Ratios, Proportions, and More… 3221.MATH.1 3221.MATH.2
Ratio The relative size of two quantities expressed as the quotient of one divided by the other The ratio of a to b is a:b or a/b
Proportions An equality between ratios resulting in a constant
Directly Proportional Dividing one value by the other gives a constant value, k y = k x This equation can be written as follows: y = k x As y increases, x increases. As y decreases, x decreases. (2 properties increase or decrease together)
Direct Proportions M1 =M2 V1V2
Inversely Proportional Multiplying one value by another gives a constant value, k xy = k As y increases, x decreases. As y decreases, x increases. The graph of this is a hyperbola.
Inverse Proportions P1V1 = P2V2
Percent % Value that gives the ratio to the whole Per centum “1 out of 100” 22% “22 out of 100” 22/100 = .22
Density Ratio of mass to volume (amount of a substance in a given volume) D = m v the density of water = 1.00 g/cm3 Units of Volume: cm3, mL, m3, dm3, L Thus, the units of density may be expressed as: (g, kg) . (cm3, mL, dm3, L)
Why is density relevant? The density of substances is an important consideration in choosing materials from which to make things. Airplanes, for example, are made of low-density materials, while bridges are made of higher-density materials. Density is also important as a conversion factor between mass and volume, and vice versa.
Find the density of a substance that has a mass of 31 g and a volume of 68 cm3.
Diamond has a density of 3.26 g/ cm3. What is the mass of a diamond that has the volume of 0.351 cm3?
The mass of fuel in an airplane must be carefully accounted for before takeoff. If a 747 contains 155,211 L of fuel, what is the mass of the fuel in kg? Assume the density of the fuel to be 0.768 g/cm3.
Acetone (fingernail-polish remover) has a density of 0.7857 g/cm3.a. What is the mass in grams of 28.56 mL of acetone?b. What is the volume in milliliters of 6.54 g of acetone?
Working with percentages • Mechanics of changing a percentage to a decimal: move decimal 2 places to left • The percentage symbol helps remind you of this %
Practice • What is 20% of 35? • 11 is what percent of 20? • 6.5% of what is 80.02? • What is 10 after being increased by 15%? • What is 201.1 after being decreased by 25%?
Percent Error Actual-Measuredx 100 Actual