- videos about decimal arithmetic.

**Add and subtract decimals**

I explain the main principle in adding or subtracting decimals: we can add or subtract "as if" there was no decimal point IF the decimals have the same kind of parts--either tenths, hundredths, or thousandths. Many students have a misconception of thinking of the "part" after the decimal point as "plain numbers." Such students will calculate 0.7 + 0.05 = 0.12, which is wrong, and I explain why in the video.

**Multiply decimals by whole numbers**

I explain how to multiply decimals by whole numbers: think of your decimal as so many "tenths", "hundredths", or "thousandths", and simply multiply as if there was no decimal point. Compare to multiplying so many "apples". For example, 5 x 0.06 is five copies of six "hundredths". Multiply 5 x 6 = 30. The answer has to be 30 hundredths (hundredths corresponding to apples), or 0.30, which simplifies to 0.3.

**Divide decimals using mental math**

I explain two basic situations where you can use mental math to divide decimals: 1) Think of "stuff" (which is tenths, hundredths, or thousandths) shared evenly between so many people; OR 2) Think how many times the divisor fits into the dividend.

**Long division with decimals**

When the dividend is a decimal, and the divisor is a whole number, long division is easy: just divide as if there was no decimal point, and then put a decimal point in the answer in the same place as it is in the dividend. I also show an example where we add decimal zeros to the dividend, in order to get an even division. Lastly I show how the fraction 3/7 is converted into a decimal using long division.