When multiplying two rational numbers, how is the sign of the product determined?
When multiplying two rational numbers, the sign of the product is determined by the signs of the individual numbers being multiplied.
If the two numbers have the same sign (both positive or both negative), the product will be positive. For example, when multiplying +3 and +2, the product is +6. Similarly, when multiplying -3 and -2, the product is +6 as well.
If the two numbers have different signs (one positive and one negative), the product will be negative. For example, when multiplying +3 and -2, the product is -6. Similarly, when multiplying -3 and +2, the product is -6 as well.
In other words, the product of two rational numbers is positive if the signs are the same, and negative if the signs are different.
When multiplying two rational numbers, the sign of the product is determined by the signs of the two numbers being multiplied.
1. If both numbers have the same sign (either both positive or both negative), then their product is positive. For example:
- (+3) * (+2) = +6
- (-4) * (-1/2) = +2
2. If one number is positive and the other is negative, then their product is negative. For example:
- (+5) * (-2/3) = -10/3
- (-8/7) * (+9) = -72/7
In summary, the sign of the product of two rational numbers is positive if the two numbers have the same sign, and negative if the two numbers have different signs.
When multiplying two rational numbers, the sign of the product is determined by the signs of the individual numbers being multiplied. Here are the rules to determine the sign of the product:
1. If both numbers have the same sign (either both positive or both negative), then the product is positive.
2. If one number is positive and the other number is negative, then the product is negative.
To illustrate this, let's consider a couple of examples:
Example 1:
Multiply -3/4 and 2/3.
Step 1: Multiply the numerators: -3 * 2 = -6.
Step 2: Multiply the denominators: 4 * 3 = 12.
Step 3: Combine the results from steps 1 and 2: (-6/12).
Since one number is negative and the other is positive, the product is negative. Therefore, -3/4 * 2/3 = -6/12.
Example 2:
Multiply -5/6 and -4/7.
Step 1: Multiply the numerators: -5 * -4 = 20.
Step 2: Multiply the denominators: 6 * 7 = 42.
Step 3: Combine the results from steps 1 and 2: (20/42).
Since both numbers are negative, the product is positive. Therefore, -5/6 * -4/7 = 20/42.
By following these rules, you can determine the sign of the product when multiplying two rational numbers.