Multiply And divide rational number unit 3 lesson 14
To multiply and divide rational numbers, follow these steps:
Multiplying Rational Numbers:
1. Multiply the numerators (top numbers) together.
2. Multiply the denominators (bottom numbers) together.
3. Simplify the resulting fraction, if possible, by dividing both the numerator and denominator by their greatest common factor.
For example:
- Multiply: (3/4) * (5/6)
- Numerator: 3 * 5 = 15
- Denominator: 4 * 6 = 24
- Simplify: (15/24) = (5/8)
Dividing Rational Numbers:
1. Multiply the first fraction by the reciprocal (or "flip") of the second fraction.
2. Simplify the resulting fraction, if possible, by dividing both the numerator and denominator by their greatest common factor.
For example:
- Divide: (3/4) ÷ (5/6)
- Multiply the first fraction by the reciprocal of the second fraction: (3/4) * (6/5)
- Numerator: 3 * 6 = 18
- Denominator: 4 * 5 = 20
- Simplify: (18/20) = (9/10)
To multiply and divide rational numbers, follow these steps:
Step 1: Write down the given rational numbers in fraction form. A rational number can be represented as a fraction, where the numerator and denominator are both integers.
Step 2: To multiply two rational numbers, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Simplify the resulting fraction if possible by canceling out any common factors.
Step 3: To divide two rational numbers, multiply the first rational number by the reciprocal (or multiplicative inverse) of the second rational number. The reciprocal of a fraction can be found by swapping the numerator and denominator. Then, follow the same steps as in multiplication to simplify the resulting fraction if possible.
Example:
Multiply: 2/3 * 4/5
Step 1: The given rational numbers are 2/3 and 4/5.
Step 2: Multiply the numerators: 2 * 4 = 8. Multiply the denominators: 3 * 5 = 15.
So, 2/3 * 4/5 = 8/15.
Step 3: The resulting fraction 8/15 is already simplified, so no further simplification is needed.
Divide: 2/3 ÷ 4/5
Step 1: The given rational numbers are 2/3 and 4/5.
Step 2: To divide, multiply the first rational number by the reciprocal of the second. The reciprocal of 4/5 is 5/4.
2/3 * 5/4 = (2 * 5) / (3 * 4) = 10/12.
Step 3: Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which in this case is 2.
10/12 ÷ 2/2 = 5/6.
So, 2/3 ÷ 4/5 = 5/6.
To multiply and divide rational numbers, follow these steps:
Multiplying Rational Numbers:
1. Multiply the numerators (the top numbers) together.
2. Multiply the denominators (the bottom numbers) together.
3. Simplify the resulting fraction, if possible, by canceling out common factors between the numerator and denominator.
For example, let's say we want to multiply the fractions 2/3 and 4/5:
1. Multiply the numerators: 2 * 4 = 8.
2. Multiply the denominators: 3 * 5 = 15.
3. Simplify the fraction if possible. In this case, the fraction is already in its simplest form, so the result is 8/15.
Dividing Rational Numbers:
1. Keep the first rational number.
2. Change the division sign to a multiplication sign.
3. Flip the second rational number by swapping the numerator and denominator.
4. Follow the steps for multiplying rational numbers.
For example, let's say we want to divide the fraction 2/3 by 4/5:
1. Keep the first rational number: 2/3.
2. Change the division sign to a multiplication sign: 2/3 * (4/5).
3. Flip the second rational number: 2/3 * (5/4).
4. Multiply the numerators: 2 * 5 = 10.
5. Multiply the denominators: 3 * 4 = 12.
6. Simplify the resulting fraction if possible. In this case, the fraction is already in its simplest form, so the result is 10/12.
Remember that when simplifying fractions, you should reduce them to their simplest form by canceling out common factors between the numerator and denominator.