In this section, we will explore the four basic operations with decimals: addition, subtraction, multiplication, and division. We will not only practice these operations but also understand why they work the way they do.
Subsection6.2.1Addition and Subtraction with Decimals
Adding and subtracting decimals is straightforward because decimal fractions behave the same as place value. The key is to line up your place values (digits) and add or subtract right to left, carrying to the next place if necessary.
GIVE A PIC OF THE ALGORITHM WITH EXPLANATION The process is the same as adding and subtracting whole numbers, but with the added step of aligning the decimal points.
When multiplying decimals, we first multiply as if there were no decimals. Then, we count the number of decimal places in both numbers and add them. This sum is the number of decimal places in our answer.
GIVE A PIC OF THE ALGORITHM WITH EXPLANATION The reason this works is because we can think of decimals as decimal fractions. For instance, 53.071 can be thought of as 53071/1000 and 6.29 as 629/100. When we multiply these fractions, we multiply the numerators (53071 * 629) and the denominators (1000 * 100), which gives us the same result as our decimal multiplication.
When dividing decimals, we move the decimal place the same number of places in the dividend and divisor so that the divisor is a whole number. Then, we perform the division as if there were no decimals.
GIVE A PIC OF THE ALGORITHM WITH EXPLANATION This works because we can think of decimals as decimal fractions. For instance, 3.24 can be thought of as 324/100 and 0.618 as 618/1000. When we divide these fractions, we multiply the dividend by the reciprocal of the divisor, which gives us the same result as our decimal division.
