Mathematics Combined

Mixed Number and how to convert to a fraction

Whole number with a fraction. To convert to a fraction (improper) multiply the whole number by the denominator of the fraction and add the resulting product to the numerator.

Adding/Subtracting fractions with different denominators

cross multiply then add for numerator; then multiply denominators together and simplify

Fraction Multiplication

Multiply the numerators together and the denominators together, then simplify the fraction. Whole numbers have a denominator of 1

dividing decimals

make a whole number and divide move decimal back the amount made to the right during the division process.

Area of Square or Rectangle

L*W

Right Triangle Area

(BASE*HEIGHT) / 2

Area of Circle

pi R²

Volume

The space of a three-dimensional object

Volume of rectangle

Area*Height

Volume of Square

L³

Volume of Sphere

4/3 pi R³

Volume of Cylinder

pi R² Height

Pythagorean theorem

Finds the lengths of a right triangle

A²+B²=C²

Circumference

pi*diameter

Diameter

2r

Equation for levers

EFFORT * EFFORT DISTANCE = RESISTANCE * RESITANCE DISTANCE

Mechanical Advantage

Resistance / Effort

Pulley Effort Equation

EFFORT = WEIGHT(resistance) / MA

Pulley Lift Equation

LIFT(height) = LENGTH OF PULL / MA

Inclined Planes and Wedges

EFFORT * INCLINE LENGTH(effort distance) = RESISTANCE * HEIGHT(resistance distance)

Wheel and Axle Equation

FORCE * LARGER WHEEL CIRCUMFERENCE = RESISTANCE * SMALLER WHEEL CIRCUMFERENCE

Resistance

weight of object

Levers; Resistance Distance

distance from weight (resistance) to fulcrum

Levers; Effort Distance

total distance from effort to fulcrum

Pulley Mechanical Advantage

# of pulleys

Screws Circumference

screw length(2) * pi

Screw MA

circumference * screw pitch

Screw Lift

Resistance or lift = effort or force *MA