Understanding Fractions
Fractions represent parts of a whole and consist of a numerator (top number) and a denominator (bottom number). Here’s how to work with the fractions provided:
1) Simplifying Fractions
- To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD).
- For example, for 3/5, since 3 and 5 have no common factors other than 1, it is already in simplest form.
2) Adding Fractions
- When adding fractions, ensure they have a common denominator. If they do not:
- Find the least common multiple (LCM) of the denominators.
- Convert each fraction to have this common denominator.
- Add the numerators and keep the common denominator.
- Simplify if necessary.
3) Subtracting Fractions
- The process is similar to addition. Make sure to find a common denominator, convert, and then subtract the numerators.
4) Multiplying Fractions
- To multiply fractions, multiply the numerators together and the denominators together.
- For example: (3/5) * (2/3) = (3*2)/(5*3) = 6/15, which simplifies to 2/5.
5) Dividing Fractions
- To divide by a fraction, multiply by its reciprocal.
- For example: (3/5) ÷ (2/3) = (3/5) * (3/2) = 9/10.
Example Problem: 3 - 2/9
- Convert 3 into a fraction: 3 = 27/9 (since 3 * 9 = 27).
- Now, perform the subtraction: 27/9 - 2/9 = (27 - 2)/9 = 25/9.
By following these steps, you can effectively work with fractions in various operations. Practice is key to mastering the concepts!