Fractions/Rational Numbers
What do you need in order to add or subtract with fractions?
Common Denominators
What are at least 2 things to remember for standard form?
Alphabetical
Combine Like Terms
No Double Signs
Solve for y:
3y + 12 = 27
3y + 12 = 27
3y = 15
y = 5
Sam has 3 bottles of water. Together, Sam and Dave have fewer than 12 bottles of water. Write an algebraic inequality where Dave's water bottles are represented by w.
x + 3 < 12
What are at least 2 letters in the alphabet that make horrible variables? Why?
s, l, o --> they look too much like 5, 1, and 0!
What is the lowest common denominator for 5/8 and 7/12
24ths --> 5/8 x 3/3 and 7/12 x 2/2
What is product of two factors form?
When you pull out the GCF from all like terms to the outside of parenthesis: __ (__ + __)
Looks like the "before" of a distributive property problem
Write an algebraic equation to match the scenario: <M and <N are angles on a line. If <M is equal to 2x and <N is equal to 3x + 30, solve for x and then the measures of <M and <N.
2x + (3x + 30) = 180
5x + 30 = 180
5x + 30 - 30 = 180 - 30
5x = 150
5x/5 = 150 /5
x = 30 so... <M = 2x = 60 and <N = 3x + 30 = 120
When would you reverse an inequality symbol while solving an algebraic inequality problem?
When you divide or multiply both sides by a negative number
What cinematic classic film includes the line "Look out, I think Moto, Moto likes you"?
Madagascar (I like 'em big, I like 'em chunky)
When dividing fractions, you really do what?
Multiply by the opposite (second) fraction/keep change flip!
Write in product of two factors form:
6k - 15m + 27
3 (2k - 5m + 7)
Molly goes to the mall and buys 5 pairs of shoes for $16 each. She also buys 5 pairs of socks for d dollars each. If she spent a total of $102.50, write an algebraic equation that would help you to find the cost of a pair of socks.
5(d + 16) = 102.50
or
5d + 80 = 102.50
Solve the following inequality and graph the solution:
1/3p + 10 (is less than or equal to) 16
1/3p + 10 (is less than or equal to) 16
1/3p (is less than or equal to) 6
p (is less than or equal to) 18
Closed circle at 18, shade to left
Finish the bad-dad joke: What do sprinters eat before a race?
Nothing, they fast!
Combine Like Terms (standard form):
4/5b - 1/3f - 2/3b + 5 + 3/4f - 2
4/5b + (-2/3b) + (-1/3f) + (3/4f) + 5 + (-2)
12/15b + (-10/15b) + (-4/12f) + (9/12f) + 3
2/15b + 5/12f + 3
Write the answer in expression form:
12x - 3(x - 4y) + 3/4(4x - 16y)
12x - 3(x - 4y) + 3/4(4x - 16y)
12x + (-3x) + 12y + 3x + (-12y)
12x + (-3x + 3x) + (12y + -12y)
12x + 0 + 0
12x
Jimbo is designing a rectangular pool where the length is 3 less than twice the width. It has a perimeter of 42 feet total. If w represents the width, create and solve an algebraic equation for how many feet the width and length of the pool are.
w = width so length = 2w - 3
w + w + (2w - 3) + (2w - 3) = 42
6w - 6 = 42
6w + 48
w = 8 --> width is 8 ft and length is 13 feet
Write and solve an algebraic inequality for the following scenario:
Tiny Tim is planning to grow his pokemon card collection this summer. He has $110 now and by the end of the summer, he wants to still have more than $75. If he buys each card, c, for $4.50, how many cards can he buy and still have more than $75?
110 - 4.50c > 75
-4.50c > -35
1c < 7.78
c < 7 cards... He can buy at most 7 cards this summer
How old will Taylor Swift turn on her birthday this year?
She was born in 1989...
2025 - 1989 = 36