Multiplying fractions might seem daunting at first, but it's actually a straightforward process once you grasp the fundamental concept: multiply straight across. This guide provides a comprehensive walkthrough, tackling common challenges and building your confidence in fraction multiplication.
Understanding the Basics: What Does "Multiply Straight Across" Mean?
When we say "multiply straight across," we mean multiplying the numerators (top numbers) together and the denominators (bottom numbers) together separately. Let's illustrate with an example:
(1/2) x (3/4) = (1 x 3) / (2 x 4) = 3/8
We multiplied the numerators (1 and 3) to get 3, and the denominators (2 and 4) to get 8. Therefore, the result of multiplying 1/2 and 3/4 is 3/8. Simple, right?
Step-by-Step Guide to Multiplying Fractions
Here's a step-by-step breakdown to make the process even clearer:
Step 1: Set up the Problem
Write down your fractions side-by-side, using the multiplication symbol (x) between them. For example: (2/5) x (1/3)
Step 2: Multiply the Numerators
Multiply the top numbers (numerators) together. In our example: 2 x 1 = 2
Step 3: Multiply the Denominators
Multiply the bottom numbers (denominators) together. In our example: 5 x 3 = 15
Step 4: Write the Result
Combine the results from steps 2 and 3 to form your answer. In our example: 2/15. This is the product of (2/5) and (1/3).
Handling Mixed Numbers: A Detailed Explanation
Mixed numbers (like 1 1/2) require an extra step before you can multiply straight across. You must first convert them into improper fractions.
Converting Mixed Numbers to Improper Fractions:
- Multiply the whole number by the denominator: In 1 1/2, multiply 1 (whole number) by 2 (denominator). This equals 2.
- Add the numerator: Add the result from step 1 to the numerator. 2 + 1 = 3.
- Keep the denominator: The denominator remains the same (2).
- Write the improper fraction: The improper fraction equivalent of 1 1/2 is 3/2.
Now you can multiply the improper fractions using the "multiply straight across" method.
Example: (1 1/2) x (2/3) becomes (3/2) x (2/3) = (3 x 2) / (2 x 3) = 6/6 = 1
Simplifying Your Answer: Reducing Fractions
Often, your answer will be an unsimplified fraction. To simplify, find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.
Example: If your answer is 12/18, the GCD of 12 and 18 is 6. Dividing both by 6 gives you 2/3. This is the simplified form.
Practice Makes Perfect: Exercises
Here are a few practice problems to help solidify your understanding:
- (1/4) x (2/5) = ?
- (3/7) x (1/3) = ?
- (2 1/2) x (4/5) = ?
- (5/6) x (3/10) = ?
By consistently practicing these steps and working through examples, you'll master multiplying fractions straight across with confidence! Remember to always simplify your answer to its lowest terms.
