Lesson 3: Interpret Numerical Expressions

Property

To compare expressions without calculating, identify the parts that are identical in both expressions. Then, reason about the parts that are different to determine which expression is larger. For positive numbers $A, B, C$ where $B > C$:

• $A + B > A + C$
• $A \times B > A \times C$
• $A - C > A - B$

Examples

Property

If $a$, $b$, and $c$ are real numbers, then:

This property allows you to multiply a sum by multiplying each addend separately and then adding the products. You 'distribute' the factor outside the parentheses to each term inside.

Examples

• Compare the expressions $6(8 + 7)$ and $6 \cdot 8 + 6 \cdot 7$. Using the distributive property, $6(8 + 7)$ can be rewritten as $6 \cdot 8 + 6 \cdot 7$. Since both expressions are the same, we know that $6(8 + 7) = 6 \cdot 8 + 6 \cdot 7$.

• Compare the expressions $4(5 + 3)$ and $4 \cdot 5 + 3 \cdot 3$. Using the distributive property, $4(5 + 3)$ can be rewritten as $4 \cdot 5 + 4 \cdot 3$. Since $4 \cdot 3 > 3 \cdot 3$, we know that $4(5 + 3) > 4 \cdot 5 + 3 \cdot 3$.