Find the Sum: Solving the Expression 28+45

Equivalent Expressions with Balancing Adjustments

Which expression is equivalent to the given equation?

28+45= 28+45=

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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?

28+45= 28+45=

2

Step-by-step solution

To determine an expression equivalent to 28+45 28 + 45 , let us consider adjusting the components to make calculations easier while maintaining equivalence.

(1) Start with the original problem: 28+45 28 + 45 .

(2) To simplify, notice that we want to make a decomposition that doesn't change the sum. Increase 28 by 2, making it 30, which is easier to work with. However, you have to subtract 2 to balance the increase. So, the expression becomes:

30+452 30 + 45 - 2

(3) Compute within this adjusted equation:

  • 30+45=75 30 + 45 = 75
  • 752=73 75 - 2 = 73

(4) Checking the original unaltered computation:

  • 28+45=73 28 + 45 = 73

Both computations yield 73 73 , verifying their equivalence.

Thus, the alternative expression for 28+45 28 + 45 that maintains equivalence is 30+452 30+45-2 , which corresponds to choice 4.

3

Final Answer

30+452 30+45-2

Key Points to Remember

Essential concepts to master this topic
  • Balance Rule: Changes must cancel out to maintain equivalence
  • Technique: Increase 28 by 2 to get 30, then subtract 2
  • Check: Both expressions equal 73 when calculated ✓

Common Mistakes

Avoid these frequent errors
  • Making adjustments without balancing
    Don't just change 28 to 30 without subtracting 2 = wrong sum of 75 instead of 73! This breaks equivalence because you added value without removing it. Always balance every adjustment by adding and subtracting the same amount.

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 would I want to change 28 + 45 to something more complicated?

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Making one number a round number like 30 can make mental math easier! Even though the expression looks longer, 30+452 30 + 45 - 2 is often faster to calculate than 28+45 28 + 45 .

How do I know which adjustments to make?

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Look for numbers close to multiples of 10! Since 28 is close to 30, increase it by 2. Then always subtract that same amount to keep the expression equivalent.

What if I accidentally add instead of subtract the adjustment?

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You'll get the wrong answer! If you increase 28 by 2 to get 30, you must subtract 2 somewhere. Adding 2 instead would give you 30+45+2=77 30 + 45 + 2 = 77 , not 73.

Can I adjust both numbers in the original expression?

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Yes! You could change 28+45 28 + 45 to 30+43 30 + 43 by adding 2 to the first number and subtracting 2 from the second. The key is that total adjustments must equal zero.

How do I verify my equivalent expression is correct?

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Calculate both expressions and compare results. 28+45=73 28 + 45 = 73 and 30+452=752=73 30 + 45 - 2 = 75 - 2 = 73 . Same result means equivalent expressions!

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