Miscellaneous

Elementary
GCD
LCM
Definitions

Percents

Ratios

Square Roots

Reverses

Junior High
Cube Roots

Mult By 9 (#1)
Mult By 9 (#2)

Mult By 8

Polynomials

Positive Integral Divisors

Sum Of Positive Integral Divisors

Relatively Prime 

Triangular Numbers

Remainders

Divide By 40

Divide By 25

Divide By 9

High School

Pentagonal Numbers

Hexagonal Numbers

Heptagonal Numbers

Octagonal Numbers

Manipulating Polygonal Numbers

Dividing Factorials #1

Dividing Factorials #2

Solving Triangular Numbers

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Ratios:

A.  Number Sense uses ratios in a variety of ways.  With ratios you simply write an expression and solve for the missing variable.

Ex [1]  5 is to 8 as 3 is to ________.

a.  When working with ratios, it is easier to think in terms of fractions.

b. So ⁵/₈ = ³/_x.  Simplifying this equation we get 5x = 24.

c.  Solving for x we get ²⁴/₅.

d.  The answer is ²⁴/₅.

Ex [2]  25 is to 100 as what is to 16? _________.

a.  Think of this as ²⁵/₁₀₀ = ^x/₁₆.

b.  Simplifying this expression we get (16)(25) = 100x.

c.  This equals 400 = 100x.  See Multiplying by 25.

d.  x = 4.

e.  The answer is 4.