Question

name:
period:
spiral review #3
this worksheet will be collected on friday.
make sure you show all your work.
monday (unit 1 - lesson 8)
for each of the following sums, identify the greatest common factor of both terms and then use the distributive property to write the sum as a product. evaluate the product and check your answer with the original sum.
(a) 15 + 40
(b) 18 + 42
tuesday (unit 1 - lesson 8)
a rectangle with a total area of 115 square feet has been broken into two rectangles with areas of 75 square feet and 40 square feet, as shown. the common length of the two smaller rectangles is a whole number that is greater than either width 1 or width 2, which are both whole numbers. from this information, determine the length, width 1, and width 2. explain how you found your answers.
length:
width 1:
width 2:

Explanation:

Step1: Find the greatest common factor of 75 and 40

The factors of 75 are \(1,3,5,15,25,75\). The factors of 40 are \(1,2,4,5,8,10,20,40\). The common factors are \(1,5\). So the greatest common factor (GCF) is \(5\).

Step2: Use the formula for the area of a rectangle (\(A = length\times width\))

Since \(A_1 = 75\) (where \(A_1\) is the area of the first - smaller rectangle) and \(A_2=40\) (where \(A_2\) is the area of the second - smaller rectangle), and \(A = length\times width\). Let the length be \(l\), width1 be \(w_1\), and width2 be \(w_2\). We know that \(A_1=l\times w_1\) and \(A_2 = l\times w_2\). Since \(l\) is the GCF of 75 and 40, \(l = 5\).
Then, for the first rectangle with \(A_1=75\) and \(l = 5\), using \(w_1=\frac{A_1}{l}\), we have \(w_1=\frac{75}{5}=15\).
For the second rectangle with \(A_2 = 40\) and \(l = 5\), using \(w_2=\frac{A_2}{l}\), we have \(w_2=\frac{40}{5}=8\). Also, \(5>8\) is false, but we note that the problem says the common length is a whole number greater than either width. There is a mis - statement in the problem description. The correct relationship based on the formula \(A = l\times w\) (where \(l\) is the common side) gives us the values.

Answer:

length: \(5\)
width 1: \(15\)
width 2: \(8\)