Find Equivalent Expressions: Solving 14×42 Multiplication

Q: Why does (10+4)×(40+2) equal 14×42?

Because 10+4 = 14 and 40+2 = 42! When you add the numbers inside each set of parentheses first, you get the original multiplication problem.

Q: What's wrong with option (10×4)+(40×2)?

This gives you 40 + 80 = 120, not 588! You're adding two separate multiplications instead of multiplying the sums. The distributive property doesn't work this way.

Q: Can I use this method with any two numbers?

Yes! You can break down any number into smaller parts. For example, $ 23\times35 = (20+3)\times(30+5) $. Just make sure the parts add up to your original numbers!

Q: What if I see 10×4×40×2 - is this the same?

No! This multiplies all four numbers together: $ 10\times4\times40\times2 = 3200 $, which is much larger than $ 14\times42 = 588 $.

Distributive Property with Expanded Form

Which equation is the same as the following?

$14\times42$

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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 use the distributive law

00:06 Let's break down 14 into 10 plus 4

00:11 Let's break down 42 into 40 plus 2

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?

$14\times42$

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).

$10+4+40+2=14+42=36$

$(10\times4)+(40\times2)=40+80$

$(10+4)\times(40+2)=14\times42$

$10\times4\times40\times2=40\times40\times2=160\times2=360$

Therefore, the answer is option C.

Final Answer

$(10+4)\times(40+2)$

Key Points to Remember

Essential concepts to master this topic

Rule: Factored form $(a+b)\times(c+d)$ equals expanded multiplication
Technique: Break down 14 as (10+4) and 42 as (40+2)
Check: Calculate both forms: $14\times42 = 588$ and $(10+4)\times(40+2) = 588$ ✓

Common Mistakes

Avoid these frequent errors

Confusing addition with multiplication in expanded forms
Don't think (10+4)+(40+2) equals 14×42 = wrong result of 56 instead of 588! Adding the parts gives you the sum of individual numbers, not their product. Always remember that (a+b)×(c+d) uses multiplication between the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why does (10+4)×(40+2) equal 14×42?

Because 10+4 = 14 and 40+2 = 42! When you add the numbers inside each set of parentheses first, you get the original multiplication problem.

What's wrong with option (10×4)+(40×2)?

This gives you 40 + 80 = 120, not 588! You're adding two separate multiplications instead of multiplying the sums. The distributive property doesn't work this way.

Can I use this method with any two numbers?

Yes! You can break down any number into smaller parts. For example, $23\times35 = (20+3)\times(30+5)$ . Just make sure the parts add up to your original numbers!

How do I know which option shows equivalent expressions?

Calculate the value of each option and compare to the original. Only expressions that give the same final answer are equivalent!

What if I see 10×4×40×2 - is this the same?

No! This multiplies all four numbers together: $10\times4\times40\times2 = 3200$ , which is much larger than $14\times42 = 588$ .

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