Ratio & Proportion

Question 1

Direct Proportion

Answer 1

When comparing two ratios and one unit increases in tandem with another unit, then the ratios are in direct proportion.

As one value increases so does the other.

Question 2

Inverse Proportion

Answer 2

Two quantities are inversely proportional to each other if when one increases the other decreases.

For example, increasing the number of designers assigned to a single program would decrease the time it takes to finish the program.

Question 3

Cross Multiply

Answer 3

Multiply the numeration of the first fraction by the denominator of the second fraction, and vice versa.If the cross-products are equal, te fractions are equal.

Question 4

How do you write the number 30 as a product of prime numbers?

Answer 4

By dividing into whole numbers such as 6 and 5 then factoring those numbers etc.

30 = 5 x 3 x 2

Question 5

Prime Number

Answer 5

A prime number has exactly two whole number factors - one and itself.

Question 6

Factor

Answer 6

A factor is a number that divides into another number without incurring any remainder.

Question 7

How can you use multiplication to check the result of a division problem?

Answer 7

1. ) Multiply the quotient by the divider.

2. ) Add the remainder to the product of item 1 above.

Question 8

When dividing one can find the remainder by…

Answer 8

finding the highest product of the divisor that does not exceed the dividend.

Question 9

To find the remainder in a division problem one…

Answer 9

1. ) Find the highest product of the divisor with some number that is not larger than the dividend.
2. ) Subtract the result of item 1 above from the dividend. (This is the remainder)

Question 10

FOIL

Answer 10

First, Outer, Inner, Last

- FOIL is method for multiplying two binomials. Multiply terms in parentheses in the following order.

Question 11

Order of Operations

Answer 11

PEMDAS

1. ) Parentheses: do calculations within parentheses
2. ) Exponents: evaluate squares, square roots and other exponents or radicals.
3. ) Multiplication & Division from L to R
4. ) Addition & Subtraction from L to R

Question 12

1. ) Zero Factor Property

2. ) Zero Product Property

Answer 12

1. ) A zero factor always gives a zero product. (a)0=0; 0(a)=0
2. ) The product of two real numbers may be 0 only if one factor is 0.
   - If ab = 0, then a = 0, and/or b = 0

Question 13

1. ) Zero Divisor Property

2. ) Zero Dividend Property

Answer 13

1.) Dividing by zero is not defined. a/o and a

Question 14

x - Axis

Answer 14

The horizontal line on a coordinate plane.

Question 15

Y - Axis

Answer 15

the vertical line on a coordinate plane.

Question 16

Origin (Graph)

Answer 16

The point of intersection of the x - axis and y - axis on a coordinate plane. The coordinates of the origin are (0,0).

Question 17

Quadrant (Graph)

Answer 17

The x - axis and y - axis divide the coordinate plane into four regions called quadrants.

Question 18

Percent Decrease

Answer 18

(old - new) / (old) x 100 = % decrease

“new” and “old” refer to the final and original amounts respectively.

Question 19

Percent Increase

Answer 19

(new - old) / (old) x 100 = % increase

“new” and “old” refer to the final and original amounts respectively.

Question 20

Complete Factoring

Answer 20

• Complete factoring of a polynomial means to find the prime factors.
  1. ) Find the greatest common factor if it exists. Examine each factor.
  2. ) If one of the factors is a binomial and the difference of two squares, factor it.
  3. ) If one of the factors is a trinomial, factor.
  4. ) The answer is the product of all of the factors, which must be a prime factor.

Question 21

What is the correct procedure for simplifying an expression containing powers or roots?

Answer 21

1. ) Simplify any expressions contained within parentheses or other similar symbols.
2. ) Simplify any powers or roots.
3. ) Do all multiplications and divisions, starting from left to right.
4. ) Do all additions and subtractions, starting from left to right.

Question 22

Quadratic Equation

Answer 22

ax2 + bx + c = 0

Question 23

Quadratic Formula

Answer 23

• Used to solve any quadratic equation by substitution of a, b, and c from the quadratic form ax^2 + bx + c = 0

x = (-b ± (√b^2 - 4ac)) / (2a)

Question 24

Theorem of Pythagoras

Answer 24

Pythagorean Theorem: “In a right triangle the square of the length of the hypotenuse (the longest side, opposite of the right angle) is equal to the sum of the squares of the lengths of the other sides.”

the formula a^2 + b^2 = c^2 is used; c = length of the hypotenuse

Question 25

What are benchmark percents and what are they useful for?

Answer 25

Although one could use basic computation to determine the solution, an estimation strategy using “benchmark” percents is usually more efficient and less prone to error.

Benchmark percents are easily computable percents like 10% and 1%.