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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.
Let x be the amount of candy in grams that we can buy for $2. If we multiply the price of a gram of candy $0.40 by the amount of candy that we can buy x, the resulting product is $2. This can be written as an equation. 0.40x = 2 To find the value of x, we can divide both sides of the equation by 0.40.
Therefore, Tiffaniqua can buy 5 grams of candy for $2.
Solve the following equations.
We can solve the equation by adding 10 to both sides. Doing this isolates x on the left-hand side of the equation.
Therefore, x=37 is the solution to the equation!
On the left-hand side we have 5 times the value of y. Since we want to find the value of y, we need to divide both sides of the equation by 5.
The value of y is 4.
In this equation, we have one third of z. We will multiply both sides of the equation by 3 to isolate z and find its value.
The value of z is 21.
To find out how much money Tearrik would earn working 4.5 hours, we need to find out how much he earns per hour. Let x be Tearrik's salary. The result of multiplying 2.5 by x is equal to 9. This can be written as an equation. 2.5x = 9 To find Tearrik's salary, we will divide both sides of the equation by 2.5.
We found that Tearrik earns $ 3.60 each hour he works. Now we can multiply his salary by 4.5 to find how much he would earn if he worked for 4.5 hours. 4.5 * 3.60 = 16.20 Tearrik would earn $16.20 if he worked 4.5 hours.
Solve the following equations. Check your answer.
To solve the equation we need to isolate x on one side of the equation. We will do this by subtracting 3 from both sides of the equation.
We found that x=4 is the solution to the equation. To check the answer, we will substitute 4 for x into the original equation.
Since both sides of the equation are equal, the solution is correct.
We will isolate a on one side of the equation to find the solution. To do so, we will add 5 to both sides of the equation.
The value of a is 24. To check if this value is correct, we will substitute 24 for a into the original equation.
Since both sides of the equation are equal, the solution is correct.
To solve the equation, we have to isolate k on one side of the equation. We will do this by subtracting 6 from both sides of the equation.
We found that k=-23. To verify if this is a correct solution, we will substitute -23 for k into the original equation.
Both sides of the equation are equal. Now we can be sure that we found the correct value.
Solve the following equations. Check your answer.
To solve the equation, we need to isolate m on one side of the equation. We will do this by dividing both sides of the equation by -8.
We found that m=7 is the solution to the equation. To check the answer, we will substitute 7 for m into the original equation.
Since both sides of the equation are equal, the solution is correct.
To find the solution, we will isolate t on one side of the equation. We will do this by dividing both sides of the equation by 2.5.
The value of t is 6. To check if this solution is correct, we will substitute 6 for t into the original equation.
Since both sides of the equation are equal, the solution is correct.
To solve the equation, we have to isolate q on one side of the equation. We will do this by multiplying both sides of the equation by 6.
We found the value of q is -72. To verify if this is the correct solution, we will substitute -72 for q in the equation.
Both sides of the equation are equal, so we can be sure that we found the correct value.