To multiply a fraction by an integer, you simply multiply the numerator (the top number) of the fraction by the integer, while keeping the denominator (the bottom number) the same.
Understanding the Process
Let's break down the process with a few examples and practical insights:
Basic Principle
The core idea is that multiplying a fraction by a whole number is like adding that fraction to itself multiple times. For instance, multiplying a fraction by 4 is equivalent to adding that fraction to itself four times.
- Key Step: Multiply the integer by the numerator only.
- Keep: The denominator of the fraction stays the same.
Steps for Multiplication
- Identify the Fraction and Integer: Note the fraction and integer you wish to multiply.
- Multiply Numerator by Integer: Multiply the numerator of the fraction by the integer.
- Keep the Denominator: Retain the original denominator.
- Simplify (if possible): Reduce the fraction to its simplest form, if necessary.
Examples
| Problem | Step 1: Numerator x Integer | Step 2: Resulting Fraction | Simplified? | Final Answer |
|---|---|---|---|---|
| (1/4) x 3 | 1 x 3 = 3 | 3/4 | No | 3/4 |
| (2/5) x 2 | 2 x 2 = 4 | 4/5 | No | 4/5 |
| (3/8) x 4 | 3 x 4 = 12 | 12/8 | Yes | 3/2 (or 1 1/2) |
| (7/10) x 4 | 7 x 4 = 28 | 28/10 | Yes | 14/5 (or 2 4/5) |
Practical Insights
- Think of Parts: Consider a fraction as representing a number of equal parts of a whole. Multiplying the numerator by an integer increases the total number of those parts while keeping the size of each part (the denominator) constant.
- Visual Aid: Imagine having a pizza cut into slices (the denominator), and you have a certain number of those slices (the numerator). Multiplying by an integer means taking several helpings of that number of slices.
- Reference Example: As shown in the provided video, if you have seven-tenths (7/10) and multiply by four, you get 28 tenths (28/10) because 7 x 4 = 28.
Conclusion
Multiplying fractions by integers is a straightforward process of multiplying the integer by the numerator and keeping the denominator unchanged. Always remember to simplify the fraction if possible for the final answer.
