Multiply and Divide Decimals
Lessons in this chapter
About Multiply and Divide Decimals
Decimals and their Multiplication and Division completes decimal arithmetic, and the whole chapter turns on knowing where the decimal point belongs.
Multiply Decimals uses a rule that looks like a trick and is not: multiply as whole numbers, then place the point so the answer has as many decimal places as both factors together. 0.3 × 0.4 is 12 with two decimal places, so 0.12, and the estimate confirms it should be small.
Divide Decimals by Powers of 10 is the cleanest lesson in the chapter. Dividing by 10 shifts every digit one place right, which is the mirror of the multiplying-by-10 shift, and it shows the decimal point as a fixed marker that digits move past.
Divide Decimals by Whole Numbers and Decimals handles the general case. Dividing by a decimal is done by shifting both numbers until the divisor is whole, which works because multiplying both by the same amount leaves the answer unchanged.
Solve Multi-Step Real World Problems on Decimals closes the chapter, and most of these are money, where a misplaced point produces an answer that is obviously wrong by a factor of ten.
All four lessons open as a 5th grade math worksheet in the page. Multiply Decimals, Divide Decimals by Powers of 10 and Solve Multi-Step Real World Problems on Decimals each set math problems that are worked one at a time and scored as you answer them. They are free to try, with no login needed for your first 3.
Frequently asked questions
Multiply Decimals uses a rule that looks like a trick and is not: multiply as whole numbers, then give the answer as many decimal places as both factors together. Divide Decimals by Powers of 10 is the cleanest lesson here, Divide Decimals by Whole Numbers and Decimals handles the general case by shifting both numbers until the divisor is whole, and Solve Multi-Step Real World Problems on Decimals closes the chapter, mostly with money. It sits in the Common Core domain Number and Operations in Base Ten (5.NBT).
The answer has as many decimal places as both factors combined. 0.3 × 0.4 has one place each, so the answer has two: 0.12.
Because you are taking a fraction of a fraction. Three tenths of four tenths is twelve hundredths, which is smaller than either.
Every digit shifts one place right, so 4.5 becomes 0.45. It is the mirror of multiplying by 10, where digits shift left.
Shift both numbers until the divisor is a whole number. 6 ÷ 0.3 becomes 60 ÷ 3, which is 20. Multiplying both by the same amount leaves the answer unchanged.
Because decimal errors are usually out by a factor of ten, and that is exactly the kind of error an estimate catches straight away.