Equivalent Expression: Finding Alternative Forms of 3×83

Distributive Property with Parenthetical Expressions

Which equation is the same as the following?

3×83 3\times83

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the expression representing the correct decomposition of the exercise
00:03 Let's use the distributive law
00:06 Let's break down 3 into 2 plus 1
00:09 Let's break down 83 into 80 plus 3
00:13 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

Which equation is the same as the following?

3×83 3\times83

2

Step-by-step solution

We solve each of the options and keep in mind the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right).

a.

3×8×3=24×3=72 3\times8\times3=24\times3=72

b.

(2+1)×(80+3)=3×83 (2+1)\times(80+3)=3\times83

c.

3+(80+3)=3+83 3+(80+3)=3+83

d.

3+83=86 3+83=86

Therefore, the answer is option B.

3

Final Answer

(2+1)×(80+3) (2+1)\times(80+3)

Key Points to Remember

Essential concepts to master this topic
  • Equivalence Rule: Expressions must produce the same numerical value
  • Technique: (2+1)×(80+3)=3×83 (2+1)\times(80+3) = 3\times83 using distributive property
  • Check: Calculate both expressions: 3×83=249 3\times83 = 249 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing multiplication with addition when breaking down expressions
    Don't think 3×83 3\times83 equals 3+83=86 3+83 = 86 ! This changes the operation from multiplication to addition, giving a completely different result. Always preserve the original operation when finding equivalent expressions.

Practice Quiz

Test your knowledge with interactive questions

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FAQ

Everything you need to know about this question

How do I know if two expressions are equivalent?

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Calculate both expressions and check if they give the same answer! For example, 3×83=249 3\times83 = 249 and (2+1)×(80+3)=3×83=249 (2+1)\times(80+3) = 3\times83 = 249 .

Why is 3×8×3 3\times8\times3 wrong?

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Because 3×8×3=72 3\times8\times3 = 72 , but 3×83=249 3\times83 = 249 . The numbers look similar, but breaking 83 into 8 and 3 changes the value completely!

What's the difference between 3×83 3\times83 and 3+83 3+83 ?

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Multiplication vs Addition! 3×83=249 3\times83 = 249 (much larger), while 3+83=86 3+83 = 86 (much smaller). The operation symbol completely changes the result.

How does (2+1)×(80+3) (2+1)\times(80+3) work?

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First, solve inside parentheses: (2+1)=3 (2+1) = 3 and (80+3)=83 (80+3) = 83 . Then multiply: 3×83=249 3\times83 = 249 . This is the distributive property in reverse!

Do I always need to calculate to check equivalence?

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Yes, when in doubt! While you can sometimes see patterns, calculating both expressions is the most reliable way to verify they're truly equivalent.

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