1.1:Expressions
What is an expression or algebraic expression?
An expressionor algebraic expression is any mathematical statement which consists of numbers.
What does P,E,M,D,A,S mean in order of operation?
Answer! P means parentheses, E means exponent, M means multiplication, D means division, a means addition, S means subtraction.
1. Translate the phrase "the quotient when the quantity 10 plus a number is divided by 2" into an expression.
Answe!(10+x)/2
What’s an equation?
Answer! An equation is a mathematical sentence formed by place the symbol = between two expression.
Answer!
Area=length x width
Solve it! (Show your work) z(x+y) ; use x=6 , y=8 ; and z=6
Answer! 84
Solve this! (Show work) 23 + 19-3 × 4
Answer! 15
A ____ is a fraction that compares two quantities measured in different units?
Answer:Rate
What’s an inequality?
Answer!
An inequality is a mathematical sentence formed by placing one of the symbols < > between two expressions.
Answer!
5%=0.05 1200x0.05x 2+1200 x0.1 =120 C
What is a variable? Give 1 example of a problem with a variable? (U don’t have to solve it)
Answer! A variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. Example:3x+2y=8
Correct these problems!
1. Incorrect: (5 + 2) x 3 - 4 ÷ 2 = 15
2. Incorrect: 10 - 2 x 3 ÷ 2 = 9
1.Correct: (5 + 2) x 3 - 4 ÷ 2 =19
2.Correct: 10 - 2 x 3 ÷ 2 = 7Answer!
1. X=5-p
2. Y = 16/p
What’s an open sentence?
Answer! An open sentence is an equation or inequality that contains an algebraic expression
One day, the temperature in Rome, Italy, was 30°C. The temperature in Dallas, Texas, was 83°F. Which temperature was higher?
Answer!
The temperature in Rome and itlay is 30°C was higher than the temperature in Dallas Texas was 28.33 degrees Celsius
Solve BOTH! (show work)
y + 9 - x; use x = 1, and y = 3
y2 - x; use x=7, and y = 7
1.11
2.42
Solve this problem (show your work)
-1x[(3-4x7)divide5]-2x24divide 6
Answer!3
Evaluate the expression
2. 15 - b when b = 9
3. t3 when t = 6
4. 3n - 5 when n = 8
Answer!
1. 43 +10=53
2. 15-9=6
3. 6x6x6=216
4.3(8)-5=24-5=19
Check whether the given number is a solution of the equation or inequality.
1.x + 9 = 17;8
2 K + 9 = 11; 10
3. 15 - 4y > 6; 2
4.2р - 1 ≥ 7; 3
Answer!
1.For the equation x + 9 = 17 and x = 8:
true, x = 8 is a solution.
2.For the equation K + 9 = 11 and K = 10:
false, K = 10 is not a solution.
3.For the inequality 15 - 4y > 6 and y = 2:
true, y = 2 is a solution.
4.For the inequality 2p - 1 ≥ 7 and p = 3:
false, p = 3 is not a solution.
State the formula that is needed to solve the problem. You do not need to solve the problem.
8. The temperature is 68°F. What is the temperature in degrees Celsius?
9. A store buys a baseball cap for $5 and sells it for $20. What is the profit?
10. Find the area of a triangle with a base of 25 feet and a height of 8 feet.
Answer!
8. C is the temperature degrees in Celsius F is the temperature in degrees Fahrenheit.
9.profit=revenue -cost
10. Area =1/2 x base x height
Name 3 key words for each multiplication,division, addition, and subtraction (rise your hand
Addition-sum, altogether, all, in all, together, total, total number, add, increase, increased by, more than. Subtraction-minus, greater than, take away, fewer than, less than, subtract, decreased by. Multiplication-product, multiply, multiplied by, times.
when you’re doing order of operation if you have a problem, where multiplication or division or addition or subtraction is next to each other what’s the rule?
Answer-you do (from left to right)
Explain what evaluate the expressions involves and give me an 2 example problems, and solve them.(it doesn't have to be hard)
Answer!
Example: Evaluating expressions involves substituting a specific value or values for variables and then performing the necessary operations to find the value of the expression. For example, consider the expression 2x + 5 when ( x = 3)
Describe a real-world situation you could model
using the equation 5x = 50. Use mental math to solve the equation.
Explain what the solution means in this situation.
(If you saw this problem, you will get 500 points even if your not the first one)
Answer!
Mental math solution:
To find the amount each friend will receive, we need to solve the equation:
5x = 50
Dividing both sides by 5:
x = 10
Explanation of the solution:
In this scenario, the solution x = 10 means that each friend will receive 10 dollars when the 50 dollars is divided equally among the 5 friends. So, if you have 50 dollars and you want to share it equally among 5 friends, each friend will get 10 dollars.
Describe and correct the error in solving the problem.
A town is fencing a rectangular field that is 200 feet long and 150 feet wide.
At $10 per foot, how much will it cost to fence the field?
Answer!
Cost = perimeter times cost per foot therefore the cost of fencing the field at 10 per foot cost 700×10 = 7000 to fence the field