Which expression is equivalent to the given equation?
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Which expression is equivalent to the given equation?
To determine an expression equivalent to , let us consider adjusting the components to make calculations easier while maintaining equivalence.
(1) Start with the original problem: .
(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:
(3) Compute within this adjusted equation:
(4) Checking the original unaltered computation:
Both computations yield , verifying their equivalence.
Thus, the alternative expression for that maintains equivalence is , which corresponds to choice 4.
If we have 67 blocks in total, how many blocks will remain if we remove 5 tens and 4 ones?
Making one number a round number like 30 can make mental math easier! Even though the expression looks longer, is often faster to calculate than .
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.
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 , not 73.
Yes! You could change to by adding 2 to the first number and subtracting 2 from the second. The key is that total adjustments must equal zero.
Calculate both expressions and compare results. and . Same result means equivalent expressions!
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