Skill 17 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Read: is less than. ↓ On the number line, 0.7 is to the left of 0.9. So, 0.7 � 0.9 0 0.9 2 2 ones . . . 6 0 6>0 hundredths 7 7 tenths Read: is greater than. • Since the ones and tenths are the same, compare hundredths. 6 hundredths are greater than 0 hundredths. So, 2.76 � 2.70. Ones are Tenths are Hundredths the same. the same. are different. ↓ 0.7 least greatest • Compare two numbers at a time. 0.94 0.50 0.98 0.50 0.98 0.94 Order Decimals Order from least to greatest: 1.38, 0.94, 0.5, 0.98. • Write the numbers in a list. Align the digits. Write zeros if needed. 1.38 This number is greatest. 0.94 None of the other 0.50 numbers has ones. 0.98 ? ? ? 1.38 same 5 � 9 same 8 � 4 0.5 , least 0.94 , 1.38 greatest Go to the next side. 0.98 , 0.94 � 0.5 0.5 � 0.98 0.98 � 0.94 In order from least to greatest, the numbers are: same 9 � 5 ↓ ↓ ↓ 79 ↓ ↓ Use Place Value Compare: 2.76 � 2.7. Use a place value table. • Align the digits by place values. • Then compare digits starting with the ones place. • Write a zero to the right of 7 in 2.7 so both numbers have the same number of places. ↓ ↓↓↓ ↓ Use a Number Line Compare: 0.7 � 0.9. The number line is labeled in intervals of tenths from 0 to 1. Find 0.7 and 0.9 on the number line. A decimal is a number with one or more digits to the right of the decimal point.There are different ways to compare decimals. Compare and Order Decimals © Houghton Mifflin Harcourt Publishing Company Name Skill Holt McDougal Mathematics Name Skill Skill 17 Practice on Your Own Order the numbers from greatest to least: 1.37, 1.56, 1.23, 1.59. List the numbers. Compare two numbers at a time. ↓ �2 1.37 � 1.56 ↓ 3 �5 ↓ 1.56 � 1.59 The ones digits are the same. ↓ 6 �9 1.37 � 1.23 1.37 � 1.56 1.56 � 1.59 ↓ 1.59 3 ↓ ↓ 1.23 1.37 � 1.23 Compare these first. Their tenths digits are different. 1.56 ↓ ↓ 1.37 Ordered from greatest to least: 1.59, 1.56, 1.37, 1.23 Use the number line. Write �, �, or � for �. 0.09 � 0.02 0.25 � 0.30 2 3 0.5 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 � 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Use place value. Write �, �, or � for 4 2.06 5 � 2.10 4.8 ones . tenths hundredths �. 6 � 4.19 ones . tenths hundredths 7.36 � 7.36 ones . tenths hundredths Order the numbers from least to greatest, or greatest to least. 7 8 3.42, 0.89, 0.91 , least 9 2.65, 0.03, 2.4, 0.5 , , greatest , least 1.18, 1.27, 1.11, 1.3 , greatest , greatest , , least Check In Exercises 10 and 11, write �, �, or � for �. 10 11 0.72 � 0.7 5.28 � 5.29 12 Order from greatest to least. 2.83, 1.7, 2.48, 2.38 80 13 Order from least to greatest. 1.38, 0.5, 1.83, 1.18 Holt McDougal Mathematics © Houghton Mifflin Harcourt Publishing Company 1 9 �� 4 + 9 4 4 1 �� � �� � �� � �� 4 4 4 4 + with circles for 95 1 ��. 4 Step 2 Group the parts. 1 � � 3 2 1 �� � �� � �� 2 2 2 1 � �2� + 2 � � 2 � �3� 1 � 1 � 1 � �4� + parts as wholes and 2 3 4 5 6 7 8 �� �� �� �� �� �� �� 2 3 4 5 6 7 8 Skill 21 3 � � + Go to the next side. 3 � �4� + written as a mixed number is 21�4�. 11 4 4 3 �� � �� � �� � �� 4 4 4 4 9 �� 4 � So, 9 1 �� � 1 � 1 � �� 4 4 1 � 2 � �4� 1 � 2�4� Step 3 Write the sum as a mixed number. These are some different names for 1: 9 4 4 1 �� � �� � �� � �� 4 4 4 4 1 �� 4 5 3 2 �� � �� � �� 3 3 3 Write each improper fraction as a mixed number. Try These Step 1 Model You can write an improper fraction as a mixed number. Write the fraction 9�4� as a mixed number. Write an Improper Fraction as a Mixed Number © Houghton Mifflin Harcourt Publishing Company Name Skill Holt McDougal Mathematics Name Skill Skill 21 Practice on Your Own Think: + Find the names for 1 in fraction form. Then add the names for 1 and the fraction. Write the sum as a mixed number. + 12 5 5 2 �� � �� � �� � �� 5 5 5 5 2 � 1 � 1 � �5� 2 � 2 � �5� 2 � 2�5� Write each improper fraction as a mixed number. � � � � � 9 �� � �� � �� � �� � �� � �� 2 2 2 2 2 2 � � � � � � � 4 � � � 8 �� � �� � �� � �� 3 3 3 3 � � � � � � 13 �� � 5 � � � � ����� �� �� �� � � � � � 7 � 2 5 7 �� � 2 � � � � 8 � � � � 15 �� � � � � � � � � � � �� 4 4 4 4 4 � � � � � � � ������� � � �� � � �� � � � � � � � 15 �� � 8 3 6 11 �� � 3 � � � � ������� � � � � �� � � � � � � � � � 9 24 �� � 5 19 �� � 6 Check Write each improper fraction as a mixed number. 10 25 �� � 8 11 27 12 17 �� � 10 �� � 4 96 Holt McDougal Mathematics © Houghton Mifflin Harcourt Publishing Company 1 1 99 1 3�2� 1 � 3 � � �� 1 � �3� � �3� � �3� � 1 1 2�3� � 1 � 1 � �3� 1 2�3� 2 ↓ ↓ 2 2 2 1 � �2� � �2� � �2� � �2� ↓ 1 � 1 � 1 � 1 � �2� � � � �� � � 3 � �4� � �4� � �4� � �4� � 3�4� � 1 � 1 � 1 � �4� 3 3 3�4� 3 Step 2 Use the denominator of the fraction to write equivalent fractions for the ones. Write each mixed number as an improper fraction. Try These 3�2� � 1 � 1 � 1 � �2� 1 Step 1 Write the whole number as a sum of ones. Write the mixed number 3�2� as an improper fraction. 1 Write a Mixed Number as a Fraction © Houghton Mifflin Harcourt Publishing Company 1 3 4 2 4 � � � �� 4 � �5� � �5� � 1 1 7 Go to the next side. So, the fraction for 3�2� is �2� . 2 1�5� � 1 � �5� 4 1�5� � �2� 7 2 � �2� � �2� � �2� � �2� 3�2� � 1 � 1 � 1 � �2� ↓ ↓ ↓ 1 Step 3 Add the numerators to find the improper fraction. Skill 22 Name Skill Holt McDougal Mathematics Name Skill Skill 22 Practice on Your Own Think: 2 Write the whole number as a sum of ones. Write equivalent fractions for the ones. Add the numerators to find the fraction. 2 2�5� � 1 � 1 � �5� 5 5 2 � �5� � �5� � �5� 12 � �5� Write each mixed number as an improper fraction. 2 1 4�2� 1 1 3 4�2� � 1 � 1 � 1 � 1 � �2� � � � 3 2�4� � � 1 � �2� � �2� � �2� � �2� � �2� � 3 � �4� � �4� � �4� � � � � � �� 3 3 2�4� � 1 � 1 � �4� � �� 4 2 3�3� 2 3�5� 2 3�5� � 2 � � � � �� � 2 3�3� � 1 � 1 � 1 � �3� � � � � � � � � � � � �� � � � �� � �� � �� � �� � 2 � �3� � �3� � �3� � �3� � � � �� 5 6 1 2�8� 1 2�8� � � � � � �� � � � � � � 5 3�6� � � �� � � � � � � �� � � �� � �� � �� 7 3 5�4� � 5 3�6� � � � � � � � � � �� � � � �� � � � � � � � � � 8 9 4 8�5� � 2 6�3� � Check Write each mixed number as an improper fraction. 10 3 5�4� � 11 12 1 6�8� � 100 3 4�5� � Holt McDougal Mathematics © Houghton Mifflin Harcourt Publishing Company 1 L I L L I L 5. � 6. � 7. 0.89, 0.91, 3.42 8. 0.03, 0.5, 2.4, 1. 7, 4, no, 37 2. 1, 2, no, 83.1 3. 2, 5, 63 4. 7, 6, 52.488 22 hundredths PRACTICE 432 56 hundredths 690 and 8. 123 thousand, © Houghton Mifflin Harcourt Publishing Company 489 and 9 tenths 7. 6 thousand, CHECK 6. 2,165.5 12. 35.613 11. 47.5 19 hundredths 5. 169.45 10. 62 CHECK 9. 0.812 8. 57.1 7. 2 6. 4, 27.595 434 and 106 thousand, 4. 106,434.19; 3 tenths 3. 890.3; 890 and 68 hundredths 2. 177.68, 177 and 57 hundredths 1. 23.57; 23 and 1.83 13. 0.5, 1.18, 1.38, 2.38, 1.7 12. 2.83, 2.48, 11. � 10. � CHECK 1.11 9. 1.3, 1.27, 1.18, 2.65 4. � PRACTICE sand, 351 and 5. 8, 4.8 3. � 3. 4, 7, yes, 28.535 3 tenths 1. 826.3; 826 and 2. 4,351.22; 4 thou- PRACTICE 17 K 2. � S 2. 1, 1, no, 13.1 S 1. � TRY THESE 16 K L TRY THESE 15 I L 1. 7, 6, yes, 8 S K I L S 2 5 10. �6� 7 11. �8� 6 12. �1�0 9 9. �9� 3 8. �8� 3 7. �6� 2 6. �3� 5 5. �7� CHECK �� 3. 1, 2, 1 2 5 4. �8� 1. 1, 4, �4� 3 2. 3, 4, �4� 1 3. 2, 5, �5� PRACTICE 2 1. 2, 3, �3� 1 2. 1, 4, �4� TRY THESE 18 K L Holt McDougal Mathematics Answers L 6. 1 1, 2, 7, 14; 2, 7�� 5. 1, 2, 3, 5, 6, 10, 6 1 4. �2� 433 �� 11. 1 2 3 1 12. 2�� or 12�� 2 10. 5�� CHECK �� 7. 32 3 8. 1�� or 3 3 9. 5�� �� or 1, 3, 5, 15; 3, 56 1 15�� 6. 1, 2, 3, 6, 9, 18; 5, 8, 10, 20, 40; �� 10, 43 15, 30; 1, 2, 4, 14. 1 1 13. �2� 12. 0 11. 1 9. 1 1 10. �2� 8. 0 7. 1 5. 0 3. 1 3. 3, 3, 3��, 6�� 4. 1, 2, 3, 4, 6, 12; 1 1. �2� 1 2. �2� 3 1 L CHECK PRACTICE 1 3. �2� 2. 1 1. 3, 3, 3��, 4�� 3 2 2. 3, 3, 3��, 5�� 3 3 PRACTICE I 20 K TRY THESE 1. 0 S © Houghton Mifflin Harcourt Publishing Company L TRY THESE 19 K L I L S 3 CHECK 1 10. 3�8� 7 11. 2�1�0 1 12. 4�4� 9. 8. 7. 6. 5. 4. 3 3 3 ��, 3, ��, 3�� 4 4 4 5 5 3 3 ��, ��, ��, 1, 1, ��, 2, 5 5 5 5 3 3 ��, 2�� 5 5 2 2 2 1 ��, ��, ��, ��, 1, 1, 1, 2 2 2 2 1 1 1 ��, 3, ��, 3�� 2 2 2 3 3 3 2 ��, ��, ��, ��, 1, 1, 1, 3 3 3 3 2 2 2 ��, 3, ��, 3�� 3 3 3 7 1�8� 4 4�5� 1 3�6� 3. 4, 4, 4, 3, 1, 1, 1, 1 1 1 1, 1, �2�, 4, �2�, 4�2� 2 2. 3, 3, 2, 1, 1, �3�, 2, 2 2 ��, 2�� 3 3 1. 2, 2, 2, 2, 1, 1, 1, 3. 1, 1, 2�4� PRACTICE 1 1. 1, 1�2� 2 2. 1, 1�3� TRY THESE 21 K L 3 4 1. 3, 3, 3��, 5�� 4 1 2. 4, 4, 4��, 3�� 2 4 3. 2, 2, 2��, 5�� S I I L S 15 11 23 12. �5� 49 11. �8� 23 10. �4� 9. 8. 7. 6. 5. CHECK 5 5 5 2 17 �� � � � � � � � �� , � � 5 5 5 5 5 1 1 � 1 � �8�, 8 8 1 7 �� � �� � �� , 1 �� 8 8 8 8 5 1 � 1 � 1 � �6�, 6 6 6 5 3 �� � � � � � � � �� , 2 �� 6 6 6 6 6 23 �� 4 44 �� 5 20 �� 3 3. 3, 3, 3, �3� 2 4. 1 � 1 � 1 � �5�, 9 1. 2, 2, 2, 2, �2� 11 2. 4, 4, �4� PRACTICE 2. 4, 4, 4, �4� 9 3. 5, �5� 1. 3, 3, 7 TRY THESE 22 K L Holt McDougal Mathematics Answers
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