Math and Measurements Page

Standard Measures as they pertain to a job.

TIME MEASURES

60 seconds (sec) = 1 minute (min)

60 min = 1 hour (hr)

24 hr = 1 day

7 days = 1 week (wk)

12 months (mon) = 1 year (yr)

365 days = 1 year (yr)

366 days = 1 leap yr

10 years (yr) = 1 decade

100 years (yr) = 1 century

LENGTH MEASURES:

12 Inches (in.) = 1 foot (ft.)

36 Inches (in.) = 1 yard (yd)

3 feet (ft.) = 1 yard (yard)

5280 feet (ft.) = 1 mile (mi)

1760 yards (yd) = 1 mile (mi)

CUSTOMARY CAPACITY

8 fluid ounces (fl oz) = 1 cup (c)

1 pint (pt) = 2 cups( c ) or 16 ounces (oz)

1 quart (qt) = 2 pints(pt) or 32 ounces (oz)

1 quart also = 4 cups

1 gallon (gal) = 4 quarts

1 gallon also = 8 pints

1 gallon also = 16 cups

8 quarts (2 gallons) also = 1 peck (pk)

4 pecks = 1 bushel (bu). This is also = to 8 gallons. This measure is used for farmers who must have a method to measure their potatoes, apples, pears, etc…

WEIGHT:

16 Ounces (OZ) = 1 Pound (LB)

2000 lb = 1 Ton (T)

PRACTICAL APPLICATIONS AND HELPFUL HINTS FOR USING U.S. STANDARD MEASURES

It is important to purchase the following tools:

Rule:

This tool is 1 ft. long. It is 12 inches long. It also clearly defines both Metric and U.S. Standard Measures for your comparisons. Please spend some time studying your Ruler.

Yardstick:

A Yardstick is 3 feet long. It is also 36 inches long. A yardstick also has the Metric Measures so that you can compare U.S. Standard Measures and Metric Measures. Please spend some time studying your Yardstick.

Tape Measure:

This measuring tool usually measures up to 12 feet. This is used for measuring lumber for linear measures. It is also used to measure the AREA AND PERIMETER of a room. This is an essential tool if you are going to be working in any construction job. It is also essential for working in a lumber or building materials company.

Table Scale:

This tool is used for measuring small amounts of food and other items that are typically used in kitchens, restaurants, or small farms. It usually measures in ounces and pounds. It usually will measure items up to about 12 or 15 pounds. There are metric comparisons on most Table Scales. Though you will probably not want to purchase this tool, it is good to study one at a restaurant if you are going to get a job as a cook or salad prep person in a restaurant.

Formulas

The following formulas will help you with measuring linear measures, square measures and capacity measures. If you wish to learn more, please see any GED Instructor in your building. They have many math books that can help with this skill.

FORMULA FOR PERIMETER OF A RECTANGLE AND A SQUARE:

RECTANGLE is a shape whose opposite sides are equal. The opposite sides are also parallel, which means that they are the same distance apart at all points.

To find the Perimeter of a rectangle, add all four sides. Perimeter = length (L) + width (w) + length (L) + width (w).

Another way to say this formula: P = 2 lengths (L) + 2 widths (w).

This method of finding a Perimeter will tell you the total of the outside measures of any rectangle.

SQUARE is a shape that has all four of its sides equal. This means that the length and width of a square are the same. To find the perimeter of a square, you can say: Perimeter = side + side + side + side. You can also say that the perimeter of a square is equal to 4S. This means take the measure of one side times 4. Example: If a room is square and one side is 8 feet long, then you can take the 8 feet times the four sides. The answer to this Perimeter problem = 32 feet.

FORMULA FOR THE AREA OF A RECTANGLE AND A SQUARE:

The flat surface of a rectangle or square is called an AREA. The Area of any figure is the number of square units it contains.

The Formula: Area = Length times Width, (A = L x W). This means that the way to determine the area of a rectangle or a square is to take the length and times it by the width.

Example: Find the area of a rectangle that measures 12 feet by 8 feet. First, we write the formula----A = L x W. Now, substitute the numbers: A = 12 x 8. Now solve the problem: Area = 96. So, this means that the area of this rectangle is 96 square feet. This means that, if you are going to lay 1 foot square ceramic tiles, you will need 96 of them to cover this flat surface. Remember, the solution (the answer) for Area is always in square units.

FORMULA FOR THE PERIMETER OF A TRIANGLE:

The triangle is a closed, three sided geometric figure. The perimeter of any triangle is the sum of its three sides. An Equilateral Triangle has all three sides that are equal. AnEquilateral Triangle has all three sides that are equal.

Perimeter = s + s + s. If a certain Equilateral Triangle has one side that is 10 feet, then using the formula, you would see that the perimeter of that triangle is 30 feet. ( 10 + 10 + 10)

An Isosceles Triangle is a triangle that has two sides that are equal. The third side is different. Still, the above formula is used. Perimeter = s + s + s.

Example: A certain Isosceles Triangle has the measures of 5 feet + 5 feet + 2 feet. The Perimeter of this Isosceles Triangle = 12 feet.

If all three sides of a triangle have different lengths, the triangle is called AScalene Triangle. The above formula is the same for this Scalene Triangle: P = s + s + s

FORMULA FOR THE AREA OF A TRIANGLE:

First, remember that a triangle is ½ of a rectangle or ½ of a square.

We do not refer to the dimensions of a triangle as length and width. We refer to the dimensions of a Triangle as Height and Base. The Area of a Triangle is ½ of the Base times the Height. Another way to say it is that the Area of a Triangle is Base times Height, divided by 2.

Example: A certain triangle has a base of 15 feet and a height of 12 feet. If the Area = ½ of the Base times the Height, then you would write the formula in this way. ½ x 15 x 12. ( .50 x 15 x 12 is the Decimal way of saying it) Another way to say it: Area = 180 divided by 2 = 90. (The 180 is the answer to what 15 x 12 equals)

FORMULA FOR VOLUME:

Volume is the space enclosed (capacity) within a three-dimensional figure,such as a bin, a box, or a room. Volume is measured in cubic units. (as in a cube)

Formula for Volume: length x width x height = Cubic unit.

If a certain cube measures 10 x15 x 4. To find out the total Volume in cubic units, multiply 10 by 15 by 4. The answer is 600 cubic units.

SOME HELPFUL HINTS IN SOLVING MEASUREMENT PROBLEMS:

1. When measuring for any perimeter, area or volume, always round off to the next number. In this way you will not be “shorting” the customer of the necessary product to complete the job that he/she is doing. Example: If a customer wants to buy carpeting for his room that is 10.5 feet by 6.25 feet, you would be safe to round up to 11 by 7 feet to make sure that the customer has enough carpet to do the job. Never round down from the actual numbers.

2. When you have measurements that are in both inches and feet, you must turn them all into feet or a fraction or decimal part of a foot to do the math. You cannot add or multiply inches and feet together. The answer will always be wrong. Example: If I have something that is 8 feet and 4 inches, I must turn it into 8.33 feet. Or, I can turn it into 8 1/3 feet. If the other side of the dimension is 7 feet and 6 inches, I can turn it into 7.5 feet, or I can turn it into the fraction of 7 ½ feet.