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.

3. TYPES OF FRACTIONS:

There are three types of fractions:

a) Proper Fraction: The numerator is less than the denominator.

Examples: 3/8

1/4

b) Improper Fraction:The numerator is greater or equal than the denominator.

Examples : 7/6 10/3

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 numeratorc) 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

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.

Example: 4/9 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.

 

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.

Example: What is 1/6 x 3/5 = 1x3 / 6x5 = 3 /15 = 1/5

c) 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

d) Finding a fraction of an amount:

To find a fraction of an amount:

1. Divide the amount by the denominator of the fraction2. 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