What is this skill?
This skill covers adding, subtracting and multiplying decimals. For adding and subtracting, the rule is to line up the decimal points so that tenths sit under tenths and hundredths under hundredths, then work as if the numbers were whole. For example, 12.5 + 3.75 becomes 12.50 + 3.75 = 16.25, and 9.2 − 4.75 becomes 9.20 − 4.75 = 4.45.
Multiplication uses a different idea. In the practice here, a decimal is multiplied by a one-digit whole number. Ignore the decimal point, multiply, and then put the decimal point back so that the answer has the same number of decimal places as the decimal factor. For 2.4 × 3, 24 × 3 = 72, and one decimal place gives 7.2. A quick estimate confirms it: 2.4 is a little more than 2, and three 2s make 6, so the answer should be a little more than 6.
Answers may be typed with or without a trailing zero: 8.5 and 8.50 are the same number, and Tutorsaurus accepts both.
Why it matters
Decimals are how money, measurements and scientific data are written. Children who can compute with them can work out change, compare prices, and measure lengths. In middle school, decimal calculations show up in nearly every topic from ratios to rates.
There is a second reason that is easy to miss. Adding decimals is where children first see that place value is what makes a method work. Lining up the points is not an arbitrary rule. It is lining up values that can be added together.
Common mistakes
- Lining numbers up on the right edge, like whole numbers, rather than on the decimal point. 12.5 + 3.75 comes out wrong this way.
- Not writing a placeholder zero when subtracting, so 9.2 − 4.75 gets muddled. Writing 9.20 helps.
- Putting the decimal point in the wrong place after multiplying. Counting the decimal places in the factors tells you how many belong in the answer.
- Treating the decimal point as a separator and computing with the parts on each side independently.
- Forgetting to carry or borrow across the decimal point. It works just like any other place.
How to help at home
- Shop with decimals. Add up three items at the store, or work out the cost of four things at $2.35 each.
- Estimate first, always. 12.5 + 3.75 is about 12 + 4, so around 16.
- Use grid paper so each digit sits in its own box. Draw the decimal point as a clear dot in a column of its own.
- Let your child choose to add zeros so both numbers have the same number of places. It makes subtraction far less confusing.
- Ask “does that answer make sense?” after every problem. A result of 72 for 2.4 × 3 shows right away that the point is missing.
Worked examples
These are real questions from the Tutorsaurus decimal operations practice, with the answers worked out.
Example 1
99.8 − 18.8 = ?
Answer: 81.0. Line up the decimal points, then subtract: 81.0.
Example 2
7.1 × 6 = ?
Answer: 42.6. Ignore the decimal point: 71 × 6 = 426. Then put one decimal place back: 42.6.
Example 3
8.96 − 6.73 = ?
Answer: 2.23. Line up the decimal points, then subtract: 2.23.