Solve the Expression: Finding the Equivalent Value of 78-9

Subtraction Decomposition with Equivalent Expressions

Which expression is equivalent to the given equation?

789= 78-9=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Which expression is equivalent to the given equation?

789= 78-9=

2

Step-by-step solution

To find an equivalent expression to 789 78 - 9 , we'll follow these steps:

  • Step 1: Calculate the original expression 789 78 - 9 .
    The result of this subtraction is 69 69 .

  • Step 2: Identify an expression that will also equal 69 69 using equivalent smaller subtractions.

  • Step 3: Examine 9 9 and represent it as 8+1 8 + 1 . Hence, the original expression can be rewritten as 7881 78 - 8 - 1 .
    Both: 789=697881=69 \begin{aligned} &78 - 9 = 69 \\ &78 - 8 - 1 = 69 \end{aligned} .

  • Step 4: Compare the stepwise approach with the provided choices.

Among the options provided, 7881 78-8-1 is equivalent to 789 78-9 as both yield the same result of 69 69 .

Therefore, the expression that is equivalent to 789 78 - 9 is 7881 78 - 8 - 1 .

3

Final Answer

7881 78-8-1

Key Points to Remember

Essential concepts to master this topic
  • Decomposition Rule: Any number can be broken into smaller additive parts
  • Technique: Replace 9 with 8+1, so 78-9 becomes 78-8-1
  • Check: Both expressions equal 69: 78-9=69 and 78-8-1=69 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of maintaining subtraction
    Don't change 78-9 to 78+8+1 = 95! This creates addition instead of keeping the original subtraction. Always ensure decomposed parts maintain the same operations as the original expression.

Practice Quiz

Test your knowledge with interactive questions

If we have 67 blocks in total, how many blocks will remain if we remove 5 tens and 4 ones?

FAQ

Everything you need to know about this question

Why does 78-8-1 equal 78-9?

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Because 8+1 = 9! When you subtract 8 and then subtract 1 more, you've subtracted a total of 9. It's like taking away 9 items in two separate steps instead of all at once.

How do I know which way to break down the number?

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Look at the answer choices! The problem gives you options, so check which decomposition matches. For example, if you see 78-8-1, you know 9 was broken into 8+1.

Can I break down 78 instead of 9?

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Yes! You could write 789 78-9 as 70+89 70+8-9 , but the answer choices will guide you toward the intended decomposition method.

What if I get a different answer when I calculate?

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Double-check your arithmetic! Both 789 78-9 and the equivalent expression should give you exactly 69 69 . If not, recheck your subtraction steps.

Why is this useful in real math?

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Breaking numbers apart makes mental math much easier! Instead of subtracting 9 at once, you might find it simpler to subtract 8, then subtract 1 more.

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