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

Distributive Property with Rectangle Area Applications

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

4+54+54+5777

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the rectangle's area using the distributive law
00:03 We'll use the formula for calculating rectangle area (side times side)
00:07 We'll substitute appropriate values according to the given data and solve for the area
00:14 We'll properly open the parentheses - 7 will multiply each factor
00:28 We'll calculate each multiplication separately and then add
00:39 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

4+54+54+5777

2

Step-by-step solution

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

We begin by writing the exercise according to the existing data:

7×(4+5) 7\times(4+5)

We then solve the exercise by using the distributive property, that is, we multiply 7 by each of the terms inside of the parentheses:

(7×4)+(7×5)= (7\times4)+(7\times5)=

Lastly we solve the exercise inside of the parentheses and obtain the following:

28+35=63 28+35=63

3

Final Answer

63

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Rectangle area equals length times width
  • Technique: Apply distributive property: 7×(4+5)=(7×4)+(7×5) 7 \times (4+5) = (7 \times 4) + (7 \times 5)
  • Check: Verify by calculating both ways: 7×9=63 7 \times 9 = 63 and 28+35=63 28 + 35 = 63

Common Mistakes

Avoid these frequent errors
  • Adding before distributing
    Don't solve (4+5) first to get 7×9 = 63 without showing distributive work! This skips the required method and doesn't demonstrate understanding of the distributive property. Always multiply 7 by each term inside the parentheses: (7×4) + (7×5).

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?
222777AAABBBCCCDDD

FAQ

Everything you need to know about this question

Why can't I just add 4+5 first to get 9, then multiply by 7?

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You could do that and get the right answer, but this problem specifically asks you to use the distributive property. The goal is to practice breaking apart the multiplication: 7×(4+5)=(7×4)+(7×5) 7 \times (4+5) = (7 \times 4) + (7 \times 5) .

How does the distributive property help with rectangle areas?

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When a rectangle's length is given as a sum like (4+5), you can think of it as two separate rectangles: one that's 4×7 and another that's 5×7. The total area is the sum of both smaller areas!

What if I forget to multiply by both numbers inside the parentheses?

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That's a common mistake! Remember: the distributive property means you distribute (give) the outside number to every number inside the parentheses. 7×(4+5) 7 \times (4+5) becomes (7×4)+(7×5) (7 \times 4) + (7 \times 5) .

Can I use the distributive property with subtraction too?

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Absolutely! If you had 7×(83) 7 \times (8-3) , it would become (7×8)(7×3)=5621=35 (7 \times 8) - (7 \times 3) = 56 - 21 = 35 . Just remember to keep the same operation sign.

How do I check if my distributive property work is correct?

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Calculate the answer both ways: First using the distributive property, then by adding/subtracting inside the parentheses first. Both methods should give you the same final answer!

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