right place!

 

Answer 2

When you multiply ANY two numbers the resulting number has decimal places that is the sum of each numbers' decimal places.

Here you have 0.47 with TWO decimal places and 0.18 with TWO decimal places the answer 846 (I did not consider the decimals yet) should have a total of FOUR decimal places rsulting in 0.0846

This theory holds good for ANY numbers, no matter how many you are multiplying just make sure the decimals are all considered in the result