Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Find the GCF of each set of numbers. 1. 15, 24 2. 30, 60 3. 54, 102 4. 12, 16, 24 3 30 6 4

Write the day of the month as the product of two factors. Problem of the Day Write the day of the month as the product of two factors. Possible answer: 12th of the month, 6  2

Learn to convert between decimals and fractions.

Vocabulary mixed number terminating decimal repeating decimal

A number that contains both a whole number greater than 0 and a fraction, such as 1 , is called a mixed number. __ 3 4 Mixed numbers 1 4 1 2 3 4 __ 4 1 1 __ 2 1 __ 4 3 2 __ 4 1 2 __ 1 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

Additional Example 1A: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. 0.67 0.67 Identify the place value of the digit farthest to the right. 100 ____ 67 The 7 is in the hundredths place, so use 100 as the denominator. Remember! Ones Tenths Hundredths Thousandths Place Value

Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. 5.9 5.9 Identify the place value of the digit farthest to the right. 10 ___ 9 5 Write the whole number, 5. The 9 is in the tenths place, so use 10 as the denominator.

Write each decimal as a fraction or mixed number. Check It Out: Example 1A Write each decimal as a fraction or mixed number. 0.73 0.73 Identify the place value of the digit farthest to the right. 100 ____ 73 The 3 is in the hundredths place, so use 100 as the denominator.

Write each decimal as a fraction or mixed number. Check It Out: Example 1B Write each decimal as a fraction or mixed number. 4.8 4.8 Identify the place value of the digit farthest to the right. 10 ___ 8 4 Write the whole number, 4. The 8 is in the tenths place, so use 10 as the denominator.

Additional Example 2A: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 20 ____ 3 .1 5 Divide 3 by 20. 20 3 .00 Add zeros after the decimal point. - 20 100 - 100 The remainder is 0. 20 ____ 3 = 0.15

Writing Math To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6

Additional Example 2B: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 3 __ 1 6 .3 3 3 Divide 1 by 3. 3 1 .000 Add zeros after the decimal point. - 9 10 The 3 repeats in the quotient. - 9 10 - 9 6.333… = 6.3 _ 1 3 __ 1 6 =

Write each fraction or mixed number as a decimal. Check It Out: Example 2A Write each fraction or mixed number as a decimal. 20 ____ 5 .2 5 Divide 5 by 20. 20 5 .00 Add zeros after the decimal point. - 40 100 - 100 The remainder is 0. 20 ____ 5 = 0.25

Write each fraction or mixed number as a decimal. Check It Out: Example 2B Write each fraction or mixed number as a decimal. 3 __ 2 7 .6 6 6 Divide 2 by 3. 3 2 .000 Add zeros after the decimal point. - 18 20 The 6 repeats in the quotient. - 18 20 - 18 7.666… = 7.6 _ 2 3 __ 2 7 =

Common Fractions and Equivalent Decimals A terminating decimal, such as 0.75, has a finite number of decimal places. A repeating decimal, such as 0.666…, has a block of one or more digits that repeat continuously 0.8 0.75 0.6 0.5 0.4 0.3 0.25 0.2 Common Fractions and Equivalent Decimals 1 5 __ 1 4 __ 1 3 __ 2 5 __ 1 2 __ 3 5 __ 2 3 __ 3 4 __ 4 5 __

Additional Example 3: Comparing and Ordering Fractions and Decimals Order the fractions and decimals from least to greatest. __ 3 __ 7 , 0.8, 4 10 3 __ 4 __ 10 7 First rewrite the fractions as decimals. = 0.75 = 0.7 Order the three decimals. 7 __ 10 3 __ 4 0.7 0.75 0.8 The numbers in order from least to greatest are , , and 0.8. 7 10 3 4

Order the fractions and decimals from least to greatest. Check It Out: Example 3 Order the fractions and decimals from least to greatest. 1 __ 4 __ , 0.35, 1 2 1 __ 2 1 __ 4 First rewrite the fractions as decimals. = 0.5 = 0.25 Order the three decimals. 1 __ 4 1 __ 2 0.25 0.35 0.5 1 __ 4 1 __ The numbers in order from least to greatest are , 0.35, and . 2

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Write each decimal as a fraction or mixed number. 1. 0.24 2. 6.75 Lesson Quiz: Part I Write each decimal as a fraction or mixed number. 1. 0.24 2. 6.75 Write each fraction or mixed number as a decimal. 3. 2 4. 6 25 ____ 6 3 4 __ 3 5 __ 2.6 8 __ 7 0.875

5. Order the fractions and decimals from least to greatest. Lesson Quiz: Part II 5. Order the fractions and decimals from least to greatest. 0.38, , 6. Jamal ran the following distances on three different days: 0.87 mile, mile, and 0.13 mile. Order the distances from least to greatest. 3 4 __ 1 5 __ 1 5 __ , 0.38, 3 4 __ 2 3 __ 2 3 __ 0.13, , 0.87

Lesson Quiz for Student Response Systems 1. Which of the following represents the given decimal as a fraction? 0.26 A. C. B. D.

Lesson Quiz for Student Response Systems 2. Which of the following represents the given decimal as a mixed number? 5.25 A. C. B. D.

Lesson Quiz for Student Response Systems 3. Which of the following represents the given mixed number as a decimal? A. 2.3 C. 3.5 B. 3.4 D. 5.2

Lesson Quiz for Student Response Systems 4. Which of the following represents the given fraction as a decimal? A. 0.2565 C. 0.5625 B. 0.5256 D. 0.6525

Lesson Quiz for Student Response Systems 5. Which of the following represents the given fractions and decimals ordered from least to greatest? A. C. B. D.