Question

tiana and yusuf each write an expression to help make 28 + 54 easier to add. tiana: 28 + 2 + 54. yusuf: 28 + 2 + 52. whose expression has the same value as 28 + 54? options: tiana, yusuf, both, neither

Explanation:

Step1: Calculate Tiana's expression

First, we calculate Tiana's expression: \(28 + 2 + 54\). We can use the associative property of addition. First, add \(28\) and \(2\): \(28 + 2 = 30\). Then add \(30\) and \(54\): \(30 + 54 = 84\). Now, calculate the original expression \(28 + 54\): \(28+54 = 82\)? Wait, no, wait, \(28 + 54 = 82\)? Wait, no, \(28+54\): \(20 + 50 = 70\), \(8 + 4 = 12\), so \(70+12 = 82\)? Wait, but Tiana's expression: \(28 + 2 + 54\). Let's recalculate. \(28+2 = 30\), \(30 + 54 = 84\). Wait, that's not equal. Wait, maybe I made a mistake. Wait, no, wait the original problem is \(28 + 54\). Wait, maybe Tiana is trying to make a ten? Wait, no, \(28 + 2 = 30\), then \(30 + 54 = 84\), but \(28 + 54 = 82\)? Wait, that can't be. Wait, no, \(28 + 54\): \(28 + 50 = 78\), \(78 + 4 = 82\). Tiana's expression: \(28 + 2 + 54 = 30 + 54 = 84\). Now Yusuf's expression: \(28 + 2 + 52\). Let's calculate that. \(28 + 2 = 30\), \(30 + 52 = 82\). Ah! So Yusuf's expression: \(28 + 2 + 52\). Let's check the original expression \(28 + 54\). Wait, \(54 = 2 + 52\)? Yes! Because \(2 + 52 = 54\). So Yusuf's expression is \(28 + (2 + 52)\) which is equal to \(28 + 54\) by the associative property of addition. Wait, but Tiana's expression is \(28 + 2 + 54\), which is \(28 + (2 + 54)=28 + 56 = 84\), which is not equal to \(28 + 54 = 82\). Wait, no, wait, I think I messed up Tiana's expression. Wait, Tiana's expression is \(28 + 2 + 54\). Let's compute \(28 + 54\) again. \(28 + 54\): \(28 + 50 = 78\), \(78 + 4 = 82\). Tiana's: \(28 + 2 = 30\), \(30 + 54 = 84\). Yusuf's: \(28 + 2 = 30\), \(30 + 52 = 82\). And \(28 + 54 = 82\). So Yusuf's expression is equal to \(28 + 54\) because \(54 = 2 + 52\), so \(28 + 54 = 28 + (2 + 52) = (28 + 2) + 52\) by associative property. Tiana's expression is \(28 + 2 + 54 = 28 + (2 + 54) = 28 + 56 = 84\), which is not equal to \(28 + 54 = 82\). Wait, but maybe I made a mistake in the original sum. Let's calculate \(28 + 54\) again. \(28 + 54\): \(28 + 50 = 78\), \(78 + 4 = 82\). Yusuf's: \(28 + 2 + 52 = 30 + 52 = 82\). Yes, that's correct. So Yusuf's expression is equal to \(28 + 54\). Wait, but the options are Tiana, Yusuf, Both, Neither. Wait, maybe I made a mistake with Tiana. Wait, Tiana's expression: \(28 + 2 + 54\). Let's see, \(28 + 54 = 82\), Tiana's: \(28 + 2 + 54 = 84\). Yusuf's: \(28 + 2 + 52 = 82\). So Yusuf's is equal. So the answer is Yusuf.

Step2: Calculate Yusuf's expression

Yusuf's expression is \(28 + 2 + 52\). Using the associative property, we can group \(28 + 2\) first: \(28 + 2 = 30\). Then add \(30\) and \(52\): \(30 + 52 = 82\). The original expression \(28 + 54\) is also \(82\) (since \(28 + 54 = 82\)). So Yusuf's expression has the same value. Tiana's expression: \(28 + 2 + 54 = 30 + 54 = 84\), which is not equal to \(82\). So only Yusuf's expression is equal.

Answer:

Yusuf (the option corresponding to Yusuf, e.g., if the options are A. Tiana, B. Yusuf, C. Both, D. Neither, then the answer is B. Yusuf)

Wait, in the given options, the buttons are Tiana, Yusuf, Both, Neither. So the correct option is Yusuf. So the answer is the option labeled "Yusuf".