| << Chapter < Page | Chapter >> Page > |
Division of signed numbers follows the same rules as multiplication. When the signs are the same, the quotient is positive, and when the signs are different, the quotient is negative.
The sign of the quotient of two numbers depends on their signs.
| Same signs | Quotient |
|---|---|
| •Two positives
•Two negatives |
Positive
Positive |
| Different signs | Quotient |
|---|---|
| •Positive&negative
•Negative&positive |
Negative
Negative |
Remember, you can always check the answer to a division problem by multiplying.
Divide each of the following:
| ⓐ | |
| Divide, noting that the signs are different and so the product is negative. |
| ⓑ | |
| Divide, noting that the signs are the same and so the product is positive. |
Just as we saw with multiplication, when we divide a number by the result is the same number. What happens when we divide a number by Let’s divide a positive number and then a negative number by to see what we get.
When we divide a number by, we get its opposite.
Dividing a number by gives its opposite.
Divide each of the following:
| ⓐ | |
| The dividend, 16, is being divided by –1. | |
| Dividing a number by –1 gives its opposite. | |
| Notice that the signs were different, so the result was negative. |
| ⓑ | |
| The dividend, –20, is being divided by –1. | |
| Dividing a number by –1 gives its opposite. |
Notice that the signs were the same, so the quotient was positive.
Now we’ll simplify expressions that use all four operations–addition, subtraction, multiplication, and division–with integers. Remember to follow the order of operations.
We use the order of operations. Multiply first and then add and subtract from left to right.
| Multiply first. | |
| Add. | |
| Subtract. |
Simplify:
The exponent tells how many times to multiply the base.
ⓐ The exponent is and the base is We raise to the fourth power.
| Write in expanded form. | |
| Multiply. | |
| Multiply. | |
| Multiply. |
ⓑ The exponent is and the base is We raise to the fourth power and then take the opposite.
| Write in expanded form. | |
| Multiply. | |
| Multiply. | |
| Multiply. |
According to the order of operations, we simplify inside parentheses first. Then we will multiply and finally we will subtract.
| Subtract the parentheses first. | |
| Multiply. | |
| Subtract. |
Simplify:
We simplify the exponent first, then multiply and divide.
| Simplify the exponent. | |
| Multiply. | |
| Divide. |
Notification Switch
Would you like to follow the 'Prealgebra' conversation and receive update notifications?
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|