Question

in 1 - 4, complete the equations that represent the picture.

1. a = l × w

4 × 5 = 20
you can write the multiplication fact that represents the area of the large rectangle.
you can write the multiplication facts that represent the area of each of the smaller rectangles.
4 × 5 = 4 × (3 + 2)
4 × 5 = (4 × 3) + (4 × 2)
4 × 5 = 12 + 8 = 20
the areas of the large rectangles are equal to the sum of the areas of the smaller rectangles.
another look!
you can use the distributive property to break an area into smaller rectangles to find more familiar facts to multiply.
you can separate a rectangle into two smaller rectangles with the same total area.
additional practice 5 - 8
apply properties: area and the distributive property

Explanation:

Step1: Solve problem 1

Part1: First equation

The area formula is \(A = l\times w\). Here \(l = 4\) and \(w = 5\), so \(4\times5=20\).

Part2: Second equation

We can split the rectangle vertically. The width \(5\) can be written as \(3 + 2\). Using the distributive property \(a\times(b + c)=a\times b+a\times c\), where \(a = 4\), \(b = 3\), \(c = 2\). So \(4\times5=4\times(3 + 2)=(4\times3)+(4\times2)=12 + 8=20\)

Step2: Solve problem 2

Part1: First equation

The area formula for a rectangle is \(A=l\times w\). Here \(l = 3\) and \(w = 7\), so \(3\times7 = 21\).

Part2: Second equation

We can split the rectangle horizontally. The width \(7\) can be written as \(3+4\). Using the distributive property \(a\times(b + c)=a\times b+a\times c\), where \(a = 3\), \(b = 3\), \(c = 4\). So \(3\times7=3\times(3 + 4)=(3\times3)+(3\times4)=9+12 = 21\)

Step3: Solve problem 3

Part1: First equation

The area formula for a rectangle is \(A=l\times w\). Here \(l = 3\) and \(w = 6\), so \(3\times6=18\).

Part2: Second equation

We can split the rectangle horizontally. The width \(6\) can be written as \(2+4\). Using the distributive property \(a\times(b + c)=a\times b+a\times c\), where \(a = 3\), \(b = 2\), \(c = 4\). So \(3\times6=3\times(2 + 4)=(3\times2)+(3\times4)=6 + 12=18\)

Step4: Solve problem 4

Part1: First equation

The area formula for a rectangle is \(A=l\times w\). Here \(l = 5\) and \(w = 6\), so \(5\times6=30\).

Part2: Second equation

We can split the rectangle horizontally. The width \(6\) can be written as \(3+3\). Using the distributive property \(a\times(b + c)=a\times b+a\times c\), where \(a = 5\), \(b = 3\), \(c = 3\). So \(5\times6=5\times(3 + 3)=(5\times3)+(5\times3)=15+15 = 30\)

Answer:

1. \(3\times5 = 15\), \(3\times2=6\), \(15 + 6=21\); \(3\times(3 + 2)=(3\times3)+(3\times2)\)
2. \(3\times3 = 9\), \(3\times4 = 12\), \(9+12 = 21\); \(3\times(3 + 4)=(3\times3)+(3\times4)\)
3. \(3\times2 = 6\), \(3\times4 = 12\), \(6 + 12=18\); \(3\times(2 + 4)=(3\times2)+(3\times4)\)
4. \(5\times3 = 15\), \(5\times3 = 15\), \(15+15 = 30\); \(5\times(3 + 3)=(5\times3)+(5\times3)\)