Fractions
Write two fractions that would simplify to 2/3.
Simplify the expression
9 - (-6)
15
Solve.
26 = 8 + v
26 = 8 + v
-8 on both sides
18 = v
If -3x + 16 = 5x, then x = ?
Collect x terms to one side.
Add 3x to both sides, 16 = 8x.
Divide by 8 on both sides to isolate x.
2 = x
What does order of operations tell us?
In math, order of operations are the rules that state the sequence in which the multiple operations in an expression should be solved.
Fill in the blank:
8 5/8 - ___ = 5 1/4
What is 3 3/8?
-$5 + $2 (debt taken away) = -$3
Tesla has $3 in debt.
Solve for n.
12 - 4 = n - 3 + 7
Combine like terms first.
12-4 = 8, -3 + 7 = 4
8 = n + 4
Subtract 4 on both sides.
4 = n
2x + 2(x+4) = 56
Distribute the 2 inside the parenthesis.
2x + 2x + 8 = 56
Combine like terms.
4x + 8 = 56
Subtract 8 from both sides.
4x = 48
Divide by 4 to isolate x.
x = 12
What is a constant?
A constant is a number that does not have a variable attached to it.
Divide:
1/8 divided by 5
1/8 * 1/5 =
1/40
Simplify -54/-9
6
Solve for y.
5/6(y) = 10
Divide both sides by 5/6.
5/6 divided by 5/6 = 5/6 * 6/5 = 30/30 = 1, cancels out.
10 divided by 5/6 = 10/1 * 6/5 = 60/5 = 12.
y = 12
Desmond solved the equation 3/4(1 + 3x) = -15 and got x = -7. How can he check to see if this answer is correct? If he is correct, show the work. If he is incorrect, what was his mistake?
Desmond can plug in -7 for x and solve to see if it is true.
3/4(1+3(-7)) = -15
3/4(1 - 21) = -15
3/4(-20) = -15
3/4 * -20/1 = -60/4 = -15
-15 = -15
What is the distributive property?
The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
What is 5/6 of ten?
5/6 * 10
5/6 * 10/1 = 50/6
8 2/6, or 8 1/3
Evelyn owes $10 to her friend, Lisbeth. Lisbeth says that if Evelyn helps her with her homework, she will give Evelyn $7. If Evelyn helps Lisbeth with her homework, who owes whom money?
Evelyn owes $10 to Lisbeth.
Lisbeth will give $7 to Evelyn for homework.
-$10 (Eveleyn owes) + $7 (Lisbeth gives) = -$3
Eveleyn will still owe $3 to Lisbeth.
Find the solution for x when a = 2, b = -2 and c = 5.
x - b = ac
x - (-2) = (2)(5)
x + 2 = 10
Subtract 2 from both sides.
x = 8
Kimmi and Leshone were working on their upper body strength by doing pushups. Leshone was able to do double the number of pushups as Kimmi. If all the girls could do 105 pushups total, how many could Leshone do?
x = number of pushups Kimmi can do
2x = number of pushups Leshone can do relative to Kimmi
x + 2x = 105
3x = 105
Divide by 3 on both sides.
x = 35.
Leshone can do 2(35) = 70 pushups.
What is the rule of multiplying and dividing negative numbers?
Same signs (positive or negative) make a positive.
Different signs (one positive, one negative) make a negative.
Find the product of:
2 1/3 * 5 1/2
2 1/3 = 7/3
5 1/2 = 11/2
7/3 * 11/2 = 77/6
12 5/6
Samara notices that 5 · 6 = -5 · -6. She generalizes this to say a · b = -a · -b for any positive values of a and b. Is she correct? Explain.
Yes, Samara is correct because for any positive value of a and b, when you multiply them you will get a positive, and if you multiply them with negatives, two negatives will make a positive every time.
Maria, Phineas, and Claire work at a local restaurant. Maria worked twice as many hours as Phineas. Claire worked 12 more hours than Maria. If Claire worked 40 hours, then how many hours did Phineas work?
Claire worked 40 hours, and she worked 12 more hours than Maria. 40 = m + 12
Solve for M (maria's hours)
40 = m + 12, subtract 12 on both sides, 28 = m
Maria worked twice as many hours as Phineas. 28 = 2p
Solve for P (Phineas hours)
28 = 2p, divide by 2 on both sides, 14 = p.
Phineas worked 14 hours.
Solve for x.
3[4 + 2(x + 4)] = -6(1-x)
Work within the parenthesis first.
3[4 + 2x + 8] = -6 + 6x
3[2x + 12] = -6 + 6x
Distribute 3.
6x + 36 = - 6 + 6x
Add 6 to both sides.
6x + 42 = 6x.
Move x to it's own side.
42 = 0
This equation is a false statement because the variable terms were canceled out.
How do you divide fractions?
You keep the first fraction the same, change divide into multiply, and then flip the second fraction.
Keep-Change-Flip