Evaluate the Expression: Finding the Value of 78-46

Expression Equivalence with Strategic Substitution

Which expression is equivalent to the given equation?

78−46 78-46

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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?

78−46 78-46

2

Step-by-step solution

To solve this problem, we first calculate the given expression:

  • 78−46=32 78 - 46 = 32

Now, we need to check each provided choice and see which of them simplifies to the same result:

Let's examine each option:

  • Choice 1: 78−48−2=30−2=2878 - 48 - 2 = 30 - 2 = 28
  • Choice 2: 78−48+1=30+1=3178 - 48 + 1 = 30 + 1 = 31
  • Choice 3: 76−46+1=30+1=3176 - 46 + 1 = 30 + 1 = 31
  • Choice 4: 76−46+2=30+2=3276 - 46 + 2 = 30 + 2 = 32

Comparing the calculated values of each expression with the original subtraction 78−46=3278 - 46 = 32, we see that
Choice 4: 76−46+2=3276 - 46 + 2 = 32
is the correct equivalent expression.

Therefore, the expression that is equivalent to 78−4678 - 46 is 76−46+276 - 46 + 2

3

Final Answer

76−46+2 76-46+2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Calculate original expression first to find target value
  • Technique: Test each option: 76−46+2=30+2=32 76 - 46 + 2 = 30 + 2 = 32
  • Check: Verify equivalent expression equals original: 78−46=32 78 - 46 = 32 ✓

Common Mistakes

Avoid these frequent errors
  • Guessing without calculating each option
    Don't pick answers that look similar without computing = wrong choice! Similar-looking expressions often have different values. Always calculate the original expression first, then test each option systematically.

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 can't I just pick the expression that looks most like the original?

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Appearances can be deceiving! For example, 78−48+1 78 - 48 + 1 looks similar to 78−46 78 - 46 , but it equals 31, not 32. Always calculate to be sure.

What's the fastest way to solve this type of problem?

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First, calculate the original expression to get your target value. Then work through each option systematically until you find the match. Don't skip steps!

How do I avoid arithmetic mistakes when checking options?

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Work left to right carefully: 76−46+2 76 - 46 + 2 becomes 30+2=32 30 + 2 = 32 . Write down each step instead of doing it all in your head.

What if two expressions give the same answer?

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That's rare but possible! Both would be correct equivalent expressions. However, in multiple choice questions, there's typically only one right answer per the given options.

Can I use different strategies to modify the original expression?

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Yes! You can add and subtract the same number, or break apart numbers strategically. For example, 78−46 78 - 46 could become (76+2)−46=76−46+2 (76 + 2) - 46 = 76 - 46 + 2 .

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