If the numerator of a fraction is less than the denominator, the fraction represents a number less than 1 and is called a proper fraction. Improper Fractions, Mixed Numbers and Decimal Numbers If the numerator of a fraction is greater than or equal to the denominator, the fraction represents a number greater than or equal to 1 and is called an improper fraction.

parts shaded equal parts five-sixths PictureFractionRead as parts shaded equal parts seven-thirds part shaded equal parts one-fourth Visualizing Fractions

Writing an Improper Fraction as a Mixed Number or a Whole Number Step 1: Divide the denominator into the numerator. Step 2: The whole number part of the mixed number is the quotient. The fraction part of the mixed number is the remainder over the original denominator. remainder original denominator quotient and

Writing a Mixed Number as an Improper Fraction Step 1: Multiply the denominator of the fraction by the whole number. Step 2: Add the numerator of the fraction to the product from Step 1. Step 3: Write the sum from Step 2 as the numerator of the improper fraction over the original denominator  ∙    

Writing a Mixed Number as a Decimal Step 1: Let the whole number part of the mixed number be the whole number part of the decimal. Step 2: Convert the fractional part of the mixed number to a decimal by dividing the numerator by the denominator.

Writing a Decimal as a Mixed Number Step 1: Say the number. Step 2: Write the decimal part of the number as a fraction. Step 3: Reduce the fraction.

Examples ① Convert each mixed number to an improper fraction: a)5b) 6 ③ Write 157 ⅙ as a decimal number rounded to two decimal places. ② Convert each improper fraction to a mixed number: a)b) ④ Write 5.09 as a mixed number.