Algebra
Simplify the expression:
4x + 7y + 5y + 6x
4x + 7y + 5y + 6x =
10x + 12y
How many square inches are in 1 square foot?
1 square foot = 12 inches x 12 inches = 144 inches2
Find the prime factorization of 750
750 = 2 x 3 x 53
How many cubic centimeters are in 1 cubic meter?
1 cubic meter = 100 cm x 100 cm x 100 cm = 1,000,000 cm3
Twenty-four meters of fencing is used to fence a rectangular garden. Let M represents the number of square meters in the area of the garden. What is the largest value that M could have?
The largest value that M could have is 36.
A perimeter of 24 meters can have the biggest area if it is made into a square, with each side length 6 meters and an area of 36 meters2.
x + x + y
x + x + y =
2x + y
How many cubic feet are in 3 cubic yards?
1 cubic yard = 3 feet x 3 feet x 3 feet = 27 feet3
3 cubic yards = 3 x 27 = 81 feet3
Find the prime factorization of 98
98 = 2 x 72
Dylan painted a wall that was 10 yards high and 1/2 of a yard wide. How many square feet did Dylan paint?
10 yards = 10 x 3 = 30 feet
1/2 yard = 1.5 feet
30 x 1.5 = 45 feet2
When a certain number N is divided by 3, the result is the same as when N is decreased by 8. What is the number N?
N=12
N/3 = N - 8
Multiply both sides by 3
N = 3N - 24
Which is true when N = 12.
Simplify the expression:
x + y + z + 2x + 2y + 2z + 3x + 3y
x + y + z + 2x + 2y + 2z + 3x + 3y =
6x + 6y + 3z
If 1 mile = 1,760 yards, then how many inches are in 1 mile?
63,360 inches
1 mile = 1,760 yards
1 yard = 3 feet = 3 x 12 = 36 inches
1,760 x 36 = 63,360 inches
Find the prime factorization of 528
528 = 24 x 3 x 11
How many square inches are in 2 square yards?
1 yard = 3 feet = 36 inches
2 square yards = 2 x 36 x 36 = 2,592 inches2
There are many three-digit numbers that are each divisible by 7 and also by 8 without a remainder in each case. What is the largest of these three-digit numbers? Hint: The number 560 is divisible by both 7 and 8, without a remainder.
952
The number must be divisible by 7 and 8, so it must be divisible by 56.
56 x 17 = 952, because 56 x 18 is a four-digit number
Simplify the expression:
t + t + t2 + t2 + t3 + 3t3
t + t + t2 + t2 + t3 + 3t3 =
2t + 2t2 + 4t3
37,500 pounds equals how many tons?
18.75 tons
1 ton = 2,000 pounds, so
37,500/2,000 = 18.75 tons
Find the prime factorization of 286
286 = 2 x 11 x 13
64 ounces is equal to how many pounds?
4 pounds
1 pound = 16 oz
So 64/16 = 4 pounds
Simplify:
42 -102 + (-5)2
-59
42 -102 + (-5)2 =
16 - 100 + 25 =
16 + 25 - 100 =
41 - 100 =
-59
Simplify the expression:
6xyz + 2xyz + xyz + xyz2
6xyz + 2xyz + xyz + xyz2 =
9xyz + xyz2
1 mile is equal to 1.61 kilometers. How many square kilometers are in 1 square mile?
1.61 km x 1.61 km = 2.5921 km2
Find the Greatest Common Factor (GCF) of 102 and 340
102 = 2 x 3 x 17
340 = 22 x 5 x 17
GCF = 2 x 17 = 34
4.5 kilograms = x milligrams. Find x.
x = 4,500,000
1 kilogram = 1000 grams and
1 gram = 1000 milligrams.
So 4.5 kilograms = 4.5 x 1000 x 1000 = 4,500,000 milligrams.
The product of two numbers is 504 and each of the numbers is divisible by 6. However, neither of the two numbers is 6. What is the larger of the two numbers?
42
504 factor pairs:
{1, 504}, but need to be divisible by 6 -->
{6, 84}, but then one of them is 6
{12, 42}, which works, so the larger number is 42