4 6 Mixed Numbers and Improper Fractions Learn

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

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 Reading Math 11 ___ is 4 read as “eleven-fourths. ”

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

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 9 __ 4 Ella hiked for hours yesterday. Write a mixed number. 9 __ 4 as Method 1: Use a model. Draw squares divided into fourth sections. Shade 9 of the fourth sections. 1 4 1 4 1 4 2 1 4 1 __ 4 1 4 1 There are 2 whole squares and 1 fourth square, or 2 __ 4 squares, shaded.

4 -6 Mixed Numbers and Improper Fractions Additional Example 1 Continued Method 2: Use division. 1 __ 24 4 9 -8 1 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 1 __ 24 hours.

4 -6 Mixed Numbers and Improper Fractions Check It Out: Example 1 7 4 Arnold biked for __ hours yesterday. Write 7 __ 4 as a mixed number. Method 1: Use a model. Draw squares divided into fourth sections. Shade 7 of the fourth sections. 1 1 4 1 4 1 4 3 __ 4 There is 1 whole square and 3 fourth squares, or squares, shaded. 3 __ 14

4 -6 Mixed Numbers and Improper Fractions Check It Out: Example 1 Continued Method 2: Use division. 3 __ 14 4 7 -4 3 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. 3 Arnold biked for 1 __ hours. 4

4 -6 Mixed Numbers and Improper Fractions Additional Example 2: Writing Mixed Numbers as Improper Fractions Write 3 2 __ 3 as an improper fraction. Method 1: Use a model. You can draw a diagram to illustrate the whole and fractional parts. 11 __ There are 11 thirds or. 3 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) + 2 __ = _____ 3 3 9+2 _____ = = 3 3 11 __ 3 Multiply the whole number by the denominator and add the numerator. Keep the same denominator. Then add. 2 33 First Multiply.

4 -6 Mixed Numbers and Improper Fractions Check It Out: Example 2 Write 4 1 __ as 3 an improper fraction. Method 1: Use a model. You can draw a diagram to illustrate the whole and fractional parts. 13 __ There are 13 thirds, or. 3 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) + 1 __ = _____ 3 3 12 + 1 ______ 3 = = 4 13 __ 3 Multiply the whole number by the denominator and add the numerator. Keep the same denominator. Then add. 1 __ 43 Multiply.