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 $28 + 54$
yusuf

explain why yusuf’s expression is correct.

yusuf correctly broke apart $54$ into $2 + 52$.

explain tiana’s mistake.

tiana added $7$ to $28$ to get to the next ten, but she did not break apart $54$.

Explanation:

First, check the value of \(28 + 54\) and the expressions of Tiana and Yusuf.

Step 1: Calculate \(28 + 54\)

\(28+54 = 82\)

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

First, calculate \(28 + 2=30\), then \(30 + 54 = 84\). Since \(84
eq82\), Tiana's expression is wrong.

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

First, calculate \(28 + 2 = 30\), then \(30+52 = 82\). Since \(82 = 28 + 54\), Yusuf's expression is correct.

for why Yusuf's expression is correct:
Yusuf used the associative property of addition. He broke \(54\) into \(2 + 52\) (because \(2+52 = 54\)). Then he first added \(28\) and \(2\) to get \(30\) (a multiple of ten, which is easier to add), and then added \(52\) to \(30\). The result of \(28 + 2+ 52\) is \(82\), which is the same as the result of \(28 + 54\) (also \(82\)).

for Tiana's mistake:
Tiana added \(2\) to \(28\) to get \(30\) (to make the addition easier by getting a multiple of ten), but she did not break down \(54\) accordingly. She directly added \(54\) to the sum of \(28\) and \(2\). So her expression \(28 + 2+ 54\) is equivalent to \(28+54 + 2\), which is \(2\) more than \(28 + 54\), so the result is wrong.

Answer:

s:

• The expression with the same value as \(28 + 54\) is Yusuf's.
• Yusuf's expression is correct because he correctly decomposed \(54\) into \(2 + 52\), and by the associative property of addition, \((28 + 2)+52=28+(2 + 52)=28 + 54\), and the result is equal to \(28 + 54\).
• Tiana's mistake is that she added \(2\) to \(28\) to get a multiple of ten, but she did not decompose \(54\) to keep the total value unchanged. Her expression actually adds an extra \(2\) compared to \(28 + 54\).