Evaluate the Expression: Finding the Value of 14X3

Q: Why break 14 into (15-1) instead of other combinations?

Breaking 14 into (15-1) is strategic! Since 15×3 = 45 is easy to calculate mentally, this decomposition creates the cleanest equivalent expression matching the answer choices.

Q: How do I know which answer choice to pick?

Use the distributive property step by step: $ (15-1) \times 3 = 15 \times 3 - 1 \times 3 = 15 \times 3 - 3 $. This matches option C exactly!

Q: Can I use different number breakdowns for 14?

Yes! You could try 14 = 10+4 or 14 = 7+7, but none of these create expressions that match the given answer choices. The (15-1) breakdown is specifically chosen to work.

Q: Why does the distributive property work here?

The distributive property states: $ a(b+c) = ab + ac $. It works the same way with subtraction: $ a(b-c) = ab - ac $. This fundamental property makes our decomposition valid!

Distributive Property with Subtraction Decomposition

Which expression is the exercise 14X3equal to?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the equivalent expression together.

00:09 We'll use an important tool called the distributive law.

00:14 Now, let's break it down. Think of fourteen as fifteen minus one.

00:19 We'll multiply each part, then subtract to simplify.

00:31 And that's how we solve this problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which expression is the exercise 14X3equal to?

Step-by-step solution

We begin by breaking down the 14 into a subtraction exercise:

$(15-1)\times3=$

Next we multiply each of the numbers inside of the parentheses by 3:

$(15\times3)-(1\times3)=$

We can already discard option A and option D since the solution must contain 15x3.

Lastly we solve the parenthesis on the right side of the equation and obtain the following:

$15\times3-3$

Therefore, the answer is C.

Final Answer

15X3 and we subtract 3

Key Points to Remember

Essential concepts to master this topic

Decomposition Rule: Break numbers into easier forms like (15-1) for 14
Distributive Property: Apply multiplication to each term: (15-1)×3 = 15×3-1×3
Verification: Check that 15×3-3 = 45-3 = 42 = 14×3 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute multiplication to all terms
Don't multiply just the first term: (15-1)×3 ≠ 15×3-1 = 44! This ignores the distributive property and gives the wrong result. Always multiply each term inside parentheses: (15-1)×3 = 15×3-1×3.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why break 14 into (15-1) instead of other combinations?

Breaking 14 into (15-1) is strategic! Since 15×3 = 45 is easy to calculate mentally, this decomposition creates the cleanest equivalent expression matching the answer choices.

How do I know which answer choice to pick?

Use the distributive property step by step: $(15-1) \times 3 = 15 \times 3 - 1 \times 3 = 15 \times 3 - 3$ . This matches option C exactly!

Can I use different number breakdowns for 14?

Yes! You could try 14 = 10+4 or 14 = 7+7, but none of these create expressions that match the given answer choices. The (15-1) breakdown is specifically chosen to work.

What if I just calculate 14×3 directly?

Direct calculation gives you 42, which is correct! But this question asks you to find an equivalent expression, not just the numerical answer. Practice these decomposition skills for algebraic thinking.

Why does the distributive property work here?

The distributive property states: $a(b+c) = ab + ac$ . It works the same way with subtraction: $a(b-c) = ab - ac$ . This fundamental property makes our decomposition valid!

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