Solve (2+1)×(60+2): Finding Equivalent Expressions

Q: Do I need to expand this using the distributive property?

No! This problem asks for an equivalent expression, not to expand or solve completely. Just simplify each parenthesis: $ (2+1) = 3 $ and $ (60+2) = 62 $.

Q: What's the difference between 3×62 and 3+(60+2)?

Huge difference! $ 3 \times 62 = 186 $ while $ 3 + (60+2) = 65 $. The first multiplies, the second adds. Always check the operation symbol!

Q: How do I know which parentheses to solve first?

It doesn't matter which you solve first! Both $ (2+1) $ and $ (60+2) $ are independent - solve each one separately, then multiply the results.

Q: Can I check my answer by calculating the full result?

Absolutely! Calculate $ 3 \times 62 = 186 $ and verify that $ (2+1) \times (60+2) $ also equals 186. This confirms your equivalent expression is correct!

Simplifying Parentheses with Multiplication

Which equation is the same as the following?

$(2+1)\times(60+2)$

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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 decomposition of the exercise

00:03 Let's solve what's inside the parentheses to find the expression

00:09 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?

$(2+1)\times(60+2)$

Step-by-step solution

Let's keep in mind that we have been given a multiplication exercise between two parentheses.

Each set of parentheses represents a number. If we solve the exercises within the parentheses, we will reveal what the two numbers are between which there is a multiplication exercise:

$2+1=3$

$60+2=62$

That is, the multiplication exercise we obtained is:

$3\times62$

Final Answer

$3\times62$

Key Points to Remember

Essential concepts to master this topic

Order Rule: Always solve inside parentheses first before multiplying
Technique: Calculate (2+1)=3 and (60+2)=62 separately first
Check: Final expression 3×62 equals original (2+1)×(60+2) ✓

Common Mistakes

Avoid these frequent errors

Converting multiplication to addition
Don't change (2+1)×(60+2) to 3+(60+2) = 65! This confuses multiplication with addition operations. Always keep the multiplication sign and calculate (2+1)=3, then multiply by (60+2)=62.

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 all the numbers together?

Because the × symbol means multiplication, not addition! You must first solve what's in each set of parentheses, then multiply those results together.

Do I need to expand this using the distributive property?

No! This problem asks for an equivalent expression, not to expand or solve completely. Just simplify each parenthesis: $(2+1) = 3$ and $(60+2) = 62$ .

What's the difference between 3×62 and 3+(60+2)?

Huge difference! $3 \times 62 = 186$ while $3 + (60+2) = 65$ . The first multiplies, the second adds. Always check the operation symbol!

How do I know which parentheses to solve first?

It doesn't matter which you solve first! Both $(2+1)$ and $(60+2)$ are independent - solve each one separately, then multiply the results.

Can I check my answer by calculating the full result?

Absolutely! Calculate $3 \times 62 = 186$ and verify that $(2+1) \times (60+2)$ also equals 186. This confirms your equivalent expression is correct!

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