Solve (35+4)×(10+5): Order of Operations Practice

Distributive Property with Parentheses

(35+4)×(10+5)= (35+4)\times(10+5)=

❤️ 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
00:00 Solve
00:03 Let's make sure to open parentheses properly
00:07 Each term in parentheses will multiply with each term in the second parentheses
00:27 Let's solve each multiplication and then sum
00:42 Let's solve one addition operation at a time
00:55 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(35+4)×(10+5)= (35+4)\times(10+5)=

2

Step-by-step solution

We begin by opening the parentheses using the extended distributive property to create a long addition exercise:

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

We 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:

(35×10)+(35×5)+(4×10)+(4×5)= (35\times10)+(35\times5)+(4\times10)+(4\times5)=

We solve each of the exercises within parentheses:

350+175+40+20= 350+175+40+20=

We solve the exercise from left to right:

350+175=525 350+175=525

525+40=565 525+40=565

565+20=585 565+20=585

3

Final Answer

585

Key Points to Remember

Essential concepts to master this topic
  • Rule: Solve operations inside parentheses before multiplying
  • Technique: Use distributive property: (35+4)×(10+5) = 35×10 + 35×5 + 4×10 + 4×5
  • Check: Verify by calculating step-by-step: 350+175+40+20 = 585 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring order of operations and multiplying before adding
    Don't multiply 35×10 first without solving parentheses = wrong sequence! This violates PEMDAS rules and creates calculation errors. Always solve what's inside parentheses completely before doing any multiplication.

Practice Quiz

Test your knowledge with interactive questions

\( 140-70= \)

FAQ

Everything you need to know about this question

Should I solve the parentheses first or use the distributive property?

+

Both methods work! You can either solve (35+4)=39 (35+4) = 39 and (10+5)=15 (10+5) = 15 first, then multiply 39×15 39 \times 15 , or use the distributive property as shown in the solution.

Why does the distributive property give four multiplication problems?

+

When you have (a+b)×(c+d) (a+b) \times (c+d) , each term in the first parentheses must multiply each term in the second parentheses. That gives you four products: ac + ad + bc + bd.

Is there a faster way to solve this?

+

Yes! You can simplify first: (35+4)=39 (35+4) = 39 and (10+5)=15 (10+5) = 15 , then just multiply 39×15=585 39 \times 15 = 585 . This is often quicker than using the distributive property.

How do I remember which operations to do first?

+

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Parentheses always come first!

What if I get a different answer than 585?

+

Double-check your arithmetic! Make sure you solved both parentheses correctly: 35+4=39 35+4=39 and 10+5=15 10+5=15 , then 39×15=585 39 \times 15 = 585 .

Can I use a calculator for this problem?

+

While calculators help, it's important to understand the steps! Practice doing these by hand first, then use a calculator to verify your answer.

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations