Solve the Expression: Finding the Equivalent Form of 31-15

Q: Why do we break 31 into 30 + 1 instead of other combinations?

Breaking 31 into 30 + 1 makes mental math easier because 30 is a round number. While 31 = 20 + 11 is also correct, 30 - 15 is much simpler to calculate than 20 - 15!

Q: How do I know which number to decompose?

Usually decompose the larger number in subtraction problems. Look for ways to make round numbers (like 30, 40, 50) that are easier to work with mentally.

Q: What if I get confused about the signs?

Remember: when you have $ (a + b) - c $, it becomes $ a - c + b $. The subtraction only affects the first part, and the + b stays positive!

Q: Are there other equivalent expressions for 31 - 15?

Yes! You could also write it as $ 32 - 15 - 1 $ or $ 31 - 10 - 5 $. The key is that all equivalent expressions must equal 16 when calculated.

Q: How can I check if two expressions are equivalent?

Calculate both! If they give the same final answer, they're equivalent. For example: $ 31 - 15 = 16 $ and $ 30 - 15 + 1 = 16 $, so they're equivalent.

Expression Equivalence with Decomposition Strategies

Which expression is equivalent to the given equation?

$31-15=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which expression is equivalent to the given equation?

$31-15=$

Step-by-step solution

To solve this problem, we aim to find an expression equivalent to the given $31 - 15$ .

Let's consider breaking down the number 31 as $30 + 1$ . Thus, we can rewrite the subtraction expression:

Step 1: Start with the original expression: $31 - 15$ .
Step 2: Rewrite 31 as $30 + 1$ , so the expression becomes $(30 + 1) - 15$ .
Step 3: Apply the subtraction to both terms: $30 - 15 + 1$ .

Thus, the equivalent expression is $30 - 15 + 1$ .

We confirm that this results in the same value as $31 - 15$ as both simplify to 16.

Therefore, the correct expression equivalent to $31-15$ is $30 - 15 + 1$ .

Final Answer

$30-15+1$

Key Points to Remember

Essential concepts to master this topic

Decomposition Rule: Break numbers into convenient parts for easier calculation
Technique: Rewrite 31 as (30 + 1), then distribute: 30 - 15 + 1
Check: Both original 31 - 15 = 16 and equivalent 30 - 15 + 1 = 16 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly applying distributive property with subtraction
Don't write (30 + 1) - 15 as 30 - 15 - 1 = 14! This changes the sign incorrectly and gives the wrong result. Always remember that (a + b) - c = a - c + b, so (30 + 1) - 15 = 30 - 15 + 1.

Practice Quiz

Test your knowledge with interactive questions

Add fifty units to the number 31.

What is the resulting number?

FAQ

Everything you need to know about this question

Why do we break 31 into 30 + 1 instead of other combinations?

Breaking 31 into 30 + 1 makes mental math easier because 30 is a round number. While 31 = 20 + 11 is also correct, 30 - 15 is much simpler to calculate than 20 - 15!

How do I know which number to decompose?

Usually decompose the larger number in subtraction problems. Look for ways to make round numbers (like 30, 40, 50) that are easier to work with mentally.

What if I get confused about the signs?

Remember: when you have $(a + b) - c$ , it becomes $a - c + b$ . The subtraction only affects the first part, and the + b stays positive!

Are there other equivalent expressions for 31 - 15?

Yes! You could also write it as $32 - 15 - 1$ or $31 - 10 - 5$ . The key is that all equivalent expressions must equal 16 when calculated.

How can I check if two expressions are equivalent?

Calculate both! If they give the same final answer, they're equivalent. For example: $31 - 15 = 16$ and $30 - 15 + 1 = 16$ , so they're equivalent.

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Solve the Expression: Finding the Equivalent Form of 31-15

Expression Equivalence with Decomposition Strategies

❤️ Continue Your Math Journey!

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we break 31 into 30 + 1 instead of other combinations?

How do I know which number to decompose?

What if I get confused about the signs?

Are there other equivalent expressions for 31 - 15?

How can I check if two expressions are equivalent?

🌟 Unlock Your Math Potential

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