1. 4-4 Decimals and Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 4-4 Decimals and Fractions 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

3. 4-4 Decimals and Fractions Problem of the Day Write the day of the month as the product of two factors. Possible answer: 12th of the month, 6  2

4. 4-4 Decimals and Fractions I can convert between decimals and fractions.

5. 4-4 Decimals and Fractions Vocabulary mixed number terminating decimal repeating decimal

6. 4-4 Decimals and Fractions A number that contains both a whole number greater than 0 and a fraction, such as 1, is called a mixed number. 3 4 __ 4 1 1 1 2 1 1 4 3 2 4 1 2 2 1 Mixed numbers 1212 1414 3434 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

7. 4-4 Decimals and Fractions Additional Example 1A: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. 0.67 Identify the place value of the digit farthest to the right. The 7 is in the hundredths place, so use 100 as the denominator. 0.67 100 ____ 67 Remember! OnesTenths Hundredths Thousandths Place Value

8. 4-4 Decimals and Fractions Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. 5.9 Identify the place value of the digit farthest to the right. Write the whole number, 5. The 9 is in the tenths place, so use 10 as the denominator. 5.9 10 ___ 9 5

9. 4-4 Decimals and Fractions Check It Out: Example 1A Write each decimal as a fraction or mixed number. 0.73 Identify the place value of the digit farthest to the right. The 3 is in the hundredths place, so use 100 as the denominator. 0.73 100 ____ 73

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

11. 4-4 Decimals and Fractions Additional Example 2A: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. Divide 3 by 20. Add zeros after the decimal point. 0 20 ____ 3 The remainder is 0..00 - 20.1 320 100 - 100 5 0 20 ____ 3 =0.15

12. 4-4 Decimals and Fractions To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6 Writing Math

13. 4-4 Decimals and Fractions Additional Example 2B: Writing Fractions as Decimals Divide 1 by 3. Add zeros after the decimal point. 0 3 __ 1 The 3 repeats in the quotient..000 - 9.3 1 3 10 - 9 3 10 = 6 - 9 3 1 3 __ 1 6 6.333… = 6.3 _ Write each fraction or mixed number as a decimal.

14. 4-4 Decimals and Fractions Check It Out: Example 2A Write each fraction or mixed number as a decimal. Divide 5 by 20. Add zeros after the decimal point. 0 20 ____ 5 The remainder is 0..00 - 40.2 5 20 100 - 100 5 0 20 ____ 5 =0.25

15. 4-4 Decimals and Fractions Check It Out: Example 2B Write each fraction or mixed number as a decimal. Divide 2 by 3. Add zeros after the decimal point. 0 3 __ 2 The 6 repeats in the quotient..000 - 18.6 2 3 20 - 18 6 20 = 7 - 18 6 2 3 __ 2 7 7.666… = 7.6 _

16. 4-4 Decimals and Fractions 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 0.80.750.6 0.50.40.30.250.2 Common Fractions and Equivalent Decimals 1 3 __ 1 5 1 4 2 5 1 2 3 5 2 3 3 4 4 5

17. 4-4 Decimals and Fractions Additional Example 3: Comparing and Ordering Fractions and Decimals Order the fractions and decimals from least to greatest., 0.8, 7 __ 10 3 __ 4 First rewrite the fractions as decimals. = 0.75 = 0.7 Order the three decimals. 3 __ 4 0 7 10 __ 10 7 3 __ 4 0.75 0.8 0.7 The numbers in order from least to greatest are,, and 0.8. 7 10 3 4

18. 4-4 Decimals and Fractions Check It Out: Example 3 Order the fractions and decimals from least to greatest., 0.35, 1 __ 4 1 2 First rewrite the fractions as decimals. = 0.5 = 0.25 Order the three decimals. 1 __ 2 0 1 4 1 2 The numbers in order from least to greatest are, 0.35, and. 1 __ 4 1 2 0.350.5 0.25 1 __ 4