第5章小数

So far, we have divided a decimal by a whole number. What happens when we divide a decimal by another decimal? Let’s look at the same multiplication problem we looked at earlier, but in a different way.

Remember, again, that a multiplication problem can be rephrased as a division problem. This time we ask, “How many times does $0.2$ go into $0.8\text{?”}$ Because $(0.2)(4)=0.8,$ we can say that $0.2$ goes into $0.8$ four times. This means that $0.8$ divided by $0.2$ is $4.$

We would get the same answer, $4,$ if we divide $8$ by $2,$ both whole numbers. Why is this so? Let’s think about the division problem as a fraction.

We multiplied the numerator and denominator by $10$ and ended up just dividing $8$ by $2.$ To divide decimals, we multiply both the numerator and denominator by the same power of $10$ to make the denominator a whole number. Because of the Equivalent Fractions Property, we haven’t changed the value of the fraction. The effect is to move the decimal points in the numerator and denominator the same number of places to the right.

We use the rules for dividing positive and negative numbers with decimals, too. When dividing signed decimals, first determine the sign of the quotient and then divide as if the numbers were both positive. Finally, write the quotient with the appropriate sign.

It may help to review the vocabulary for division:

Now we will divide a whole number by a decimal number.

We often apply decimals in real life, and most of the applications involving money. The Strategy for Applications we used in The Language of Algebra gives us a plan to follow to help find the answer. Take a moment to review that strategy now.

Be careful to follow the order of operations in the next example. Remember to multiply before you add.