Question

Select why this equation is true or false without adding.

52 + 27 = 49 + 24

A. )True because, if we compare 52 to 27 and 49 to 24 they are exactly the same

distance apart on a number line. They just have different starting and ending points.

B.). True because, both 52-27 and 49-24 result in the same answer of 25.

C). False because, if 3 is subtracted from 52 to get 49, then, 49 and 27 more would not

equal 49 and 24 more. Putting together two larger numbers is not the same as

putting together two smaller numbers.

D). False because 52 + 27 does not equal 49

.

Answer 1

Answer: Choice C

False because if 3 is subtracted from 52, then 49 and 27 more would not equal 49 and 24 more. Putting together two larger numbers is not the same as putting together two smaller numbers.

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Step-by-step explanation:

If we break up 52 into 49+3, then we can do the following rearrangement.

52 + 27 = 49 + 24

49 + 3 + 27 = 49 + 24

3 + (49+27) = 49 + 24

Notice that the 49+27 on the left is clearly larger than 49+24 on the right, mainly due to the 27 being larger than 24.

Then adding on 3 more means that the left side gets even larger.

So without having to add either side and simplify fully, we can see that the left side is larger than the right side. There's no way the two sides are the same number.

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Perhaps another quick way is to simply look at the units digits.

The 2 and 7 from 52 and 27 add to 2+7 = 9

The 9 and 4 from 49 and 24 add to 9+4 = 13 and we only care about the 3

The mismatch of the 9 and 3 is more evidence that the two sides aren't the same number.