Question

maya and seth each write an expression to help make 25 + 46 easier to add.
maya
25 + 5 + 41
seth
25 + 5 + 46
whose expression has the same value as 25 + 46?
maya
explain why maya’s expression is correct.
maya correctly broke apart
?
into 5 + 41.

Explanation:

Step1: Analyze Maya's expression

Maya's expression is \(25 + 5 + 41\). We know that \(5 + 41 = 46\) (since \(5+41 = 46\) by basic addition). So, substituting back, Maya's expression becomes \(25+(5 + 41)=25 + 46\) (by the associative property of addition, \(a+(b + c)=(a + b)+c\)).

Step2: Analyze Seth's expression

Seth's expression is \(25+5 + 46\). Combining the first two terms, we get \(25 + 5=30\), then \(30+46 = 76\). But \(25+46=71\), and \(25 + 5+41=25+(5 + 41)=25 + 46 = 71\). So Seth's expression is \(25+5 + 46=30 + 46=76\), which is not equal to \(25 + 46\).

Step3: Find the number Maya broke apart

We know that in Maya's expression, she has \(25+5 + 41\) and the original expression is \(25 + 46\). So she broke apart \(46\) into \(5+41\) (since \(5 + 41=46\)).

Answer:

Maya's expression has the same value as \(25 + 46\) because she used the associative property of addition by breaking \(46\) into \(5 + 41\) (so \(25+5 + 41=25+(5 + 41)=25 + 46\)), while Seth's expression changes the sum. The number Maya broke apart is \(46\).