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

Decimals and Fractions Course 1 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

Decimals and Fractions Course 1 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

Decimals and Fractions Course 1 4-4 Decimals and Fractions Learn to convert between decimals and fractions.

Insert Lesson Title Here Course 1 4-4 Decimals and Fractions Insert Lesson Title Here Vocabulary mixed number terminating decimal repeating decimal

Decimals and Fractions Course 1 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 Mixed numbers 14 12 34 __ 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 Course 1 4-4 Decimals and Fractions Additional Example 1A: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. A. 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 Course 1 4-4 Decimals and Fractions Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. B. 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.

Decimals and Fractions Course 1 4-4 Decimals and Fractions Try This: Example 1A Write each decimal as a fraction or mixed number. A. 0.73 0.73 Identify the place value of the digit farthest to the right. 100 ____ 73 The 7 is in the hundredths place, so use 100 as the denominator.

Decimals and Fractions Course 1 4-4 Decimals and Fractions Try This: Example 1B Write each decimal as a fraction or mixed number. B. 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 Course 1 4-4 Decimals and Fractions Additional Example 2A: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 20 ____ 3 A. .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

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

Decimals and Fractions Course 1 4-4 Decimals and Fractions Try This: Example 2A Write each fraction or mixed number as a decimal. 20 ____ 5 A. .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

Decimals and Fractions Course 1 4-4 Decimals and Fractions Try This: Example 2B Write each fraction or mixed number as a decimal. 3 __ 2 B. 7 .6 6 6 Divide 2 by 3. 3 2 .000 Add zeros after the decimal point. - 18 20 The six repeats in the quotient. - 18 20 - 18 7.666… = 7.6 _ 2 3 __ 2 7 =

Common Fractions and Equivalent Decimals Course 1 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 Common Fractions and Equivalent Decimals 0.2 0.25 0.3 0.4 0.5 0.6 0.75 0.8 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 Course 1 4-4 Decimals and Fractions 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 a decimal. = 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

Decimals and Fractions Course 1 4-4 Decimals and Fractions Try This: Example 3 Order the fractions and decimals from least to greatest. __ , 0.35, 1 1 __ 4 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 The numbers in order from least to greatest are , 0.35, and 1 __ . 2

Decimals and Fractions Insert Lesson Title Here Course 1 4-4 Decimals and Fractions Insert Lesson Title Here Lesson Quiz: Part 1 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 7 __ 0.875 8

Insert Lesson Title Here Course 1 4-4 Decimals and Fraction Insert Lesson Title Here Lesson Quiz: Part 2 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