Multiplying rational numbers involves multiplying fractions, decimals, and integers. When multiplying fractions, multiply the numerators and the denominators separately. For decimals, multiply as you would with whole numbers, then place the decimal point in the product according to the total number of decimal places in the factors. Remember, a positive times a positive is positive, a negative times a negative is positive, and a positive times a negative (or vice versa) is negative.
For example, to multiply $\frac{1}{2}$ and $\frac{3}{4}$, you multiply the numerators (1 * 3 = 3) and the denominators (2 * 4 = 8), resulting in $\frac{3}{8}$. When multiplying -2.5 and 3.2, you multiply 25 and 32 to get 800, then place the decimal point two places from the right, resulting in -8.00 or -8.
| Term | Definition |
|---|---|
| Numerator | a) The result of multiplication |
| Denominator | b) Any number that can be expressed as a fraction $\frac{p}{q}$, where p and q are integers and q ≠ 0 |
| Rational Number | c) The bottom number in a fraction |
| Product | d) A whole number (not a fraction) that can be positive, negative, or zero |
| Integer | e) The top number in a fraction |
When multiplying rational numbers, if the signs are the ________, the result is positive. If the signs are ________, the result is negative. To multiply fractions, multiply the ________ and the ________ separately. A ________ number can be written as a simple fraction. Multiplying two negative rational numbers results in a ________ product.
Explain why it's important to understand the rules of multiplying negative numbers when dealing with financial transactions involving debt and credit.
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