How do you multiply algebraic fractions Year 8?

To multiply algebraic fractions, you follow a simple two-step process, similar to multiplying regular numerical fractions:

1. Multiply the numerators together: This means multiplying the top parts of the fractions.
2. Multiply the denominators together: This means multiplying the bottom parts of the fractions.
3. Simplify the fraction if possible: Look for common factors in the numerator and denominator and cancel them out to get the simplest form.

Let's break this down with examples:

Example 1:

Multiply: (x/2) * (3/y)

• Step 1: Multiply the numerators: x * 3 = 3x
• Step 2: Multiply the denominators: 2 * y = 2y
• Step 3: Combine and simplify (if possible): 3x / 2y (In this case, it's already simplified).

Example 2:

Multiply: (4/a) * (a^2/8)

• Step 1: Multiply the numerators: 4 * a^2 = 4a^2
• Step 2: Multiply the denominators: a * 8 = 8a
• Step 3: Combine: 4a^2 / 8a
• Step 4: Simplify. Both the numerator and denominator have common factors: 4 and 'a'.
  • 4a^2 / 8a = (4 * a * a) / (4 * 2 * a)
  • Cancel out the common factors: a / 2

Example 3:

Multiply: (x+1)/5 * 2/(x+1)

• Step 1: Multiply the numerators: (x+1) * 2 = 2(x+1)
• Step 2: Multiply the denominators: 5 * (x+1) = 5(x+1)
• Step 3: Combine: 2(x+1) / 5(x+1)
• Step 4: Simplify. Notice that (x+1) is a common factor in both the numerator and denominator.
  • Cancel out the common factor: 2/5

In summary, according to the provided information: To multiply algebraic fractions, multiply the numerators together and multiply the denominators together, then simplify if you can.