Question

LESSON 11

Multiply & Divide Rational Numbers

Answer 1

[AI-generated answer — Bot GPT 3.5]

To multiply rational numbers, including fractions, decimals, and negative numbers, you can follow the steps below:

1. Multiply the numerators (the top numbers) together to find the new numerator.
2. Multiply the denominators (the bottom numbers) together to find the new denominator.
3. Simplify the newly obtained fraction, if possible, by reducing it to its simplest form.

Let's look at an example:

Example 1:
Multiply 3/4 and -2/5.

Step 1: Multiply the numerators together: 3 * -2 = -6.
Step 2: Multiply the denominators together: 4 * 5 = 20.
Step 3: Simplify the fraction: Since -6 and 20 have a common factor of 2, we can divide both by 2 to get -3/10.

Therefore, 3/4 multiplied by -2/5 is equal to -3/10.

To divide rational numbers, you can use a similar process:

1. Keep the first fraction as is.
2. Multiply the first fraction by the reciprocal (flipped version) of the second fraction.
3. Simplify the result, if possible.

Let's look at an example:

Example 2:
Divide -3/4 by 1/5.

Step 1: Keep the first fraction as is: -3/4
Step 2: Multiply the first fraction by the reciprocal of the second fraction: (-3/4) * (5/1) = -15/4.
Step 3: Simplify the fraction: Since -15 and 4 have a common factor of 1, the result is already in its simplest form.

Therefore, -3/4 divided by 1/5 is equal to -15/4.

Remember to always simplify your fractions when possible to get the final answer.

Answer 2

Multiply & Divide Rational Numbers Quick Check

Answer 3

[AI-generated answer — Bot GPT 3.5]

Sure! Please provide the rational numbers you would like to multiply and divide.

Answer 4

[AI-generated answer — Step-by-Step Bot]

To multiply and divide rational numbers, follow these steps:

1. Multiply rational numbers:
- Multiply the numerators of the fractions.
- Multiply the denominators of the fractions.
- Simplify the resulting fraction if possible.

For example, let's multiply the fractions 2/3 and 4/5.
- Multiply the numerators: 2 * 4 = 8
- Multiply the denominators: 3 * 5 = 15
- Simplify the fraction: 8/15

2. Divide rational numbers:
- Flip the second fraction (divisor) by swapping the numerator and denominator.
- Multiply the first fraction (dividend) by the flipped second fraction.
- Simplify the resulting fraction, if possible.

For example, let's divide the fractions 2/3 by 4/5.
- Flip the second fraction: 4/5 becomes 5/4.
- Multiply the first fraction by the flipped second fraction: 2/3 * 5/4 = 10/12.
- Simplify the fraction: 10/12 can be simplified to 5/6.

Remember to simplify the resulting fractions whenever possible.

Answer 5

[AI-generated answer — Explain Bot]

To multiply and divide rational numbers, follow these steps:

1. Begin by multiplying or dividing the numerators (top numbers) together.
2. Next, multiply or divide the denominators (bottom numbers) together.
3. Simplify the resulting fraction if possible, by reducing it to its simplest form.

Let's take a look at some examples:

Example 1: Multiply Rational Numbers
Multiply: 3/4 * 2/5

Step 1: Multiply the numerators: 3 * 2 = 6
Step 2: Multiply the denominators: 4 * 5 = 20

The resulting fraction is 6/20, which can be simplified. Both the numerator and denominator can be divided by 2, resulting in the simplified fraction of 3/10.

Example 2: Divide Rational Numbers
Divide: 2/3 ÷ 1/4

Step 1: Invert the second fraction (the one you are dividing by): 1/4 becomes 4/1.
Step 2: Multiply the first fraction by the inverted second fraction: 2/3 * 4/1 = 8/3.

The resulting fraction is 8/3, which is an improper fraction. To convert it to a mixed number, divide the numerator by the denominator: 8 ÷ 3 = 2 remainder 2. Therefore, the simplified form is 2 2/3.

Remember to always simplify your fractions whenever possible to express your answer in the simplest form.