use properties of rational numbers to multiply the following
To multiply rational numbers, we can use the property of multiplying fractions. Let's say we want to multiply two rational numbers, a/b and c/d, where a, b, c, and d are integers.
The multiplication of two rational numbers is given by:
(a/b) * (c/d) = (a*c) / (b*d)
Therefore, to multiply the given rational numbers, just multiply the numerators and denominators:
(4/5) * (3/8) = (4*3) / (5*8) = 12/40
However, we can simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and denominator, and dividing both by that.
The GCD of 12 and 40 is 4. So, dividing both numerator and denominator by 4:
12/40 = (12/4) / (40/4) = 3/10
Therefore, the product of (4/5) and (3/8) is 3/10.
To multiply rational numbers, you can use the following properties:
1. Commutative Property: The order of the numbers does not matter in multiplication.
2. Associative Property: The grouping of numbers does not affect the result of multiplication.
3. Distributive Property: You can distribute the multiplication across addition or subtraction.
Let's use these properties to multiply the following rational numbers:
Example 1:
Multiply 3/4 by 5/6.
Using the commutative property, we can rearrange the order of numbers:
3/4 * 5/6 = 5/6 * 3/4
Now, multiply the numerators and denominators straight across:
(5 * 3) / (6 * 4) = 15/24
Simplifying the fraction, we can divide both numerator and denominator by their greatest common divisor, which is 3:
15 ÷ 3 / 24 ÷ 3 = 5/8
So, 3/4 multiplied by 5/6 equals 5/8.
Example 2:
Multiply (2/5) * (3/7).
Using the commutative property, we can rearrange the order of numbers:
(2/5) * (3/7) = (3/7) * (2/5)
Now, multiply the numerators and denominators straight across:
(3 * 2) / (7 * 5) = 6/35
So, (2/5) multiplied by (3/7) equals 6/35.