Multiply and divide rational numbers quick check
To multiply rational numbers, multiply the numerators together and multiply the denominators together.
For example:
- To multiply 1/2 and 3/4: (1 * 3) / (2 * 4) = 3/8
To divide rational numbers, flip the second fraction and then multiply.
For example:
- To divide 3/4 by 1/2: (3/4) * (2/1) = (3 * 2) / (4 * 1) = 6/4 = 3/2
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Use the properties of operations and rules for multiplying and dividing to solve
To multiply rational numbers, follow these steps:
Step 1: Multiply the numerators of the rational numbers.
Step 2: Multiply the denominators of the rational numbers.
Step 3: Simplify the resulting fraction, if possible, by canceling out common factors.
For example, let's multiply the rational numbers 2/3 and 4/5:
Step 1: 2/3 * 4/5 = (2 * 4) / (3 * 5) = 8/15
Step 2: No common factors to cancel.
Step 3: The result is 8/15.
To divide rational numbers, follow these steps:
Step 1: Invert the divisor (the number you are dividing by) to create its reciprocal.
Step 2: Multiply the dividend (the number you are dividing) by the reciprocal of the divisor.
Step 3: Simplify the resulting fraction, if possible, by canceling out common factors.
For example, let's divide the rational numbers 2/3 by 4/5:
Step 1: Reciprocal of 4/5 is 5/4.
Step 2: (2/3) / (4/5) = (2/3) * (5/4) = (2 * 5) / (3 * 4) = 10/12
Step 3: Common factor of 2 cancels out, resulting in 5/6.
So, the product of 2/3 and 4/5 is 8/15, and the quotient of 2/3 divided by 4/5 is 5/6.
To multiply and divide rational numbers, follow these steps:
Multiplication:
1. Multiply the numerators (the top numbers) together.
2. Multiply the denominators (the bottom numbers) together.
3. Simplify the resulting fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Example: Multiply 3/4 and 5/6
Step 1: 3 * 5 = 15 (numerator)
Step 2: 4 * 6 = 24 (denominator)
Step 3: 15/24 can be simplified by finding the GCD of 15 and 24, which is 3. Divide both numerator and denominator by 3 to get 5/8.
Division:
1. Flip the second fraction upside down to find its reciprocal.
2. Multiply the first fraction by the reciprocal of the second fraction.
3. Simplify the resulting fraction, if possible, by following the steps mentioned earlier.
Example: Divide 2/3 by 4/5
Step 1: Reciprocal of 4/5 is 5/4.
Step 2: 2/3 * 5/4 = 10/12.
Step 3: 10/12 can be simplified by finding the GCD of 10 and 12, which is 2. Divide both numerator and denominator by 2 to get 5/6.
Remember to always simplify the resulting fraction to its simplest form if possible.