Question

1. which one doesnt belong? which expression does not represent the area of the rectangle?

5 × 78 (5 × 70) + 8 350 + 40 (5 × 70) + (5 × 8)

Explanation:

Step1: Recall the area formula of a rectangle

The area formula of a rectangle is \(A = l\times w\) (where \(l\) is the length and \(w\) is the width). Here, if \(l = 78\) and \(w=5\), then \(A=5\times78\).

Step2: Use the distributive property

By the distributive property \(a\times(b + c)=a\times b+a\times c\). Since \(78=70 + 8\), then \(5\times78=5\times(70 + 8)=(5\times70)+(5\times8)\).

Step3: Calculate the values

\(5\times70 = 350\) and \(5\times8 = 40\), so \((5\times70)+(5\times8)=350 + 40\).

Step4: Analyze \((5\times70)+8\)

\((5\times70)+8=350+8 = 358\), while \(5\times78=(5\times70)+(5\times8)=350 + 40=390\). So \((5\times70)+8\) does not represent the area of the rectangle.

Answer:

\((5\times70)+8\) does not represent the area of the rectangle.