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Converting Between Mixed Numbers and Improper Fractions

Learn to convert between mixed numbers and improper fractions with examples and step-by-step methods. Understand the concepts of improper fractions, proper fractions, and mixed numbers with visual aids and practical applications.

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Converting Between Mixed Numbers and Improper Fractions

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  1. Learn to convert between mixed numbers and improper fractions.

  2. Vocabulary improper fraction proper fraction

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

  4. 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. You can write an improper fraction as a mixed number.

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

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

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

  9. 3 __ 4 3 __ 4 Check It Out: Example 1 Continued Method 2: Use division. 1 7 4 Divide the numerator by the denominator. - 4 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.

  10. 2 __ 3 11 __ 3 Additional Example 2: Writing Mixed Numbers as Improper Fractions Write 3 as an improper fraction. 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.

  11. 2 (3• 3) + 2 __ __________ 3 2 9 + 2 _____ 3 3 11 __ 3 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. Then add. Multiply the whole number by the denominator and add the numerator. = 3 3 = 3 Keep the same denominator. = First Multiply.

  12. 1 __ 3 13 __ 3 Check It Out: Example 2 Write 4 as an improper fraction. 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.

  13. 1 (3• 4) + 1 __ __________ 3 1 12 + 1 ______ 3 13 __ 3 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. Then add. Multiply the whole number by the denominator and add the numerator. = 4 3 __ 4 = 3 Keep the same denominator. = Multiply.

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