Decimal arithmetic
Prices, weights and measures rarely come out whole. How do the four operations work when the numbers have a decimal point?
Where you are 8 inside
What this area is about
Decimals are place value carried to the right of the point, so the four operations work just as they do for whole numbers. The new question each time is where the point goes. For adding and subtracting, line up the places. For multiplying, count decimal places. For dividing, carry the point straight up, and make a decimal divisor whole first.
How these fit together
Adding and subtracting. Adding and subtracting decimals lines up tenths with tenths and hundredths with hundredths, as in 3.4 + 1.25.
Multiplying. Multiplying a decimal by a whole number is equal groups, such as 2.65 \times 4. Where the point goes in a product explains why the decimal places in the factors set the places in the answer. The standard algorithm multiplies as if the numbers were whole, then places the point.
Dividing. Dividing a decimal by a whole number runs long division with the point carried straight up. Dividing by a decimal scales both numbers by a power of ten so the divisor is whole, and the standard algorithm does that with longer numbers, as in 3.15 \div 0.45.
Using them. Decimal problems in words decides which operation a story about money or measures needs.
A path through it
Add and subtract first. Then multiply by a whole number, see where the point lands, and learn the algorithm. Divide by a whole number next, then by a decimal. Word problems come last.
After this, percents of a quantity and terminating and repeating decimals build on it.