Question

40 tiana and yusuf each write an expression to help make 28 + 54 easier to add.
40 tiana
28 + 2 + 54
40 yusuf
28 + 2 + 52
40 whose expression has the same value as 28 + 54?
40 yusuf
40 explain why yusuf’s expression is correct.
40 yusuf correctly broke apart? into 2 + 52.

Explanation:

Sub - question 1: Whose expression has the same value as \(28 + 54\)?

We calculate the value of \(28+54\), Tiana's expression \(28 + 2+54\) and Yusuf's expression \(28+2 + 52\).

Step 1: Calculate \(28 + 54\)

\(28+54=82\)

Step 2: Calculate Tiana's expression \(28 + 2+54\)

First, add \(28\) and \(2\): \(28 + 2=30\)
Then, add \(30\) and \(54\): \(30+54 = 84\)

Step 3: Calculate Yusuf's expression \(28+2 + 52\)

First, add \(28\) and \(2\): \(28+2 = 30\)
Then, add \(30\) and \(52\): \(30 + 52=82\)

Since \(28 + 54=82\) and Yusuf's expression also equals \(82\), the answer is Yusuf.

Sub - question 2: Explain why Yusuf’s expression is correct.

Yusuf's expression is \(28+2 + 52\). We know that \(54=2 + 52\) (because \(2+52 = 54\)). So, by the associative property of addition (\(a+(b + c)=(a + b)+c\)), \(28+54=28+(2 + 52)=28+2+52\). So Yusuf's expression is equivalent to \(28 + 54\) because he correctly decomposed \(54\) into \(2+52\) and used the associative property of addition.

Sub - question 3: Yusuf correctly broke apart \(\boldsymbol{?}\) into \(2 + 52\).

We know that in the original expression \(28+54\), and Yusuf's expression is \(28+2 + 52\). Since \(54=2 + 52\), Yusuf correctly broke apart \(54\) into \(2+52\).

Answer:

s:

1. Yusuf
2. Because \(54 = 2+52\), so \(28 + 54=28+(2 + 52)=28+2+52\) (by associative property of addition)
3. \(54\)