Math Tools Chap. 9-12

By Ginna Royalty

Chapter 9: Directional Measurements

How fast is that-Journalists can never rely on numbers that are just given to them, they should always check numbers related to time, rate and distance.

The basic formulas for time, rate and distance are all the same, but different parts get switched around depending on what solution is needed.

Formulas:

Distance = rate x time

Rate = distance ¸ time

Time = distance ¸ rate

Although speed and velocity are often used interchangeably, they are different measurements. Speed measures how fast something is going, and velocity also indicates direction.

Formula: average speed is another word for rate, so simply plug speed into the rate formula. Average speed = distance ¸ time

Acceleration = (ending velocity – starting velocity) ¸ time

Ending velocity = (Acceleration x time) + starting velocity

A g-force is an acceleration measure, and one “g” represents the normal force of gravity on the Earth’s surface.

Math problem: 

Zionsville is 126 miles away from Cincinnati. How long would it take for the average biker to reach Cincinnati if the rider pedaled five hours a day at an average speed of 12 mph?

Time = 126 miles ¸ 12 mph = 10.5 hours

10.5 hours ¸ 5 hours/day = 2.1 days  

Chapter 10: Area Measurements

ConversionsJournalists need to be able to express accurate and clear measurements for their readers. Analogies are a great way to explain measurements because readers are able to visualize the information. However, analogies won’t work if they don’t understand the comparison and they also don’t convey exact measurements. Another way to explain measurements is by using simple, accurate numbers.

Smaller spaces are measured in square inches or square feet. Larger areas are measured in square feet, square yards or square rods. Fields and farms are measured in acres. States, cities and counties are measured in square miles.

Formulas:

Perimeter = (2 x length) + (2 x width)

Area = length x width

Area of a triangle = .5 base x height

Circumference of a circle = 2P x radius

Area of a circle = P x radius2

Math problem: A fence outside Emily’s house has a length of 12 feet and width of 7 feet. What is the perimeter?

Perimeter = (2 x 12) + (2 x 7) = 24 + 14 = 38

Chapter 11: Volume Measurements

common liquid conversionsVolume measurements play an important role in journalism and many details are needed. Terms like a ton, box, barrel and cord take on different meanings in the business world. Liquid measurements can be used in things like recipes and bodies of water.

There are many common liquid conversions that journalists should know including pints to quarts, quarts to gallons, etc.

Formula: Volume = length x width x height

Firewood is sold by a measurement called a cord. A cord is 128 cubic feet when the wood is neatly stacked in a line or row.

There are three different types of tons:

  • A short ton is equal to 2,000 pounds
  • A long ton is equal to 2,240 pounds
  • A metric ton is equal to 1,000 kilograms, or 2,204.62 pounds

Ton conversions:

  • Short to long ton: Multiply by .89
  • Short to metric ton: Multiply by .9
  • Long to short ton: Multiply by 1.12
  • Long to metric ton: multiply by 1.02
  • Metric to short ton: multiply by 1.1
  • Metric to long ton: multiply by .98

Math problem:

How many ounces are there in 9 tablespoons of milk if 2 tablespoons = 1 fluid ounce.

 9/2 = 4.5 fluid ounces

 Chapter 12: The Metric System

10 copyAlmost the whole world uses the metric system, besides the United States. The metric system is an important part of international commerce and science and is important for journalists to understand.

The international decimal-based metric system is based on multiples of 10. Every measurement uses standard language for each level: giga, mega, milli, micro, etc.

The meter is the basic unit of length. Mass is also derived from the meter. The metric system is based on the decimal system, so people can change from one unit to another by multiplying or dividing by 10, 100, 1,000 or other multiples of 10.

To convert American lengths to metric:

Multiply:

  • Inches by 25.4 to find millimeters or 2.5 to find centimeters
  • Feet by 30 to find centimeters or 0.3 to find meters
  • Yards by 90 to find centimeters or 0.9 to find meters
  • Miles by 1.6 to find kilometers

To convert metric lengths to American:

Multiply:

  • Millimeters by 0.04 to get inches
  • Centimeters by 0.4 to get inches
  • Centimeters by 0.033 to get feet
  • Meters by 39 to get inches
  • Meters by 3.3 to get feet
  • Meters by 1.1 to get yards
  • Kilometers by 0.62 to get miles

To convert American area measurements to metric:

Multiply:

  • Square inches by 6.5 to find square centimeters
  • Square feet by 0.09 to find square meters
  • Square yards by 0.8 to find square meters
  • Square miles by 2.6 to find square kilometers
  • Acres by 0.4 to find hectares

To convert metric measurements to American:

Multiply:

  • Square centimeters by 0.16 to get square inches
  • Square meters by 11 to get square feet
  • Square meters by 1.2 to get square yards
  • Hectares by 2.5 to get acres
  • Square kilometers by 0.4 to get square miles

To covert American mass measurements to metric:

Multiply:

  • Ounces by 28 to find grams
  • Pounds by 0.45 to kilograms
  • Pounds by .07 to get stones
  • Short tons by 0.9 to find metric tons

To convert metric mass measurements to American:

Multiply:

  • Grams by 0.035 to get ounces
  • Grams by 0.002 to get pounds
  • Kilograms by 35 to get ounces
  • Kilograms by 2.2 to get pounds
  • Metric tons by 1.1 to get tons

To convert American volume measurements:

Multiply:

  • Teaspoons by 5 to find milliliters
  • Tablespoons by 15 to find milliliters
  • Fluid ounces by 30 to find milliliters
  • Cups by 0.24 to find liters
  • Pints by 0.47 to find liters
  • Quarts by 0.95 to find gallons
  • Gallons by 3.8 to find liters
  • Cubic feet by 0.03 to find cubic meters
  • Cubic yards by 0.76 to find cubic meters

To convert metric volumes to American forms:

Multiply:

  • Milliliters by 0.034 to get fluid ounces
  • Milliliters by 0.002 to get pints
  • Liters by 2.1 to get pints
  • Liters by 1.06 to get quarts
  • Liters by 0.26 to get gallons
  • Cubic centimeters by 0.06 to get cubic inches
  • Cubic meters by 35 to get cubic feet
  • Cubic meters by 1.3 to get cubic yards

To convert Fahrenheit to Celsius:

Celsius = .56 x (Fahrenheit -32)

To convert Celsius to Fahrenheit:

Fahrenheit = (1.8 x Celsius) + 32

Math problem:

 975 meters = How many millimeters?

 1 millimeter = 1/1000 of a meter

 975 x 1/1000 = .975 millimeters

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