Multiplying fractions in Grade 10 involves a straightforward process: you multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together. This gives you a new fraction, which you may then need to simplify.
The Process Explained
Here’s a step-by-step breakdown:
- Identify Numerators and Denominators: In a fraction, the numerator is the number above the fraction bar, and the denominator is the number below. For instance, in the fraction 3/4, 3 is the numerator and 4 is the denominator.
- Multiply Numerators: Multiply the numerators of all the fractions you are working with. For example, if you have to multiply 1/2 2/3, then you multiply 12 = 2
- Multiply Denominators: Next, multiply the denominators of all the fractions you are working with. Using the same example from step 2: 2/3 1/2, you then multiply 2 3 = 6
- Combine Results: Place the product of the numerators over the product of the denominators to get your new fraction. Using steps 2 and 3: 2/6
- Simplify (If Necessary): Reduce the resulting fraction to its lowest terms. This is achieved by finding the greatest common divisor of the numerator and denominator and then dividing each by that number. In the example, the greatest common divisor of 2 and 6 is 2, dividing each by 2: 2 / 2 = 1 and 6 / 2 = 3, so 2/6 becomes 1/3.
Example:
Let's say you need to multiply 3/4 and 2/5:
- Multiply numerators: 3 * 2 = 6
- Multiply denominators: 4 * 5 = 20
- Combine: 6/20
- Simplify: Both 6 and 20 can be divided by 2, resulting in 3/10.
Therefore: 3/4 * 2/5 = 3/10
Simplifying Fractions
Simplifying fractions is crucial for expressing them in their simplest form. A fraction is in its simplest form when the numerator and the denominator have no common factors other than 1. You can determine this by finding the greatest common factor (GCF) of the numerator and the denominator and then dividing both by that number.
Practical Insights
- Canceling: You may be able to "cancel" or divide out common factors between a numerator and a denominator before multiplying. This often makes the calculation simpler.
- Mixed Numbers: If you have mixed numbers, convert them into improper fractions before multiplying.
- Whole Numbers: Remember, a whole number can be written as a fraction with 1 as its denominator. For example, 5 is 5/1.
| Step | Action | Example: 2/3 * 3/4 |
|---|---|---|
| 1. Identify | Numerators & Denominators | 2 & 3 are numerators, 3 & 4 are denominators. |
| 2. Multiply Numerators | 2 * 3 = 6 | 2 * 3 = 6 |
| 3. Multiply Denominators | 3 * 4 = 12 | 3 * 4 = 12 |
| 4. Combine | Numerator from Step 2 over Denominator from Step 3 | 6/12 |
| 5. Simplify | Divide by greatest common factor (in this case, 6) | 6 / 6 = 1; 12 / 6 = 2, resulting in 1/2 |
By following these steps, multiplying fractions becomes a manageable and straightforward task.
