Rewrite Expressions in Equivalent Forms

Imagine a shirt costs a dollars. There's a five-percent sales tax on top. What's the total cost?

We can write the total as a plus zero point zero five a.

Both terms have an a — they're like terms. Can we combine them into one?

Here's the trick: a by itself means the same thing as one a.

So a plus zero point zero five a is the same as one a plus zero point zero five a.

Now add the coefficients: one plus zero point zero five equals one point zero five.

That gives us a single, simpler term: one point zero five a.

This new form reveals something powerful — a five-percent increase is the same as multiplying by one point zero five.

Quick check. If the shirt costs twenty dollars, then one point zero five times twenty is twenty-one dollars.

Equivalent forms help us see meaning. a plus zero point zero five a equals one point zero five a.