Equivalent Expression: Finding Another Form of 52×2×62

Q: How do I know which expression is equivalent without calculating everything?

Look for expressions that use the same operations in the same order. The correct answer $ (50+2)\times2\times(60+2) $ keeps all the multiplication signs, just breaks down 52 and 62.

Q: Why doesn't option A work if it's close to the original numbers?

Close isn't the same! Option A gives $ 50\times2\times60 = 6,000 $ while the original gives $ 52\times2\times62 = 6,448 $. Even small changes in numbers create big differences in results.

Q: What's the difference between equivalent expressions and approximations?

Equivalent expressions give exactly the same answer when calculated. Approximations give close but not identical results. This question asks for equivalent, so the answers must be exactly equal.

Q: How can I quickly spot wrong answers that mix operations?

Check the operation symbols first! If the original has multiplication (×) throughout, the equivalent expression should too. Options with + signs mixed in are usually wrong.

Q: Why do we need to follow order of operations here?

Order of operations ensures everyone gets the same answer from the same expression. Parentheses first, then multiplication from left to right - this gives us one correct result to compare.

Distributive Property with Numerical Expressions

Which equation is the same as the following?

$52\times2\times62$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the expression that represents the correct factorization of the exercise

00:03 Let's use the distributive law

00:06 Let's break down 52 into 50 plus 2

00:10 Let's break down 62 into 60 plus 2

00:16 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which equation is the same as the following?

$52\times2\times62$

Step-by-step solution

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

$50\times2\times60=100\times60=6,000$

$(50+2)+(2+60+2)=52+64$

$(2\times3)+60+60=6+120$

$(50+2)\times2\times(60+2)=52\times2\times62$

Therefore, the answer is option D.

Final Answer

$(50+2)\times2\times(60+2)$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiplication distributes over addition inside parentheses completely
Technique: (50+2)×2×(60+2) = 52×2×62 by distributive property
Check: Calculate both expressions to verify they equal 6,448 ✓

Common Mistakes

Avoid these frequent errors

Confusing addition and multiplication operations
Don't change multiplication to addition like (50+2)+(2+60+2) = wrong operation! This gives 116 instead of 6,448 because addition and multiplication are completely different operations. Always keep the original operation symbols when finding equivalent expressions.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

How do I know which expression is equivalent without calculating everything?

Look for expressions that use the same operations in the same order. The correct answer $(50+2)\times2\times(60+2)$ keeps all the multiplication signs, just breaks down 52 and 62.

Why doesn't option A work if it's close to the original numbers?

Close isn't the same! Option A gives $50\times2\times60 = 6,000$ while the original gives $52\times2\times62 = 6,448$ . Even small changes in numbers create big differences in results.

What's the difference between equivalent expressions and approximations?

Equivalent expressions give exactly the same answer when calculated. Approximations give close but not identical results. This question asks for equivalent, so the answers must be exactly equal.

How can I quickly spot wrong answers that mix operations?

Check the operation symbols first! If the original has multiplication (×) throughout, the equivalent expression should too. Options with + signs mixed in are usually wrong.

Why do we need to follow order of operations here?

Order of operations ensures everyone gets the same answer from the same expression. Parentheses first, then multiplication from left to right - this gives us one correct result to compare.

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