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

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

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 __ is read as “eleven-fourths.” Reading Math 11 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 __

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

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 __ There are 2 whole squares and 1 fourth square, or 2 squares, shaded __

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 Ella hiked for 2 hours. 1 4 __

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 __ There is 1 whole square and 3 fourth squares, or 1 squares, shaded __

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 Arnold biked for 1 hours. 3 4 __

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 __ Count the thirds in the diagram.

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. = _____ 3 = 11 3 __ First Multiply. Then add

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 __ Count the thirds in the diagram.

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. = ______ 3 = 13 3 __ Multiply. Then add.