Two ways to simplify
There are two equivalent ways to simplify an expression like 6(20 + 5): either add inside the parentheses first (6 times 25 = 150) or distribute the 6 to each term (6 times 20 + 6 times 5 = 120 + 30 = 150). Both methods are valid and produce the same answer. This Grade 7 math skill from Saxon Math, Course 2 illustrates the Distributive Property in both directions and helps students choose the most efficient approach for a given expression — a flexibility essential for mental math and algebraic manipulation.
Key Concepts
Property An expression like $6(20 + 5)$ can be simplified two ways: add first, $6(25)$, or distribute first, $6 \cdot 20 + 6 \cdot 5$.
Examples Simplify $6(20+5)$: Method 1 is $6(25)=150$. Method 2 is $6 \cdot 20 + 6 \cdot 5 = 120+30=150$. Simplify $6(20 5)$: Method 1 is $6(15)=90$. Method 2 is $6 \cdot 20 6 \cdot 5 = 120 30=90$.
Explanation It's like having two different cheat codes for the same level! You can either handle the operation inside the parentheses first or unleash the Distributive Property to break the problem apart. No matter which path you choose, you'll always arrive at the same correct answer.
Common Questions
What are the two ways to simplify an expression like 6(20 + 5)?
Method 1: Add inside the parentheses first — 6(25) = 150. Method 2: Distribute the 6 to each term — 6 x 20 + 6 x 5 = 120 + 30 = 150. Both give the same answer.
What is the Distributive Property?
The Distributive Property states that a(b + c) = ab + ac. You can multiply the outside number by each term inside the parentheses and add the results.
When is it more efficient to add inside first vs distribute?
If the numbers inside add to a convenient value (like 25), adding first is often faster. If the numbers inside are awkward to add, distributing may be easier (especially in algebra with variables).
Why do both methods give the same answer?
The Distributive Property guarantees equivalence: a(b + c) = ab + ac is always true. This mathematical law ensures both approaches are valid.
When do students learn the two ways to simplify?
The Distributive Property is introduced in Grade 3-5 and formalized in Grade 7. Saxon Math, Course 2 covers it in Chapter 3 as a mental math and algebraic thinking tool.
How does the Distributive Property apply to algebra?
In algebra, 3(x + 4) must be distributed as 3x + 12 because you cannot add x and 4 directly. The distributive method is the ONLY option when variables are involved.
What is a common mistake with the Distributive Property?
Students sometimes distribute to only the first term: 6(20 + 5) = 120 + 5 = 125 (wrong). Always multiply the outside factor by EVERY term inside the parentheses.