Calculate Rectangle Area: Using Distributive Property with (9+4)(3+2)

Q: Why can't I just add 9+4 and 3+2 first, then multiply?

You absolutely can do that! Both methods work: $ (3+2)(9+4) = 5 \times 13 = 65 $ or using distributive property gives the same answer. The distributive property just shows you why multiplication works this way.

Q: Do I have to multiply every single term when using distributive property?

Yes! Each term in the first parentheses must multiply each term in the second. For $ (3+2)(9+4) $, you get: 3×9 = 273×4 = 122×9 = 182×4 = 8 Then add: 27+12+18+8 = 65

Q: How do I remember which dimensions are length and width?

For area calculations, it doesn't matter which you call length or width! Rectangle area is always the same: one dimension times the other dimension. The labels are just for organization.

Distributive Property with Rectangle Dimensions

Calculate the area of the rectangle below using the distributive property.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's find the area of the rectangle using the distributive law.

00:17 We'll use the formula: Area equals length times width.

00:21 Remember, pay attention to the parentheses!

00:25 We're using the distributive law, which means we multiply each term by each term.

00:42 Alright, let's calculate these products together.

01:00 Now, it's time to add them up.

01:06 And that's how we find the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the area of the rectangle below using the distributive property.

Step-by-step solution

The area of a rectangle is equal to its length multiplied by the width.

We begin by writing the following exercise using the data shown in the figure:

$(3+2)\times(9+4)=$

We solve the exercise using the distributive property.

That is:

We multiply the first term of the left parenthesis by the first term of the right parenthesis.

We then multiply the first term of the left parenthesis by the second term of the right parenthesis.

Now we multiply the second term of the left parenthesis by the first term of the left parenthesis.

Finally, we multiply the second term of the left parenthesis by the second term of the right parenthesis.

In the following way:

$(3\times9)+(3\times4)+(2\times9)+(2\times4)=$

We solve each of the exercises within the parentheses:

$27+12+18+8=$

Lastly we solve the exercise from left to right:

$27+12=39$

$39+18=57$

$57+8=65$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle area equals length times width using distributive property
Technique: Expand (3+2)(9+4) = 3×9 + 3×4 + 2×9 + 2×4
Check: Verify by calculating (3+2)(9+4) = 5×13 = 65 ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't calculate (3+2) + (9+4) = 5 + 13 = 18! This gives perimeter, not area. Always multiply length times width for rectangle area: (3+2) × (9+4) = 5 × 13 = 65.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why can't I just add 9+4 and 3+2 first, then multiply?

You absolutely can do that! Both methods work: $(3+2)(9+4) = 5 \times 13 = 65$ or using distributive property gives the same answer. The distributive property just shows you why multiplication works this way.

Do I have to multiply every single term when using distributive property?

Yes! Each term in the first parentheses must multiply each term in the second. For $(3+2)(9+4)$ , you get:

3×9 = 27
3×4 = 12
2×9 = 18
2×4 = 8

Then add: 27+12+18+8 = 65

What if I make an arithmetic mistake in one of the multiplications?

Double-check each multiplication step! Common errors are 3×4=11 or 2×9=16. Write out each step clearly and use the simple method (5×13=65) to verify your distributive property answer.

Is the distributive property just making the problem harder?

It might seem harder now, but understanding distributive property helps you with algebra later! When you see expressions like $(x+3)(x+2)$ , you'll know exactly how to expand them using the same pattern.

How do I remember which dimensions are length and width?

For area calculations, it doesn't matter which you call length or width! Rectangle area is always the same: one dimension times the other dimension. The labels are just for organization.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Algebraic Technique questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Calculate Rectangle Area: Using Distributive Property with (9+4)(3+2)

Distributive Property with Rectangle Dimensions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just add 9+4 and 3+2 first, then multiply?

Do I have to multiply every single term when using distributive property?

What if I make an arithmetic mistake in one of the multiplications?

Is the distributive property just making the problem harder?

How do I remember which dimensions are length and width?

🌟 Unlock Your Math Potential

More Questions

Area of a Rectangle

Rectangle Area: Identifying Equivalent Expressions for (3x+5)(x+9)

Find Time Expression: Painting a 7X × (30X+4) Meter Fence

Calculate Rectangular Prism Volume Using Areas of 15 cm² and 24 cm²

Calculate Cuboid Volume: Rectangle Base 12 cm² with Height 3

The Distributive Property for 7th Grade

Solve for X: Rectangle with Area 78 cm² and Width 3 cm

Calculate Building Volume: Find Expression for 21×15×(14+30X) Meters³

Calculate Rectangle Area: Using Distributive Property with (4+5) × 7

Solve the Two-Digit Multiplication: 29 × 28

Extended Distributive Property

Calculate the Area of a Rectangle: Visual Geometry Problem

Calculate Area: Finding (23x+12)×(20x+7) for a Canvas

Solve (a+3a)(5+2)=112: Find the Value of Variable a

Solve (9+17x)×(6+1)=420: Find the Value of X