1. 4-6 Mixed Numbers and Improper Fractions Learn to convert between mixed numbers and improper fractions.

2. 4-6 Mixed Numbers and Improper Fractions Vocabulary improper fraction proper fraction

3. 4-6 Mixed Numbers and Improper Fractions An improper fraction is a fraction in which the numerator is greater than or equal to the denominator such as. 11 4 __ is read as “eleven-fourths.” Reading Math 11 4 ___

4. 4-6 Mixed Numbers and Improper Fractions Whole numbers can be written as improper fractions. The whole number is the numerator, and the denominator is 1. For example, 7 =. When the numerator is less than the denominator, the fraction is called a proper fraction. 7 1 __

5. 4-6 Mixed Numbers and Improper Fractions You can write an improper fraction as a mixed number.

6. 4-6 Mixed Numbers and Improper Fractions Additional Example 1: Application Ella hiked for hours yesterday. Write as a mixed number. 9 4 __ 9 4 Method 1: Use a model. Draw squares divided into fourth sections. Shade 9 of the fourth sections. 1414 1414 1414 1414 1 4 __ There are 2 whole squares and 1 fourth square, or 2 squares, shaded. 1414 1414 1414 1414 1414 1414 1414 1414 1 2 1 4 __

7. 4-6 Mixed Numbers and Improper Fractions Additional Example 1 Continued Method 2: Use division. 1 4 __ Divide the numerator by the denominator. To form the fraction part of the quotient, use the remainder as the numerator and the divisor as the denominator. 4 9 - 8 2 1 Ella hiked for 2 hours. 1 4 __

8. 4-6 Mixed Numbers and Improper Fractions Check It Out: Example 1 Arnold biked for hours yesterday. Write as a mixed number. 7 4 __ 7 4 Method 1: Use a model. Draw squares divided into fourth sections. Shade 7 of the fourth sections. 1414 1414 1414 1414 3 4 __ There is 1 whole square and 3 fourth squares, or 1 squares, shaded. 1414 1414 1414 1414 1 3 4 __

9. 4-6 Mixed Numbers and Improper Fractions Check It Out: Example 1 Continued Method 2: Use division. 3 4 __ Divide the numerator by the denominator. To form the fraction part of the quotient, use the remainder as the numerator and the divisor as the denominator. 4 7 - 4 1 3 Arnold biked for 1 hours. 3 4 __

10. 4-6 Mixed Numbers and Improper Fractions Additional Example 2: Writing Mixed Numbers as Improper Fractions Write 3 as an improper fraction. 2 3 __ Method 1: Use a model. You can draw a diagram to illustrate the whole and fractional parts. There are 11 thirds or. 11 3 __ Count the thirds in the diagram.

11. 4-6 Mixed Numbers and Improper Fractions Additional Example 2 Continued Method 2: Use multiplication and addition. When you are changing a mixed number to an improper fraction, spiral clockwise as shown in the picture. The order of operations will help you remember to multiply before you add. 2 3 __ 3 = (3 3) + 2 __________ 3 Multiply the whole number by the denominator and add the numerator. Keep the same denominator. = 9 + 2 _____ 3 = 11 3 __ First Multiply. Then add. 2 3 3

12. 4-6 Mixed Numbers and Improper Fractions Check It Out: Example 2 Write 4 as an improper fraction. 1 3 __ Method 1: Use a model. You can draw a diagram to illustrate the whole and fractional parts. There are 13 thirds, or. 13 3 __ Count the thirds in the diagram.

13. 4-6 Mixed Numbers and Improper Fractions Check It Out: Example 2 Continued Method 2: Use multiplication and addition. When you are changing a mixed number to an improper fraction, spiral clockwise as shown in the picture. The order of operations will help you remember to multiply before you add. 1 3 __ 4 = (3 4) + 1 __________ 3 Multiply the whole number by the denominator and add the numerator. Keep the same denominator. = 12 + 1 ______ 3 = 13 3 __ 1 3 4 Multiply. Then add.