Outline the steps necessary to multiply two numbers when one is a fraction and the other an integer, to understand the concept of multiplication with mixed number types.
user
Sure, here are the steps to multiply a fraction and an integer:

1. **Simplify**: If the numerator and denominator of the fraction have a common factor, simplify by dividing both by that factor. This is known as the "canceling" property. For example, 10/20 simplifies to 1/2.

2. **Numerator x Integer**: Multiply the numerator of the fraction by the integer.

3. **Product x Denominator**: Multiply the product from step 2 by the denominator of the fraction.

4. **Fractions to a Mixed Number**: If the product from step 3 has a numerator greater than the denominator, it is a mixed number. In this case, divide the numerator by the denominator to get the whole number part, and place the remainder over the same denominator for the fraction part.

5. **Simplify**: If necessary, simplify the mixed number by finding a common denominator and combining like terms.

Here's a worked-out example:

Multiply 1/4 by 12.

1. **Simplify**: 12 is already in lowest terms, so we move to the next step.

2. **Numerator x Integer**: 1 * 12 = 12

3. **Product x Denominator**: 12 * 4 = 48

4. **Fractions to a Mixed Number**: Since the product is greater than the denominator, we have a mixed number. 48 divided by 4 is 12 with a remainder of 0. So, the mixed number is 12 last quart.

5. **Simplify**: There's no need for simplification here, as the remainder is zero.

So, 1/4 * 12 is equal to 12 last quart or simply 12 and 1/4, if simplified further.
assistant
Outline the steps necessary to multiply two numbers when one is a fraction and the other an integer, to understand the concept of multiplication with mixed number types.
user
1. Identify the fraction and the integer: The first step is to identify which number is a fraction and which one is an integer.

2. Convert the integer into a fraction: To multiply a fraction by an integer, you need to convert the integer into a fraction. You can do this by placing the integer over 1 (since any number divided by 1 remains unchanged). For example, if your integer is 5, it would be written as a fraction like this: 5/1.

3. Multiply the numerators: Now that both numbers are in fraction form, multiply the numerators (top numbers) of the two fractions together. This will give you the new numerator for your answer.

4. Multiply the denominators: Next, multiply the denominators (bottom numbers) of the two fractions together. This will give you the new denominator for your answer.

5. Simplify the resulting fraction (if necessary): If the resulting fraction can be simplified or reduced, divide both the numerator and denominator by their greatest common factor.

6. Write your answer as a simplified fraction or mixed number: Once you have simplified the resulting fraction, write your answer either as a proper fraction or as a mixed number, whichever is appropriate based on the problem's context.

Here's an example using the numbers 3 (integer) and 2/5 (fraction):

1. Identify the fraction and the integer: 3 and 2/5
2. Convert the integer into a fraction: 3 becomes 3/1
3. Multiply the numerators: 3 * 2 = 6 (new numerator)
4. Multiply the denominators: 1 * 5 = 5 (new denominator)
5. Simplify the resulting fraction: The resulting fraction is already simplified, as 6 and 5 have no common factors.
6. Write your answer as a simplified fraction: 6/5

Since 6/5 is an improper fraction, you may want to convert it into a mixed number: 6/5 = 1 1/5. So, the final answer is 1 1/5.
assistant