The document provides information about fractions including: 1) Definitions of the different types of fractions such as proper, improper, and mixed fractions. 2) Methods for converting between improper and mixed fractions. 3) The concept of equivalent fractions and how to simplify fractions. 4) Techniques for comparing fractions including finding a common denominator or converting to decimals. 5) Procedures for performing operations like addition, subtraction, multiplication, and division on fractions.

1. I.E.S. MARÍA BELLIDO - BAILÉN
BILINGUAL SECTION – MARÍA ESTHER DE LA ROSA
UNIT 3. FRACTIONS
1. TALKING ABOUT FRACTIONS - VOCABULARY:
We use ordinal numbers (at the end position) to talk about fractions.
•1/2 - a half 1/3 - a third 2/3 - two thirds
•1/4 - a quarter (a fourth) 3/4 - three quarters (three fourths)
•1/5 - a fifth 2/5 - two fifths 1/6 - a sixth
•5/6 - five sixths 1/7 - a seventh 1/8 - an eighth
•1/10 - a tenth 7/10 - seven tenths 1/20 - a twentieth
•47/100 - forty-seven hundredths 1/100 - a hundredth
•1/1,000 - a thousandth
If we have a whole number with a fraction, we use the word “AND” between the
two parts.
2 3/5 = two and a three-fifths
2. DEFINITION:
A fraction is a part of a whole.
Numerator
Denominator
We call the top number the Numerator, it is the number of parts you have.
We call the bottom number the Denominator, it is the number of parts the
whole is divided into.

2. 3. TYPES OF FRACTIONS:
There are three types of fractions:
a) Proper Fraction: The numerator is less than the denominator.
3 1
Examples: /8 /4
b) Improper Fraction:The numerator is greater or equal than the denominator.
Examples : 7 10
/6 /3
c) Mixed Fraction: It´s a whole number and a proper fraction together.
Examples: 1 1/3 2 1/4 16 2/5
4. CONVERTING IMPROPER FRACTIONS TO MIXED FRACTIONS
To convert an improper fraction to a mixed fraction, follow these steps:
a) Divide the numerator by the denominator.
b) Write down the whole number answer.
c) Then write down any remainder above the denominator.
Example: Convert 11/4 to a mixed fraction.
Divide: 11÷4 =2 with a remainder of 3. Write down the 2 and then write down the remainder (3)
above the denominator (4), like this: 2 1/4.
5. CONVERTING MIXED FRACTIONS TO IMPROPER FRACTIONS
To convert a mixed fraction to an improper fraction, follow these steps:
a) Multiply the whole number part by the fraction's denominator.
b) Add that to the numerator
c) Then write the result on top of the denominator.
Example: Convert 3 2/5 to an improper fraction:
Multiply the whole number by the denominator: 3 × 5 = 15. Add the numerator to that:
15 + 2 = 17. Then write that down above the denominator, like this 17/5

3. 6. EQUIVALENT FRACTIONS:
Equivalent Fractions have the same value, even though they may look
different. They are really the same because when you multiply or divide both
the top an bottom by the same number, the fraction keeps it´s value. for
example:
Four-Eighths =Two-Quarters = One-Half
It is usually best to show an answer using the simplest fraction (1/2 in this case).
That is called Simplifying, or Reducing the Fraction. There are two ways to
simplify a fraction:
Method 1: Try dividing both the top and bottom of the fraction until you can't go any
further (try dividing by 2,3,5,7,... etc). Example: 24/108 = 12/54 = 6/27 = 2/9
Method 2: Divide both the top and bottom of the fraction by the G.C.D. Example: 8/12
The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common
divisor is 4. . Divide both top and bottom by 4, and the answer is 2/3
7. COMPARING FRACTIONS
Sometimes we need to compare two fractions to discover which is larger or
smaller. There are two easy ways to compare fractions: using decimals; or
using the same denominator
a) The Decimal Method of Comparing Fractions : We can convert fractions to
decimals by dividing the numerator by the denominator, and then compare the
decimals.
Example: which is bigger: 3/8 or 5/12 ? . Anyway, these are the answers I get:
3
/8 = 0.375, and 5/12 = 0.4166... So, 5/12 is bigger.
b) The Same Denominator Method: If two fractions have the same
denominator then they are easy to compare.
4
Example: /9 is less than 5/9 (because 4 is less than 5)
But if the denominators are not the same you need to find the L.C.M. of the two
denominators.
Example: Which is larger: 5/6 or 13/15?
The Least Common Multiple of 6 and 15 is 30. So, let's do some multiplying to make each
denominator equal to 30 : 25/30 or 26/30. Now we can easily see that 26/30 is the larger fraction, so
13
/15 is the larger fraction.

4. 8. OPERATIONS
a) Adding and Subtracting Fractions:
• With the same denominator: You can add or sustract fractions doing
the addition or the substraction of the numerators.
Example: 6/18 + 3/18 =
9
/18 Finally, simplify the fraction. 9/18 = ½
• With different denominators:
Here are the steps to follow:
1. Find the Least Common Multiple of the denominators (which is
called the Least Common Denominator).
2. Change each fraction (using equivalent fractions) to make their
denominators the same as the least common denominator.
3. Then you add TtThen you add (or subtract) the fractions, as you
wish!
4. Finally, simplify the fraction if you can do it.
Example: What is 1/6 + 7/15 ?
1. The Denominators are 6 and 15, so the Least Common Multiple of 6 and 15 is 30.
2. When you multiply 6 × 5 you get 30, and when you multiply 15 × 2 you also get 30. Note:
what you do to the bottom of the fraction, you must also do to the top. So, we must do:
1 × 5 and 7× 2 and the new numerators are 5 and 14.
3. Now we can easily do the addition by adding the top numbers:
5
/30 + 14/30 = 19/30 Finally, it isn´t possible to simplify the fraction.
b) Multiplying Fractions: There are three simple steps to multiply fractions
1. Multiply the top numbers (the numerators).
2. Multiply the bottom numbers (the denominators).
3. Simplify the fraction if needed.

5. Example: What is 1/6 x 3/5 = 1x3 / 6x5 = 3 /15 = 1/5
χ) Dividing Fractions: There are three simple steps to divide fractions
1. Turn the second fraction (the one you want to divide by) upside-down (this is now a
reciprocal). (Why Turn the Fraction Upside Down? Because division is the inverse (opposite) of multiplying)
2. Multiply the first fraction by that reciprocal
3. Simplify the fraction (if needed)
Example: ⅜ : 3/5 is also ⅜ × 5/3 = 3x5/8x3 = 15
/24 = 5/8
δ) Finding a fraction of an amount:
To find a fraction of an amount:
1. Divide the amount by the denominator of the fraction
2. Then, multiply the answer by the numerator of the fraction.
Example: Find 3/2 of 230 euros
1. 230:2 = 115 euros.
2. 115 x 3 = 345 euros