How to Use Area Models and the Distributive Property to Multiply?
Step 1: Understand the Area Model:
Step 2: Break down the Numbers:
Step 3: Use the Distributive Property:
Step 4: Draw the Area Model:
Step 5: Multiply and Add:
Using Area Models and the Distributive Property to Multiply – Example 1:
Solution:
\(20 × 4 = 80\)
Tutor-style math help
Expanding Expressions with the Distributive Property: what to notice and how to work it
Expressions skill
Expression problems ask you to translate, simplify, or evaluate. The safest approach is to turn words into symbols one phrase at a time.
What to notice first
Modeling questions are about choosing the correct type of change: constant addition, repeated multiplication, or a quadratic pattern.
Common student mistake
Do not decide from one pair of values. Check whether the change stays constant or the multiplier stays constant.
Key formulas and cues
\(\text{twice }x=2x\)
\(\text{5 less than }x=x-5\)
\(\text{evaluate means substitute first}\)
A reliable path
- Name the variableChoose a letter for the unknown quantity.
- Translate in chunksTurn each phrase into an operation, keeping order words attached.
- Simplify or evaluateCombine like terms or substitute the given value.
Worked examples
Translate a phrase
Example: Seven more than twice a number
- Let the number be x.
- Twice the number is 2x.
- Seven more than that adds 7.
Answer: \(2x+7\)
Evaluate carefully
Example: \(3x-4\) when \(x=5\)
- Replace x with 5.
- Multiply before subtracting.
- Compute 15 – 4.
Answer: \(11\)
Try one before moving on
Try: Write 'three less than four times a number.'
Answer: \(4x-3\).
Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.
x
Expanding Expressions with the Distributive Property: pop-up practice
Answer these quick questions, then use the feedback to decide which part of the lesson to review.
Choose an answer to begin.
1. Translate '5 less than n.'
2. Evaluate \(2x+1\) when \(x=6\).
3. Like terms must have the same:
\(4 × 4 = 16\)
\(80 + 16 = 96\)
Therefore, \(24 × 4 = 96\).
Original price was: $109.99.$54.99Current price is: $54.99.
Original price was: $109.99.$54.99Current price is: $54.99.
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