1. Numerator Denominator
Fraction =

2. Fractions Represent Division6 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

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)

4. 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

5. 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

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

7. 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

8. 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

9. 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
five tenths; the numerator is 5, the denominator is 10
𝟐𝟐𝟒 𝟏,𝟎𝟎𝟎 Ex
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 𝟑𝟔 𝟏𝟎𝟎

10. 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, 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.