Module: Measurements: Length, Time, Weight, and Liquid

Module: Measurements: Length, Time, Weight, and Liquid

Objectives

Use a standard ruler.
Use a standard measuring cup.
Use a calendar.
Memorize the following English equivalencies: 12 in = 1 ft; 3ft = 1 yd; 16 oz = 1 lb; 2,000 lbs. = 1 ton; 2 pts = 1 qt; 4 qts = 1 gal
Recognize common abbreviations for common English units.
Compare English units using the symbols greater than (>), less than (<), or equal to (=).
Solve applied word problems involving English units.

The standard units of measurement commonly used in the United States are for length, time, liquid, and weight. It is necessary to memorize these units and equivalents. This information is useful not only in math courses but also in everyday life. The graph below shows the units of measurement that you need to know to successfully work through this learning packet. The larger units are on the left. The smaller equivalent units are on the right. Also, note how each unit is abbreviated.

UNITS OF MEASURE

Measures of length

1 foot (ft) = 12 inches (in)

1 yard (yd) = 36 inches

1 yard = 3 feet

Measures of Time

1 minute (min) = 60 seconds (sec)

1 hour (hr) = 60 minutes

1 day (da) = 24 hours

1 year (yr) = 365 days

Liquid Measures

1 quart (qt) = 2 pints

1 gallon (gal) = 4 quarts

Measures of Weight

1 pound (lb) = 16 ounces (oz)

1 ton (T) = 2000 pounds

Measures of Length

1 foot (ft)=12 inches (in)

1 yard (yd)=36 inches

1 yard=3 feet

In many situations you encounter in everyday life, you need to be able to change one unit of measurement to another. This is called measurement conversions. For example, if you need to know how many quarts you can get from a certain number of gallons, you have to convert (change) gallons to quarts. One method used to convert measurements is to multiply or divide. When converting from a larger unit to a smaller unit, multiplication is required. This is because you will get more of the smaller unit than the larger unit. When converting from a smaller unit to a larger unit, division is required because you will be getting fewer of the larger unit. For example, if you need to convert 2 hours to minutes, you need to multiply 2 by the number of equivalent units (minutes) in one hour. There are 60 minutes in one hour, so 60 X 2 = 120 minutes. Notice that you get more of the smaller unit (120). To convert 120 minutes to hours, divide 120 by 60 because you’re converting from a smaller unit (minutes) to a larger unit (hours).

Study the following examples before completing the exercise on measures of length:

Example 1: How many inches are in 5 feet?

You are converting from a smaller unit to a larger one. Multiplication is necessary.
Recall that there are 12 inches in one foot, so 5 X 12 = 60 inches.
Therefore, there are 60 inches in 5 feet.

Example 2: How many yards are in 15 feet?

You are converting from a smaller unit to a larger one. Division is required.
There are 3 feet in one yard. 15/3 = 5 yards.
So, there are 5 yards in 15 feet.

Example 3: 18 inches = _____yards?

You are converting from a smaller unit to a larger one. Division is required.
Recall that there are 36 inches in a yard, so 18/36 = ½.
If you get a fractional answer, make sure it is reduced to lowest terms.

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #1

Topic: Basic Unit Conversion

Directions: Change each measurement to the new unit. Write fractional answers in lowest terms.

72 inches = ______yards6. 15 inches = ______feet

6 feet = ______yards7. 16 feet = ______yards

3 yards = ______feet8. 10 feet = ______inches

5 feet = ______inches9. 90 feet = ______yards

100 inches = ______yards10. 4 1/3 yards ______inches

The Ruler

The ruler below is a standard 12-inch ruler (one foot). Each different fraction of an inch is represented by a line of different height on the ruler (for example 1/16, 1/8, ¼, ½, etc.). The smallest divisions represent 1/16 inch. To find how far one point on the ruler is from another point, count the number of sixteenths between the points. In some cases, you will need to reduce the fractional unit to lowest terms. For example, if a point on the ruler is 4/16 inch, you need to state it as ¼ inch.

Example 1: Place a dot that shows 3 5/16 inches on the ruler. First locate the whole number 3. Then, count five 1/16 inches from 3. The dot shows

3 5/16 inches.

Example 2: The dot on the ruler below shows 4 8/16. The fraction 8/16 needs to be reduced to lowest terms. Therefore, we write the fraction as 4 ½.

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #2

Topic: Using a Ruler

Directions: Place a dot on the rulers below that show the indicated length in inches.

3 ¼ inches

5 3/8 inches

5/16 inch

2 ½ inches

1 9/16 inches

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #2A

Topic: Measuring with a Ruler

Directions: Measure the following lines with a ruler. Round your answers to the nearest 1/16-inch and reduce fractional answers to lowest terms.

1.______=_____ inches

2.______=_____ inches

3. __=_____ inch

4.______=_____ inches

5. ______=_____ inch

Time

A day is divided into hours, minutes, and seconds. You can change units of time by multiplying or dividing. Remember, to change larger units to smaller units, multiply. To change smaller units to larger units, divide. Memorize the following units of time and their equivalents.

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

Example 1: Six hours is how many minutes?

You need to convert from a larger unit to a smaller one, so multiplication is necessary. There are 60 minutes in one hour, so multiply 6 times 60 (6 x 60)
The answer is 360 minutes.

Example 2: Convert 540 seconds to minutes.

Division is required since you’re converting from a smaller unit to a larger one.
There are 60 seconds in a minute, so divide 540 by 60 (540/60)
The answer is 9 minutes.

Example 3: Change 45 minutes to hours.

Division is necessary since you’re changing from a smaller unit to a larger one.
There are 60 minutes in one hour, so divide 45 by 60 (45/60)
The answer is ¾ or .75 hr.

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #3

Topic: Changing Time Units I

Directions: Change the units of time. Write fractional answers in lowest terms. You may use a calculator for problems 6 – 10.

180 minutes = _____hours.6. 40 seconds = _____minutes

10 days = _____hours.7. 36 hours = _____days

6 minutes = _____seconds8. 15 seconds = _____minutes

Half hour _____minutes9. 190 minutes =_____hours

144 hrs. = _____days 10. 2 ½ hrs. = _____minutes

The Calendar

A calendar year is divided into months, weeks, and days. The partial calendar below shows the months and days for October, November, and December in the year 2004. NOTE: To change a larger unit to a smaller unit, multiply. To change a smaller unit to a larger unit, divide.

October 2004 / November 2004 / December 2004
Su Mo Tu We Th Fr Sa
1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31 / Su Mo Tu We Th Fr Sa
1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 / Su Mo Tu We Th Fr Sa
1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31
Oct 11 Columbus Day / Nov 11 Veterans Day / Dec 24 ‘Christmas Day’ observed
Oct 31 Halloween / Nov 25 Thanksgiving Day / Dec 25 Christmas Day
Dec 31 ‘New Year’s Day’ observed

7 days = 1 week

52 weeks = 1 year

12 months = 1 year

Example 1: Sixty months is how many years?

You are asked to change from a smaller unit to a larger unit, so division is needed to find the answer.
Since there are 12 months in one year, divide 60 by 12 (60/12)
The answer is 5 years.

Example 2: Change 2 years to weeks.

You are asked to change from a larger unit to a smaller unit, so multiplication is needed to find the answer.
There are 52 weeks in one year, so in 2 years, multiply 52 by 2 (52 x 2)
The answer is 104 weeks.

Example 3: Change 75 months to years.

A smaller unit is being changed to a larger one. Division is required.
Since there are 12 months in a year, divide 75 by 12 (75/12)
The answer is 6 ¼ or 6.25 years

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #4

Topic: Using a Calendar

Directions: Use the three months in 2004 to write each day and date.

Thirteen days after November 11

______

Two weeks before October 29

______

The fourth Monday in November

______

Four days after the last Friday in October

______

Nine days before November 23

______

On what day does Christmas Day fall?

______

Maria wants to avoid paying finance charges if she pays the bill in full within 30 days. If she purchases an item on October 6, when is the latest she can pay the bill without paying finance charges?

______

Lue’s mother’s birthday is three weeks from November 10. When is her birthday?

______

A child must be on medication for 10 days before going back to school. If she starts taking the medication on November 28, when can she return to school?

______

Jose buys a computer but must return it within 15 days for a full refund. If he buys the computer on December 3, when is the latest he can return it for a refund?

______

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #5

Topic: Changing Time Units II

Directions: Change the following units of time. Write fractional answers in lowest terms. You may use the GED calculator for problems 6 – 10.

8 days = ______hours6. 9 days = ______weeks

4 weeks = ______days7. 75 days =______weeks

12 years = ______months8. 100 weeks = ______years

3 years = ______days9. 2 ½ years = ______days

84 days = ______weeks 10. 30 weeks = ______year(s)

Liquid Measures

Measuring the amount of milk in a bottle, the amount of juice or water in a pitcher, or the number of gallons of gas in a container are examples of using liquid measurements. For this unit, you will need to memorize the following liquid measurements and their equivalents:

1 qt. = 2 pts.

4 qts. = 1 gal.

Let’s review the rules for changing one unit to another. To change from a larger to smaller unit, multiply the number of smaller units in each larger unit. To change from smaller to larger units, divide by the number of smaller units in each larger unit. Remember, a remainder can be written as a number of smaller units OR as a fraction of the larger unit. Study the following examples:

Example 1: Eight gallons is how many quarts?

Multiplication is required to get the answer since you’re changing a larger unit into a smaller one.
There are 4 quarts in one gallon, so multiply 4 x 8
The answer is 32 quarts.

Example 2: Twelve pints is how many quarts?

Division is required since you’re converting from a smaller unit to a larger one.
There are 2 pints in one quart, so perform 12 divided by 2 (12/2)
The answer is 6 quarts.

Example 3: 18 quarts are how many gallons?

Division is required since you are changing from a smaller unit to a larger one.
There are 4 quarts in one gallon, so divide 18 by 4 (18/4)
The answer is 4 ½ gallons. You may also write this answer using 2 units of measurements: 4 gallons and 2 quarts. The remainder of 2 is the number of quarts left over.

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #6

Topic: Changing Liquid Measurement Units

Directions: Change the following units of liquid measurements. Some answers will need to be expressed as fractions reduced to lowest terms. You may use the GED calculator for problems 6 – 10.

4 gallons = _____ quarts6. 24 gallons = _____ quarts

6 quarts = _____ pints7. 50 quarts = _____ pints

14 pints = _____ quarts8. 42 quarts = _____ gallons

22 quarts = _____ gallons9. 2 quarts = _____ gallons

30 pints = _____ quarts 10. 1 ½ quart = _____ pints

The Measuring Cup

In the home, the most common tool for measuring capacity is the measuring cup. The vertical scale on the measuring cup shows capacity in fluid ounces (on the right) and fractions of a cup (on the left). Study the measuring cup and the example below:

Example: Six fluid ounces is what fraction of a cup?

To the right of the cup, locate 6 fluid ounces (fl. oz.)
Then, read over to the left to get the equivalent measure in cups.
The fraction is ¾, so 6 fl. oz. = ¾ cup.

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #7

Topic: Using a Measuring Cup

Directions: Shade the following measuring cups for the amount indicated.

½ cup

How many fl. oz.? _____

2 fl. oz.

How many cups? _____

1 cup

How many fl. oz.? _____

Comparing English Units

Sometimes it is necessary to compare units of measurements. We use the symbols less than (<), greater than (>), or equal to (=). When comparing units, be sure to read them from left to right and convert both units to the smaller unit. Study the following examples before completing the exercise.

Example 1: 44 in _____ 3 ft

First, convert 3 feet into inches. You are converting from large to small; therefore, multiplication is necessary.
Multiply 3 by 12 since there are 12 inches in one foot. This equals 36 inches.
Now reading from left to right, 44 in > 36 in.

Example 2: 3 hrs. _____ 200 min.

First, convert 3 hours into minutes. You are converting from a large unit to a smaller one, so multiplication is necessary.
Multiply 3 by 60 since there are 60 minutes in 1 hour. This equals 180 minutes.
Now reading from left to right, 180 min < 200 min.

Example 3: 50 qts _____ 8 gal

First, convert 8 gallons into quarts.
Multiply 8 by 4 since there are 4 quarts in 1 gallon. This equals 32 quarts.
Now reading from left to right, 50 qts > 32 qts.

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #8

Topic: Comparing English Units

Directions: Use the symbols greater than (>), less than (<), or equal to (=) to compare the following English units. Be sure to read the units from left to right.

6 ft _____ 100 in6. 12 ft _____ 5 yd

48 oz _____ 2 lb7. 9 ft. _____ 500 in

30 qts. _____ 5 gal8. 7 gal _____ 30 qt

48 in _____ 4 ft9. 130 min _____ 2 hr

5. 2 T _____ 4,000 lb10. 40 yd _____ 120 ft

Assigned To: ______

Date Assigned: ______

Subject Area: Measurement – Exercise #9

Topic: Applied Problem Solving Involving English Units

Directions: Read each problem carefully. Solve the problem and write the answer on the line provided. Be sure that your final answer is reasonable (makes sense).

Mia’s birthday is in 42 days. How many weeks is it until her birthday?

______weeks

Jose attended a meeting with his son’s teacher for 45 minutes. For what fraction of an hour was the meeting?

______hour

3.Robert’s daughter, Rachael, is participating in a reading club contest at school. The student who reads the most minutes in one month will be the winner. For the first week, she read 4 ½ hours. How many minutes has she read?

______minutes

4. Juanita is paid by the hour for word processing at the office. On Monday, she

word processed documents for 300 minutes. For how many hours will she be paid?

______hours

5. Skin is the largest human organ. On average, a person’s skin weighs 384 ounces.

How many pounds does an average person’s skin weigh?

______pounds

6. A teacher needed 40 more pints of milk for his field trip. How many quarts did

he need?

______quarts

7. The Ali family uses 14 quarts of milk every week. How many gallons of milk

does the family use each week?

______gallons

8. Mary’s salary is $380 per week. What is her annual (yearly) salary?

______anually

9. Mr. Jones needs to deliver 3 tons of cement to a business. How many pounds

is this?

______pounds

10. Below are 2 recipes for pizza dough and pizza sauce. Double the ingredients for the recipe and write the new amounts on the blanks for the new recipe to the right.

Pizza doughNew recipe

1 tsp. active dry yeast_____tsp. active dry yeast

¾ cup warm water_____cups warm water

½ teaspoon salt_____teaspoon salt

1 ¾ to 2 cups unsifted flour_____to_____cups unsifted flour

Pizza sauceNew recipe

½ 6 oz. tomato paste_____6 oz. tomato paste

1/3 cup water_____cup water

½ teaspoon salt_____teaspoon salt

¼ teaspoon pepper_____teaspoon pepper

½ teaspoon oregano_____teaspoon oregano

½ teaspoon basil_____teaspoon basil

1/8 teaspoon garlic powder_____teaspoon garlic powder

Measurement Answer Key

Exercise 1Exercise 3

1. 21. 360

2. 22. 240

3. 93. 360

4. 604. 30

5. 2 7/95. 6

6. 1 ¼6. 2/3

7. 5 1/37. 1 1/2

8. 1208. 1/4

9. 309. 3 1/6

10. 15610. 150

Exercise 2

Have your teacher check these answers.

Exercise 2AExercise 4

1 9/161. November 24
1 3/162. October 15
3/163. November 22
2 5/164. November 2
11/165. November 14

6. Saturday

7. November 5

8. December 1 9. December 9

10. December 17

Exercise 5Exercise 7

1924, ¼, 8
28
144
1,095Exercise 8
12
1 2/71. <
10 5/72. >
1 12/133. >
912 ½4. =
15/265. =

6. <

Exercise 67. <

8. <

16 9. >
12 10. =
7
5 ½
15
96
100
10 ½
½
3

Exercise 9

6
¾
270
5
24
20
3 ½
$19,760
6,000
2 tsp. active dry yeast

11/2 cups warm water

1 teaspoon salt

3 ½ to 4 cups unsifted flour

1 6 oz. Tomato paste

2/3 cup water

1 teaspoon salt

½ teaspoon pepper

1 teaspoon oregano

1 teaspoon basil

¼ teaspoon garlic powder