Pre-Algebra
x = 2
What makes something an proper fraction vs. an improper fraction?
If a/b is a fraction then:
- proper if a < b
- improper if a >= b
Compute 3/4 + 1/5
19/20
Fully reduce the fraction 10/35
2/7
Which NFL team won the most Super Bowls?
Double points: What other team won the most?
If 12345 + y = 67899, what is y?
y = 67899 - 12345 = 55554
Convert 5 and 3/11 to an improper fraction
58/11
Compute (2/3)^3
Hint: rewrite the problem using multiplication!
2^4/3^4 = 16/81
Fully reduce the fraction 36/60
3/5
Name 2 Native American Tribes/Nations
Chocktaw, Cherokee, Tomahawk, Chayuga, Apache, Navajo
What are the 2 steps (in order) we must do to solve the equation
13t + 24 = 167?
1. subtract 24 on both sides:
13t = 143
2. Divide by 13 on both sides:
t = 11
Mr. Lorzano converts the improper fraction 15/4 to 2 and 7/4. What did he do wrong and how can we fix it?
The fraction part of a mixed number must be a proper fraction. So he should write 3 and 3/4
Compute 5/6 + 5/12 + 5/24. Improper fraction is fine!
35/24 or 1 and 11/24
Yitzi wants to reduce 48/64 so he does the following:
1. Reduce by 2: 48/64 --> 24/32
2. Reduce by 2: 24/32 --> 12/16
3. Reduce by 2: 12/16 --> 6/8
4. Reduce by 2: 6/8 --> 3/4
What could Yitzi have reduced the original fraction by to get the answer in only 1 step?2^4 = 16
What countries are the Andes mountains in? Name at least 3.
Peru, Bolivia, Chile, Ecuador, Argentina, Colombia
Solve the equation
2x + 4x + 6x = 100 + (-2) * 8
12x = 84
x = 7
Compute (2 and 3/4) + (5 and 2/4) + (1 and 1/4)
9 and 2/4
Compute and reduce the double fraction 1/2/3/4
Hint: Every fraction is a hidden division problem. Try (1/2)/(3/4)
4/6 --> 2/3
Mordechai says that 6/11 cannot be reduced further because 11 is a prime number. Is his reasoning correct? Why or why not?
It cannot be reduced further, but his reasoning is incorrect. It is not because 11 is prime, but because the GCD of 6 and 11 is 1. Or in other words, 6 and 11 are coprime.
What did the 13th Amendment to the Constitution do?
Abolish slavery except as a punishment for crimes
Solve the system of equations:
5a + 8b = 62
a = b + 2
(a, b) = (6, 4)
Compute (2 and 3/5)^2 as a mixed number
6 and 19/25
1. convert to improper fraction: 13/5
2. multiply by itself: 13/5 * 13/5 = 169/25
3. convert back to mixed number: 169/25 -> 6 and 19/25
Compute 127/997 ÷ (5/3 ÷ 10/6). No need to reduce
Hint: there is a very easy way and a very hard way. Don't get scared!127/999 since (5/3 ÷ 10/6) = 1
The butterfly method will always let us add/subtract fractions correctly, but it is not always the most efficient method. Why?
Hint: It may be helpful to explain how you could approach a problem like 16/20 + 38/40
Multiplying denominators with the butterfly method always gives us a common denominator, but not always the lowest common denominator, which may make the arithmetic unnecessarily complicated.
How many students need to be in a class for at least 2 of them to be guaranteed to have the same birth month?
13