Decimal Operations
Lessons in this chapter
About Decimal Operations
Decimal Operations is the last decimal chapter, consolidating all four operations at multi-digit length before decimals become a tool rather than a topic.
Add and Subtract Multi-digit Decimals is alignment practice at scale. The decimal points line up and the shorter number is padded with zeros, and with longer numbers that padding is what prevents misalignment.
Multiply and Divide Multi-Digit Decimals brings the two harder operations together. For multiplication the answer carries as many decimal places as both factors combined; for division both numbers shift until the divisor is whole.
From here decimals appear inside percents, ratios and statistics rather than on their own, which is why this chapter is where they have to become automatic. The estimation habit is what keeps them honest, since almost every decimal error is out by a factor of ten and an estimate catches that immediately.
The two lessons here, Add and Subtract Multi-digit Decimals and Multiply and Divide Multi-Digit Decimals, each open as a 6th grade math worksheet in the page. The math problems are worked one at a time and scored as you go, which catches a misplaced decimal point on the question it happened on rather than at the end of a page. Free to try, with no login needed for your first 3.
Frequently asked questions
Two lessons, both about keeping place value straight once the numbers get long. Add and Subtract Multi-digit Decimals lines the decimal points up so that digits meaning the same thing are added together. Multiply and Divide Multi-Digit Decimals then handles the rules that feel arbitrary until the reason is clear: counting decimal places in a product, and shifting the point in both numbers before dividing. The chapter sits in the Common Core domain The Number System (6.NS).
Line up the decimal points and pad the shorter number with zeros. With multi-digit decimals the padding is what prevents misalignment.
The answer has as many decimal places as both factors combined. 1.25 × 0.4 has two places plus one, so three: 0.500.
Shift both numbers until the divisor is a whole number, then divide normally. Multiplying both by the same power of ten leaves the answer unchanged.
Because almost every decimal error is out by a factor of ten, which is exactly what an estimate catches. A rough answer first makes a misplaced point obvious.
Because from here decimals appear inside percents, ratios and statistics rather than as a topic. They have to be automatic by the end of it.