3-8 to 3-10 Mixed Numbers and Improper Fractions What You’ll Learn To write a mixed number as an improper fraction To write a mixed number as an improper fraction To write an improper fractions as a mixed number To write an improper fractions as a mixed number To relate fractions and decimals To relate fractions and decimals Compare rational numbers Compare rational numbers

Mixed Numbers and Improper Fractions If the numerator of a fraction is less than the denominator, the fraction is called a proper fraction. If the numerator of a fraction is less than the denominator, the fraction is called a proper fraction. If the numerator is equal to or greater than the denominator, the fraction is called an improper fraction. If the numerator is equal to or greater than the denominator, the fraction is called an improper fraction. An improper fraction can be rewritten as a mixed fraction (whole number + a proper fraction) An improper fraction can be rewritten as a mixed fraction (whole number + a proper fraction) For example, 5/3 is an improper fraction. It can be rewritten as 1 2/3, which is a mixed fraction. For example, 5/3 is an improper fraction. It can be rewritten as 1 2/3, which is a mixed fraction.

Example 1: Writing improper Fractions Write 4 2/3 as an improper fraction Write 4 2/3 as an improper fraction Multiply the denominator by the whole number Multiply the denominator by the whole number Add the numerator Add the numerator The denominator remains the same The denominator remains the same + 4 2/3 = 42/3 4 2/3 = 42/3 x = (3 x 4) + 2 = 14 = (3 x 4) + 2 =

Example 2: Writing a Mixed Number Divide the numerator by the denominator Divide the numerator by the denominator The Quotient is the whole number The Quotient is the whole number The Reminder is the numerator The Reminder is the numerator The Denominator remains the same The Denominator remains the same Write 30/8 as a mixed number Write 30/8 as a mixed number /8 = 3 6/8 30/8 = 3 6/8

Fractions and Decimals Fractions can be written in decimal number format, and vice versa. Fractions can be written in decimal number format, and vice versa. For example, 1/4 = 0.25 For example, 1/4 = 0.25

Example 1: Write the fraction 5/8 as a decimal Step 1: Divide the numerator by the denominator Step 1: Divide the numerator by the denominator (1) 5 ÷ 8 = ? (1) 5 ÷ 8 = ? Step 2: Complete the division problem Step 2: Complete the division problem (2) 5 ÷ 8 = (2) 5 ÷ 8 = Answer: Answer: 0.625

Example 2: Write the mixed number 2 3/4 as a decimal Step 1: Separate the mixed number 2 3/4 into a whole number and a fraction. The whole number will always remain a whole number, but the fraction can be changed into a decimal. Step 1: Separate the mixed number 2 3/4 into a whole number and a fraction. The whole number will always remain a whole number, but the fraction can be changed into a decimal. (1) whole number: 2; fraction: 3/4 (1) whole number: 2; fraction: 3/4 Step 2: Write the fraction 3/4 as a decimal by dividing the numerator by the denominator. Step 2: Write the fraction 3/4 as a decimal by dividing the numerator by the denominator. (2) 3/4 = 3 ÷ 4 = 0.75 (2) 3/4 = 3 ÷ 4 = 0.75 Step 3: Put the whole number and the decimal back together to get the complete decimal number Step 3: Put the whole number and the decimal back together to get the complete decimal number (3) 2 3/4 = 2.75 (3) 2 3/4 = 2.75

Repeating Decimals If the same block of digits in a decimal repeats without end, the decimal is a repeating decimal. If the same block of digits in a decimal repeats without end, the decimal is a repeating decimal. Repeating block can be one or more digits Repeating block can be one or more digits _ = 5.35 The digit “5” repeats = 5.35 The digit “5” repeats _ =0.17 The digits “17” repeats =0.17 The digits “17” repeats

Example 3: Write 3/11 as a decimal Example 3: Write 3/11 as a decimal Divide the numerator by the denominator Divide the numerator by the denominator Find the repeating digits Find the repeating digits “27” “27” Record answer only to the repeating digits Record answer only to the repeating digits

Example 4: Writing as a Fraction Write the decimal number over the decimal place value Write the decimal number over the decimal place value = 325/ = 325/1000 Find the GCF Find the GCF 325: 1,5,13,25,65, : 1,5,13,25,65, : 1,2,5,10,20,25,50,100,500, : 1,2,5,10,20,25,50,100,500,1000 Reduce fraction using GCF Reduce fraction using GCF 325/1000 = 325/25 / 1000/25 325/1000 = 325/25 / 1000/25 13 / / 40

3-10 Rational Numbers Ration number is a number that can be written as a quotient of two integers, where the divisor is not 0. Ration number is a number that can be written as a quotient of two integers, where the divisor is not /3 - 2/ ½ 3 ½