Find Equivalent Expressions for 160×6: Multiplication Practice

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

Look for expressions that use the distributive property or other algebraic properties. For example, $ (100+60) \times (3+3) $ shows the same structure as $ 160 \times 6 $ since 100+60=160 and 3+3=6.

Q: Why can't I just add instead of multiply?

Addition and multiplication are completely different operations! $ 160 + 6 = 166 $ but $ 160 \times 6 = 960 $. The operation symbol determines what calculation you perform.

Q: What's wrong with option (100×60)×6?

This expression equals $ 6000 \times 6 = 36000 $, which is much larger than our target of 960. The parentheses changed 100+60 to 100×60, creating a completely different calculation.

Q: How does the distributive property work here?

The distributive property lets us rewrite $ 160 \times 6 $ as $ (100+60) \times 6 $. We can also factor 6 as (3+3), giving us $ (100+60) \times (3+3) $ which equals the same result!

Q: Do I always need to follow order of operations?

Yes, always! Calculate what's in parentheses first, then multiplication and division from left to right, then addition and subtraction from left to right. This ensures you get the correct answer every time.

Distributive Property with Equivalent Expressions

Which equation is the same as the following?

$160\times6$

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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 We'll use the distributive law

00:06 We'll break down 160 into 100 plus 60

00:09 We'll break down 6 into 3 plus 3

00:15 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?

$160\times6$

Step-by-step solution

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

$160+6=166$

$(100\times60)\times6=6,000\times6$

$(100+60)+(3+3)=160+6$

$(100+60)\times(3+3)=160\times6$

Therefore, the answer is option D.

Final Answer

$(100+60)\times(3+3)$

Key Points to Remember

Essential concepts to master this topic

Rule: Distributive property states $(a+b) \times c = (a \times c) + (b \times c)$
Technique: Factor numbers: 160 = 100 + 60 and 6 = 3 + 3
Check: Calculate both expressions: $160 \times 6 = 960$ and $(100+60) \times (3+3) = 960$ ✓

Common Mistakes

Avoid these frequent errors

Confusing addition with multiplication in equivalent expressions
Don't think $160 + 6 = 166$ equals $160 \times 6 = 960$ ! Addition and multiplication give completely different results. Always check that your equivalent expression uses the same operations or applies properties correctly like the distributive property.

Practice Quiz

Test your knowledge with interactive questions

$12:(2\times2)=$

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 distributive property or other algebraic properties. For example, $(100+60) \times (3+3)$ shows the same structure as $160 \times 6$ since 100+60=160 and 3+3=6.

Why can't I just add instead of multiply?

Addition and multiplication are completely different operations! $160 + 6 = 166$ but $160 \times 6 = 960$ . The operation symbol determines what calculation you perform.

What's wrong with option (100×60)×6?

This expression equals $6000 \times 6 = 36000$ , which is much larger than our target of 960. The parentheses changed 100+60 to 100×60, creating a completely different calculation.

How does the distributive property work here?

The distributive property lets us rewrite $160 \times 6$ as $(100+60) \times 6$ . We can also factor 6 as (3+3), giving us $(100+60) \times (3+3)$ which equals the same result!

Do I always need to follow order of operations?

Yes, always! Calculate what's in parentheses first, then multiplication and division from left to right, then addition and subtraction from left to right. This ensures you get the correct answer every time.

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