Numerator Denominator Fraction =

Fractions Represent Division 6 3 • 6 ÷ 3 is the same as the fraction line means “divide” 1 3 • Proper fraction – the numerator is smaller than the denominator. ex. 6 3 • Improper fraction – the numerator is larger than the denominator. ex. • Mixed number – combination of a whole number and a part. ex. 1 2 3 • Equivalent Fractions – look different but represent the same amount, are equal when simplified. Multiply or divide the top and bottom of a fraction by the same number ex. = = 6 9 8 12 2 3

Simplifying Fractions • Divide by common factors to simplify fractions • The numbers cannot be reduced (divided) down further • When simplified, numerator and denominator have a GCF of 1 ex. 𝟐 𝟑 Factors of 2: 1 x 2 Factors of 3: 1 x 3 Greatest Common Factor of 2 and 3 = 1 (in this case the only common factor)

Simplify Fractions Practice Write in Simplest Form by dividing by Common Factors. 18 24 ÷ 2 = 9 12 3 4 ÷ 3 = 9 15 3 5 2 3 Already Simplest Form, GCF of top and bottom = 1

Mixed Numbers and Improper Fractions Mixed Number: The sum of a whole number and a fraction: 1 + 1 2 1 1 2 1 whole apple plus half an apple Improper Fractions: If all pieces were the same amount w/more parts than the whole 3 2 1 2 1 2 1 2 Three halves

Mixed Numbers to Improper Fractions *A mixed number can change into an improper fraction* + 1 4 5 multiply Multiply the whole and the denominator 5 x 4 = 20 Then add the numerator 20 + 1 = 21 Last, put that number over the denominator 21 4

Improper Fractions to Mixed Numbers Divide the numerator by the denominator and leave the remainder as a fraction. 5 6 Show remainder in fraction form 3 23 6 6 23 18 5 How many sixths are left over, because 6 was the divisor 23 6 5 6 3 Therefore, is equal to

Comparing Fractions > < = Least Common Denominator: the smallest multiple both denominators have in common compare the numerators ex. Compare 𝟓 𝟖 and 𝟕 𝟏𝟐 using > < = *LCM of 8 and 12 is 24 𝟓 𝟖 = 𝟏𝟓 𝟐𝟒 𝟕 𝟏𝟐 = 𝟏𝟒 𝟐𝟒 𝟏𝟓 𝟐𝟒 > 𝟏𝟒 𝟐𝟒 x 3 x 2 therefore x 3 x 2 𝟓 𝟖 > 𝟕 𝟏𝟐

Fractions to Decimals 1. Identify the place value of the last decimal place. 2. Write as a fraction, with the place value as the denominator. 3. Simplify when appropriate 𝟓 𝟏𝟎 Ex. 0.5 five tenths; the numerator is 5, the denominator is 10 𝟐𝟐𝟒 𝟏,𝟎𝟎𝟎 Ex. 0.224 Two hundred twenty four thousandths; the numerator is 224, the denominator is 1,000 One and thirty-six hundredths; The whole number is 1, numerator is 36, the denominator is 100 Ex. 1.36 1 𝟑𝟔 𝟏𝟎𝟎

Fractions to Decimals Divide the top number by the bottom number. OR If the denominator is a factor of a decimal place value (ex. A number that multiplies to 10, 100, 1000, 10000 etc). Then you can write an equivalent fraction. Ex. Write 𝟑 𝟓 as a decimal. Since 5 is a factor of 10, we can make an equivalent fraction with 10 as the denominator. 5 x 2 = 10, so 3 x 2 = 6. The new fraction would be 𝟔 𝟏𝟎 which means 0.6, six tenths.