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1 4- Multiplying by 0, 00, and,000 Can you see a pattern in these multiplications? , , ,9 When you multiply a number by 0, 00, or,000, the product contains the same digits as the original number. However, the decimal point moves according to these rules. multiply by 0 multiply by 00 multiply by,000 Many people use this fact as a mental math strategy. move to the right one place move to the right two places move to the right three places Find each product mentally , ,40 5., Now you can use this mental math strategy to estimate some products. The secret is to recognize when one of the factors is fairly close to 0, 00, or,000. An example is shown at the right ,000, , ,8 So,.8 97 is about,8. Estimate by rounding one number to 0, 00, or, ,5.548, ,. 9. CHALLENGE Find the product,000.5 mentally. How is this different from the other exercises on this page? , Glencoe/McGraw-Hill and Connections, Course

2 4- Modeling the Distributive Property Just as you can model numbers, you can also model operations. For example, here is a model of the operations in the distributive property. 5 ( 5) Write a distributive property statement for each model ( ). (4 7) 4 7 Make a model for each statement (4 5) 4. ( 4) 4 Write a statement for each model Glencoe/McGraw-Hill 4 and Connections, Course

3 4- A Logic Puzzle Here is a puzzle that will help you brush up on your logical thinking skills. The product. 8. is in both the circle and the triangle, but not in the square. Place the product in the diagram at the right Write.7 in the.7 correct region of the diagram..7 Use the given information to place the product in the diagram above.. The product 4.9. is in both the triangle and the square, but not in the circle.. The product is in the triangle, but not in the circle or the square.. The product.4 0. is not in the circle, the square, or the triangle. 4. The product is in both the square and the circle, but not in the triangle. 5. The product is in the circle, but not the triangle or the square.. The product is in the circle, the square, and the triangle. 7. The product.5.8 is in the square, but not the circle or triangle. 8. If you did all the calculations correctly, the sum of all the numbers in the diagram should be a nice number. What is the sum? Glencoe/McGraw-Hill 5 and Connections, Course

4 4-4 Tiling a Floor The figure at the right is the floor plan of a family room. The plan is drawn on grid paper, and each square of the grid represents one square foot. The floor is going to be covered completely with tiles.. What is the area of the floor?. Suppose each tile is a square with a side that measures one foot. How many tiles will be needed?. Suppose each tile is a square with a side that measures one inch. How many tiles wil be needed? 4. Suppose each tile is a square with a side that measures six inches. How many tiles will be needed? Use the given information to find the total cost of tiles for the floor. 5. tile: square, foot by foot cost of one tile: $.50. tile: square, inches by inches cost of one tile: $ tile: square, 4 inches by 4 inches cost of one tile: $ tile: square, feet by feet cost of one tile: $ 9. tile: square, foot by foot cost of two tiles: $ tile: rectangle, foot by feet cost of one tile: $7.99. Refer to your answers in Exercises 5-0. Which way of tiling the floor costs the least? the most? Glencoe/McGraw-Hill and Connections, Course

5 4-5 Unit Pricing The unit price of an item is the cost of the item given in terms of one unit of the item. The unit might be something that you count, like jars or cans, or it might be a unit of measure, like ounces or pounds. You can find a unit price using this formula. unit price cost of item number of units For example, you find the unit price of the tuna in the ad at the right by finding the quotient The work is shown below the ad. Rounding the quotient to the nearest cent, the unit price is $0.5 per ounce. TUNA 89 ounce can Find a unit price for each item.. 5-pound bag. 8-ounce jar. CARROTS PEANUT $.9 BUTTER $.49 Grade A Jumbo EGGS Dozen $.59 $0. per pound $0.4 per ounce $0. per egg Give two different unit prices for each item. 4. Frozen 5. Purr-fect. BURRITOS CAT FOOD 5-ounce pkg /$ for $.9 -ounce can $0.70 per package; $0. per can; $.50 per jar; $0.4 per ounce $0. per ounce $0. per ounce Circle the better buy. 7. Mozarella Mozarella 8. Cheese Cheese /$4 /$ 0-ounce pkg 8-ounce pkg 8-ounce pkg Dee-light Chicken Wings $ pound bag 5-pound bag Old Tyme SPAGHETTI SAUCE -ounce jars /$ Top Q Chicken Wings $.9 8-ounce bag Glencoe/McGraw-Hill 7 and Connections, Course

6 4- Foreign Exchange The form of money that is used in a country is called the currency of that country. The rate of exchange tells you what amount of a foreign currency you would receive in exchange for one U.S. dollar. The rate changes daily. The chart at the right shows a few rates of exchange on a recent day. On this day, how many German marks would you get in exchange for $75 (U.S.)? Multiply: Round to hundredths:.48 You would get.48 German marks. Rates of Exchange Country Amount per (currency) U.S. Dollar Britain (pound) Canada (dollar).555 France (franc) Germany (mark).0 India (rupee).04 Italy (lira) 8.75 Japan (yen) 9.0 Mexico (peso) 0.50 Spain (peseta) 0.5 Yugoslavia (dinar) 0. Use the chart above. Find the amount of each currency that you would receive for $5 (U.S.).. marks. yen. pesos 4. Canadian dollars To change from an amount of foreign currency to U.S. dollars, you divide. You probably want to use a calculator to find the actual amount, but you can use compatible numbers to make an estimate. At the right you see how to estimate the number of U.S. dollars you would receive for 500 Indian rupees. 500 rupees.04?.04 is about So, 500 rupees is about $0. Use the chart above. Estimate the number of U.S. dollars that you would receive for each amount. 5. 4,500 pesetas 7. 7 dinars francs 8. 0,000 lira 9. When traveling in Canada, you find a handbag on sale for $0. You have $50 (U.S.). Do you have enough money? 0. Would you receive a greater amount of U.S. currency in exchange for 00 Canadian dollars or for 00 German marks? Glencoe/McGraw-Hill 8 and Connections, Course

7 4-7 It s in the Cards Below each set of cards, a quotient is given. Use the digits on the cards to form a division sentence with that quotient. Use as many zeros as you need to get the correct number of decimal places. For example, this is how to find a division for the cards at the right. 4 Quotient: You know that 4 8. So, one division is Quotient: Quotient: 0.04 Quotient: Quotient: Quotient: Quotient: Quotient: Quotient: 0.0 Quotient: Quotient: 0.5 Quotient: Quotient: CHALLENGE Use the cards at the right. Write four different divisions that have the quotient ; ; ; Glencoe/McGraw-Hill 9 and Connections, Course

8 4-8 Length, Mass, or Capacity? When you encounter a problem about measurement, you won t necessarily see or hear one of the words length, mass, or capacity. Often you need to decide what type of measurement is involved, then choose the best unit of measure. Tell whether each question most likely involves length, mass, or capacity.. Do I have enough milk to make this recipe?. Do I have enough string to tie around this package?. Will this punch bowl fit inside that box? 4. Will this amount of punch fit inside that bowl? 5. Is that tunnel high enough for this truck to drive through it?. Is that bridge strong enough for this truck to drive over it? Circle the most reasonable measure for each object. 7. height of a doorway 8. load limit of an elevator g kg L ml m cm,000 g,000 kg,000 L,000 ml,000 m,000 cm 9. amount of water in a bathtub 50 g.5 kg 50 L 5 ml.5 m 50 cm 0. amount of cereal in a cereal box 400 g 4 kg 4,000 ml 4 L 0.4 m 400 cm Name an item that you think has the given measure.. about kg. about 0 cm. about 50 ml 4. about 5 g Glencoe/McGraw-Hill 0 and Connections, Course

9 4-9 Other Metric Units Meters, millimeters, centimeters, and kilometers are the most commonly used metric units of length. But did you know that there are other units, like decimeters, dekameters, and hectometers? This table shows how all these units are related to the meter. kilometer hectometer dekameter meter decimeter centimeter millimeter (km) (hm) (dam) (m) (dm) (cm) (mm) km hm dam m dm cm mm,000 m 00 m 0 m m 0. m 0.0 m 0.00 m Each unit in the table is ten times as large as the unit to its right. So, km 0 hm, and hm 0 dam. It follows that km (0 0) dam, or km 00 dam. Use the chart to complete each statement dm cm. 5 hm dam km hm ,000, m = dm = cm = mm 8. km = hm = dam = m 00,00 0. dm mm 4. km dam.. dam dm Complete each chart, modeling it on the chart above. 9. kilogram hectogram dekagram gram decigram centigram milligram (kg) (hg) (dag) (g) (dg) (cg) (mg) kg hg dag g dg cg mg,000 g 00 g 0 g g 0. g 0.0 g 0.00 g 0. kiloliter hectoliter dekaliter liter deciliter centiliter milliliter (kl) (hl) (dal) (L) (dl) (cl) (ml) kl hl dal L dl cl ml,000 L 00 L 0 L L 0. L 0.0 L 0.00 L Glencoe/McGraw-Hill and Connections, Course