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| 13 Theory slides |
| 10 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
Zosia's brother is 10 years older than she is. Also, Zosia's brother is half their father's age.
The Properties of Equality are rules that allow manipulation of an equation in such a way that an equivalent equation is obtained. These properties will be reviewed in sets. The first set of properties is shown below.
For any real number, the number is equal to itself.
a=a
For all real numbers, the order of an equality does not matter. Let a and b be real numbers.
If a=b, then b=a.
For all real numbers, if two numbers are equal to the same number, then they are equal to each other. Let a, b, and c be real numbers.
If a=b and b=c, then a=c.
Select the appropriate property for each example.
Some of the most commonly used inverse operations are addition and subtraction. These operations fall under the Addition Property of Equality and the Subtraction Property of Equality.
Adding the same number to both sides of an equation results in an equivalent equation. Let a, b, and c be real numbers.
If a=b, then a+c=b+c.
Subtracting the same number from both sides of an equation results in an equivalent equation. Let a, b, and c be real numbers.
If a=b, then a−c=b−c.
One of Davontay's hobbies is playing the saxophone. He plays in the school band and wants to join a local community band as well. He goes to the music store to buy more reeds for his saxophone since he will be spending more time playing. After spending $20 on reeds, he is left with $140.
Heichi like collecting a particular brand of clothing. He is inspecting his wardrobe before going to the mall. He notices that he has 7 shirts and 4 more shirts than pairs of pants.
The other most common type of inverse operations are the multiplication and division operations. These are valid by the following properties of equality.
Given an equation, multiplying each side of the equation by the same number yields an equivalent equation. Let a, b, and c be real numbers.
If a=b, then a×c=b×c.
Dividing each side of an equation by the same nonzero number yields an equivalent equation. Let a, b, and c be real numbers.
If a=b and c=0, then a÷c=b÷c.
LaShay's hobbies include playing golf with her father. She wants to go to the golf course to practice. She knows that her school is one quarter of the way from her house to the golf course.
Consider that the school is about 2.5 miles from LaShay's house.
Zain is in the chess club at their school. During one game, their opponent has double the pieces that Zain has. Zain's opponent has 6 pieces left on the board.
LHS/2=RHS/2
Cancel out common factors
Simplify quotient
Calculate quotient
Find the value of the variable on each equation using the Properties of Equality.
The challenge at the beginning of the lesson gave some information about Zosia's family.
Then, the following exercises were presented.
To find the value of b, we need to find the value of a first. We will start by isolating a in the first equation.
We found that a=3. Now this value can be substituted into the second equation to find the value of b.
Therefore, the value of b is 13.
The perimeter of the rectangle is 196 centimeters.
The perimeter of a rectangle is the sum of the lengths of its four sides. We can see that the rectangle has two long sides and two short sides. This means that if we multiply each given expression by 2 and add them together, we can write an expression for the perimeter.
We are given that the rectangle has a perimeter of 196 centimeters. This means that we can set our expression for the perimeter equal to 196.
Now that we know that x = 14, we can substitute this value into the given expressions to find the lengths of the sides.
Longer Side | Shorter Side |
---|---|
5x | 2x |
5( 14) | 2( 14) |
70 cm | 28 cm |
The side lengths of the rectangle are 70 centimeters and 28 centimeters.