Lesson 6. Convert Units of Length To convert a unit of measure, multiply by a conversion factor. A conversion factor is a rate in which the two quantities are equal, but are expressed in different units. 2,2 ft 5 mi Step Choose a conversion factor. mile 5 5,280 feet, so use the conversion factor mile 5,280 feet. 2,2 ft 3 mi 5,280 ft 5 2,2 ft 3 mi 5,280 ft 5 5,280 2,2 mi 5 2_ 5 mi Customary Units of Length foot (ft) 5 2 inches (in.) yard (yd) 5 36 inches yard 5 3 feet mile (mi) 5 5,280 feet mile 5,760 yards So, 2,2 ft 5 2_ 5 mi. When converting metric units, move the decimal point to multiply or divide by a power of ten. dm 5 hm 0 0 0 0 0 0 hecto- deka- meter deci- centi- milli- Step Start at the given unit. Step 3 Move the decimal point that same number of spaces in the same direction. Fill any empty place-value positions with zeros. So, dm 5 0.0 hm...5 miles 5 yards 2. 0.8 hectometers 5 millimeters 3. 8 inches 5 feet. 5 centimeters 5 dekameters R
Lesson 6.2 Convert Units of Capacity Capacity is the measure of the amount that a container can hold. When converting customary units, multiply the initial measurement by a conversion factor. 35 c 5 qt Step Choose a conversion factor. quart 5 cups, so use the conversion factor quart cups. 35 c 3 qt c 5 35 c 3 qt c 5 35 qt 5 8 3_ qt You can rename the fractional part using the smaller unit. Customary Units of Capacity 8 fluid ounces (fl oz) 5 cup (c) 2 cups 5 pint (pt) 2 pints 5 quart (qt) cups 5 quart quarts 5 gallon (gal) 8 3_ quarts 5 8 quarts, 3 cups So, 35 c 5 8 3_ qt, or 8 qt, 3 c. When converting metric units, move the decimal point to multiply or divide by a power of ten. 26 cl 5 hl 0 0 0 0 0 0 hecto- deka- liter deci- centi- milli- Step Start at the given unit. Step 3 Move the decimal point that same number of spaces in the same direction. Fill any empty place-value positions with zeros. So, 26 cl 5 0.0026 hl.. 0.72 kiloliters 5 deciliters 2. 78 qt 5 gal, qt 3. 52 liters 5 hectoliters. 5 pints 5 cups R5
Lesson 6.3 Convert Units of Weight and Mass In the customary system, weight is the measure of the heaviness of an object. When converting customary units, multiply the initial measurement by a conversion factor. 9 lb 5 oz Step Choose a conversion factor. 6 ounces 5 pound, so use the conversion factor 6 ounces pound. Customary Units of Weight pound (lb) 5 6 ounces (oz) ton (T) 5 2,000 pounds 9 lb 3 6 oz 5 9 So, 9 lb 5 30 oz. 3 6 oz 5 30 oz 5 30 oz In the metric system, mass is the measure of the amount of matter in an object. When converting metric units, move the decimal point to multiply or divide by a power of ten. 3. dag 5 mg 0 0 0 0 0 0 hecto- deka- gram deci- centi- milli- Step Start at the given unit. Step 3 Move the decimal point that same number of spaces in the same direction. Fill any empty place-value positions with zeros. So, 3. dag 5 3,000 mg.. 3.2 dg 5 hg 2.,500 pounds 5 tons 3. 3.5 grams 5 milligrams. 3 pounds 5 ounces R6
Lesson 6. Transform Units To solve problems involving different units, use the relationship among units to help you set up a multiplication problem. Green peppers are on sale for $.80 per pound. How much would 2.5 pounds of green peppers cost? Step Identify the units. You know two quantities: pounds of peppers and total cost. You want to know the cost of 2.5 pounds. $.80 per lb 5 $.80 Step 2 Determine the relationship among the units. The answer needs to be in dollars. Set up the multiplication problem so that pounds will divide out. $.80 3 2.5 lb 5 $.80 3 2.5 lb 5 $.50 Step 3 Use the relationship. So, 2.5 pounds of peppers will cost $.50. Solve.. If 2 bags of cherries cost $5.50, how much do 7 bags cost? a. What are you trying to find? 2. The area of a living room is 2 square yards. If the width is 2 feet, what is the length of the living room in yards? a. What is the width in yards? b. Set up the problem. b. Set up the problem. c. What is the cost of 7 bags? c. What is the length in yards? R7
Lesson 6.5 Problem Solving Distance, Rate, and Time Formulas Use a formula to solve the problem. A bug crawls at a rate of 2 feet per minute. How long will it take the bug to crawl 25 feet? Read the Problem What do I need to find? I need to find Solve the Problem Write the appropriate formula. t 5 d r. What information do I need to use? Substitute the values for d and r. I need to use the the bug crawls and the at which the bug crawls. t 5 ft 2 min ft How will I use the information? First I will choose the formula because I need to find time. Next I will Rewrite the division as multiplication by the reciprocal. t 5 25 ft 3 min 2 ft 5 min substitute for d and for r. Then I will to find the time.. A family drives for 3 hours at an average rate of 57 miles per hour. How far does the family travel? 2. A train traveled 283.5 miles in 3.5 hours. What was the train s average rate of speed? R8