When you solve linear equations, especially ones that have fractions or decimals, using fraction multiplication is really helpful. Let’s break it down step by step!

Why It’s Important

Using fraction multiplication helps remove fractions from an equation. This makes it easier to work with.

For example, let’s look at this equation:

$$\frac{1}{2}x + 3 = 5$$

Steps to Solve It

1. Get Rid of the Fraction: First, we need to multiply every part of the equation by the bottom number of the fraction (the denominator). In this case, we multiply by 2:

   $$2 \left(\frac{1}{2}x\right) + 2(3) = 2(5)$$

   This simplifies to:

   $$x + 6 = 10$$

2. Isolate the Variable: Next, we want to find out what $x$ is. So, we subtract 6 from both sides:

   $$x = 10 - 6$$

   Now we find that $x = 4$.

Working with Decimal Equations

Fraction multiplication also helps when we deal with decimals. For example:

$$0.4x + 1.2 = 2.8$$

To get rid of the decimal, we can multiply everything by 10:

$$10(0.4x) + 10(1.2) = 10(2.8)$$

This becomes:

$$4x + 12 = 28$$

Now, we can isolate $x$ just like we did before!

Wrapping Up

In short, fraction multiplication makes solving equations easier. It helps us get rid of tricky fractions and decimals, so we can solve the problems faster and more simply.