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Name Date Class California Standards AF2.1 LESSON Review for Mastery 4-9 Metric Measurements You can use the relationships in this table to help you convert metric units. Length 1 cm 10 mm 1 m 100 cm 1,000 mm 1 km 1,000 m Mass 1 g 1,000 mg 1 kg 1,000 g Capacity 1 L 1,000 mL 1 kL 1,000 L To change larger units to smaller units, multiply. 1 L 1,000 mL Liters are larger than milliliters, so multiply by 1,000. Move the decimal point 3 places to the right: 5.300 5.3 L mL 5.3 1,000 5,300 5.3 L 5,300 mL To change smaller units to larger units, divide. 46 cm 1 m 100 cm Centimeters are smaller than meters, so divide by 100. Move the decimal point 2 places to the left: 046 m 46 100 0.46 46 cm 0.46 m Convert each measure. 1. 15 cm to millimeters 2. 964 g to kilograms Think: 1 cm Think 1 kg mm Multiply 15 by . 15 cm = g Divide 964 by 964 g mm 3. 4.9 kL to liters kg 4. 3,531 cm to meters 4.9 by 4.9 kL = 3,531 by 3,531 cm L 5. 468 mg to grams 468 mg = Copyright © by Holt, Rinehart and Winston. All rights reserved. m 6. 0.69 kL to liters 0.69 kL g 34 L Holt Mathematics California Standards Extension of California Standards AF2.1 NS2.3 LESSON Review for Mastery LESSON Review for Mastery 4-8 Dividing Decimals 4-9 Metric Measurements You can use the relationships in this table to help you convert metric units. To divide a decimal by a decimal: Step 1: Make the divisor a whole number by moving the decimal point to the right. Length 1 cm 10 mm 1 m 100 cm 1,000 mm 1 km 1,000 m Step 2: Move the decimal point in the dividend the same number of places. Remember to place the decimal in the quotient directly above the decimal point in the dividend. Capacity 1 L 1,000 mL 1 kL 1,000 L To change larger units to smaller units, multiply. Step 3: Divide. 1.68 0.3 Divide: Mass 1 g 1,000 mg 1 kg 1,000 g 0.3 1.68 5.6 苶6 苶.8 苶 3冄1 15 18 18 1 L 1,000 mL Liters are larger than milliliters, so multiply by 1,000. Move the decimal point 3 places to the right: 5.300 5.3 L mL 5.3 1,000 5,300 5.3 L 5,300 mL 3 16.8 The divisor, 0.3, has 1 decimal place. Move the decimal point 1 place to the right in both the divisor and the dividend. To change smaller units to larger units, divide. 46 cm 1 m 100 cm Centimeters are smaller than meters, so divide by 100. Move the decimal point 2 places to the left: 046 m 46 100 0.46 Complete. 46 cm 0.46 m 0.8 苶.4 苶8 苶 1. 5.6冄4 a. How many decimal places are in the divisor? 1 b. How many places do you need to move each decimal point? Convert each measure. 1. 15 cm to millimeters 1 56冄4苶4 苶.8 苶 c. Rewrite the division. d. Complete the division. What is the quotient? Think: 1 cm 10 Multiply 15 by 10 150 15 cm = 0.8 Multiply 0.7 405 1.2 苶6 苶.4 苶5 苶 3. 0.09冄3 苶.7 苶0 苶8 苶 4. 0.59冄0 . 33 Copyright © by Holt, Rinehart and Winston. All rights reserved. California Standards Holt Mathematics Divide 4.2 4.2 There are 3 x 1.9 e 7.1 7.1 9.3 7.1 2.2 e w 8.3 8.3 4.12 w b 5.75 5.7g 5.7 45.6 g 5.75 4.18 6.2 b 5.7g 45.6 5. 6f 8 f : 3 There are 5 8 2 8 1 4 apples and 8 8 to 3 , or 5 3 or : n 15 0.14 0.14 n 15 0.14 0.14 n Copyright © by Holt, Rinehart and Winston. All rights reserved. 6.3 2.1 • 16 3 to 5 , 1 m 35 Copyright © by Holt, Rinehart and Winston. All rights reserved. 8 , or 8 apples and pieces of fruit in all. So, the to 2 , or 1 : 2 1 2 , or . 6. daisies to roses 3 8 3 to 4; 3:4; 4 8 to 9; 8:9; 9 8. roses to all flowers 9 29 3 3 to 2; 3:2; 2 • to 5 8 ratio of apples to all pieces of fruit is 3 5 5. roses to irises 1.34 m 9.1 6.3 5 , or . A large bouquet of flowers is made up of 18 roses, 16 daisies, and 24 irises. Write each ratio in all three forms. m 9.1 6.3 8. 8 There are , or . 5 : 4. apples to all pieces of fruit bananas and oranges. So, the ratio of 3 oranges and apples. So, the ratio of oranges to apples is 8 3 7. irises to daisies 7. You can read the ratios as 2 to 8 or 1 to 4. 5 There are , or . bananas to oranges is 5.75 11.95 8.04 Ratio in simplest form 1 to 4 1:4 3. bananas to oranges 6f 8.04 6. 5.7 1.9 7.3 b 5.75 6.2 4. 8.3 8 5.4 x w 8.3 4.12 3. 1.9 Ratio 2 to 8 2:8 bananas. So, the ratio of apples to bananas is x 1.9 5.4 2. Holt Mathematics In a basket of fruit, there are 8 apples, 3 bananas, and 5 oranges. Write each ratio in all three forms. 1. apples to bananas 2. oranges to apples a 75.6 e 7.1 9.3 L 34 • writing a fraction Solve. 1. 690 NS1.2 • using the word to • using a colon (:) • Use division to solve a multiplication equation involving decimals, and use multiplication to solve a division equation involving decimals. y 2.5 0.69 kL g Tamara has 2 dogs and 8 fish. The ratio of dogs to fish can be written in three different ways. n 24.8 15.2 n 24.8 24.8 15.2 24.8 n 40 a 18 4.2 a 18 4.2 m A ratio is a comparison of two numbers. • Use addition to solve a subtraction equation involving decimals, and use subtraction to solve an addition equation involving decimals. 3.6y 9 3.6 3.6 100 3,531 by 35.31 LESSON You can solve equations with decimals the same way you solve equations with whole numbers. Remember to always perform the same calculation on both sides of the equation to keep the two sides equal. 3.6y 9 kg Review for Mastery 5-1 Ratios Review for Mastery LESSON 4-10 Solving Equations Containing Decimals x 1.45 6.7 x 1.45 1.45 6.7 1.45 x 8.15 g 6. 0.69 kL to liters 0.468 California Standards 0.964 3,531 cm L Copyright © by Holt, Rinehart and Winston. All rights reserved. AF1.1 1,000 1,000 5. 468 mg to grams 468 mg = 1,000 Divide 964 by 4. 3,531 cm to meters 4.9 by 4,900 4.9 kL = Think 1 kg 964 g mm 3. 4.9 kL to liters Divide. 苶.6 苶4 苶 2. 5.2冄3 2. 964 g to kilograms mm 9 to 29; 9:29; 6.3 57.33 Holt Mathematics Copyright © by Holt, Rinehart and Winston. All rights reserved. 9 36 Holt Mathematics Holt Mathematics