AI Tutor
If a pizza slice costs xx dollars and a drink costs 22, buying 33 combo meals means you multiply everything in your order by 33 to get 3x+63x + 6.
What if you only buy half an order, or your prices involve discounts and negative decimal rates? The exact same rule applies.

The Distributive Property

The distributive property states that multiplying a single term by a sum inside parentheses is equivalent to multiplying each term individually: a(b+c)=ab+aca(b + c) = ab + ac.
A rational number is any number that can be written as a fraction pq\frac{p}{q}, which includes whole numbers, decimals, and negative fractions.
How do we handle expressions when the multiplier outside is a fraction? Let's trace each step.

Distributing Fractions and Decimals

Consider the expression 23(6x+9)\frac{2}{3}(6x + 9). You multiply 23\frac{2}{3} by the first term, 6x6x, and then by the second term, 99.
Multiplying the first part gives 23⋅6x=123x=4x\frac{2}{3} \cdot 6x = \frac{12}{3}x = 4x, and the second part gives 23⋅9=183=6\frac{2}{3} \cdot 9 = \frac{18}{3} = 6.
What happens when our outside multiplier or inside terms carry negative signs?

Handling Negative Signs