Numerator
Fraction =
Denominator
Fractions Represent Division
•
6 ÷ 3 is the same as
6
3 the fraction line means “divide”
• Proper fraction – the numerator is smaller than the denominator. ex.
•
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
1
3
6
3
Simplify Fractions Practice
Write in Simplest Form by dividing by Common Factors.
18
24
9
15
2
3
÷ 2=
÷ 2=
9
12
÷ 3=
÷ 3=
3
4
3
5
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
1
2
1
2
1
2
3
2
Three halves
Mixed Numbers to Improper Fractions
*A mixed number can change into an improper fraction*
+1
54
multiply
Multiply the whole and the denominator
Then add the numerator
5 x 4 = 20
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.
23
6
Therefore,
6
23
6
3
23
18
5
5
6
is equal to
Show remainder in fraction form
How many sixths are left over, because 6 was the divisor
3
5
6
Comparing Fractions > < =
• Least Common Denominator:
the smallest multiple both denominators have in common
• compare the numerators
ex.
Compare
and
using > < =
*LCM of 8 and 12 is 24
x3
x2
= =
x3
x2
𝟓 𝟕
𝟖 𝟏𝟐
>
therefore
>
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
Ex.
0.5
Ex.
0.224 Two hundred twenty four thousandths;
the numerator is 224, the denominator is 1,000
Ex.
1.36
five tenths; the numerator is 5, the denominator is 10
One and thirty-six hundredths;
The whole number is 1, numerator is 36,
the denominator is 100
1
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.
𝟑
𝟓
Ex. Write 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 which means 0.6, six
𝟔
tenths.
𝟏𝟎
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.
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)