Negative and Positives
What is the relationship between 330 and -330?
The relationship is that they are the same distance from each other. (330)
¼ cup of sugar, ⅛ cup of sprinkles, ⅓ cup of powdered sugar , ⅙ cup of flour: Based on the information above,what is the total amount of items needed in the cake?
Common denominator = 24
¼= 5/24, ⅛= 3/24, ⅙= 4/24. ⅓= 8/24, ⅙= 4/24
Answer: 1
Find the sum of (4a+8b-2) and (3b-5)
4a+11b-7
(i+o)+(i+o)+(i+o)+(i+o)+(i+o)+(i+0)+(i+o)= ??
7(i+0)
Rewrite the expressions by collecting like terms:
1/2k - 3/8k = ??
1/8k
Solve these three questions: (70 pts each question)
5+(-20)= ??, 10+(-32)+8= ??, 8+(-9)+(-3)= ??
5+(-20) = -15
10+(-32)+8= -14
8+(-9)+(-3)= -4
Akira got the expression 9x+3 and wrote her answer as 3+9x. Is her answer equivalent? How do you know?
Yes, it's equivalent because she is using commutative property, you can change the numbers and still get the same answer.
Write 25h÷ 5h in standard form.
25h times 1/5h
25h/5h
25h/5 times h/h
5 times 1
Answer: 5
1x4x8x4= ??
4(1+8)
Rewrite the expressions by collecting like terms:
2r/5 + 7r/15 = ??
13/15r
Sarah lost 10 pounds by running each week. By winter she gained 2 ⅙ pounds. Represent this situation with an expression involving signed numbers. What is the overall change in Sarah's weight?
-10+ 2 ⅙
= (-10 + 2)+ ⅙
= (-8) + ⅙
= -7 ⅚
Answer: -7 ⅚ pounds.
What is the definition of Equivalent expression? Give two examples and explain why they are equivalent.
Definition: Expressions that work the same even though they look different. Two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same values for the variables.
Examples: 3(x+3) and 3x + 9 || 6(x^2 + y +2) and 6x^2 + 6y + 12. They are all equivalent because the value of both expressions remains the same for any value of x.
Write 4m+8n+20 as a product of two factors.
4(1m+2n+5)
3j+(j+h)+3k= ??
3(j+k)
Write 4 + 6 = 8 in as many true equations as you can using the if-then moves. Identify which moves are used.
4+6+4=8+4 (Addition)
4-6-4=8-4 (Subtraction)
(4+6)÷4= 8÷4 (Division)
4(4+6)=4(8) (Multiplication)
Make this Equation into a real-life situation: (-13)+3
Answers may vary...
Example Answer: Lilly spent 13 dollars on lollypops, her mom gave her three more dollars to buy a newspaper, how much money does she have?
(-13)+3= -10
She has $-10.
For every 42 pounds of glass, there are 63 pounds of paper. What is the constant of proportionality? Make a ratio.
Ratio: 42:63
Constand of proportionality: k= 42/63 = 2/3
Find the result when 6m + 3 is subtracted from 8m.
8m+(6m +3)
8m+(-(6m+3)
8m+(-6m)+(-3)
2m+(-3)
Answer: 2m-3
2h+(6+h)+6x2= ??
3(h+6)
Rewrite the expressions by collecting like terms:
-1/3a - 1/2b - 3/4 + 1/2b + 2/3b + 5/6a = ??
1/2a - 2/3b - 3/4
A football team loses 5 yards every 10 minutes. How many yards did the team lose after 20 minutes?
After 10 minutes the team loses 5 yards: -5
20/10 = 2
-5 x 2 = -10
After 20 minutes the team will lose -10 yards.
What is the definition of "Constant of Proportionality?
What is the equation for the constant of proportionality? (250 pts each question)
The constant ratio of two proportional quantities (x and y). The constant of proportionality, k, is the constant value of the ratio of two proportional quantities y and x.
Equation: y=kx
Write (c+d)+(c+d)+(c+d)+(c+d)+(c+d) as the product of two factors.
5(c+d)
3x+(2+x)+5x2= ??
4(x+3)
Write 6 + 12 = 24 in as many true equations as you can using the if-then moves. Identify which moves are used.
6+12+12=24+12 (Addition)
6-12-12=24-12 (Subtraction)
(6+12)÷12=24÷12 (Division)
12(6+12)=12(24) (Multiplication)