5/4 Inches to 2/3 Inch in Simplest Form.

#### Lesson 2: Comparison and Reducing Fractions

/en/fractions/introduction-to-fractions/content/

### Comparing fractions

In Introduction to Fractions, nosotros learned that fractions are a manner of showing

**office**

of something. Fractions are useful, since they let us tell exactly how much we have of something. Some fractions are larger than others. For example, which is larger:

six/8

of a pizza or

7/8

of a pizza?

In this paradigm, nosotros can meet that

vii/eight

is larger. The illustration makes information technology easy to

**compare**

these fractions. Simply how could nosotros have done it without the pictures?

Click through the slideshow to acquire how to compare fractions.

Every bit you saw, if two or more than fractions have the same denominator, you can compare them past looking at their numerators. As you can meet below,

iii/4

is larger than

i/4. The larger the numerator, the larger the fraction.

### Comparing fractions with different denominators

On the previous folio, we compared fractions that have the same

**bottom numbers**, or

**
denominators
**. But you know that fractions tin take

**whatever**

number as a denominator. What happens when y’all need to compare fractions with different bottom numbers?

For example, which of these is larger:

two/three

or

one/v? Information technology’south difficult to tell just by looking at them. After all,

2

is larger than

1, merely the denominators aren’t the same.

If yous look at the picture, though, the departure is clear:

2/3

is larger than

ane/5. With an analogy, information technology was easy to compare these fractions, but how could we have done it without the picture?

Click through the slideshow to larn how to compare fractions with different denominators.

### Reducing fractions

Which of these is larger:

4/eight

or

1/two?

If you lot did the math or fifty-fifty simply looked at the picture, you might have been able to tell that they’re

**equal**

. In other words,

iv/8

and

1/two

mean the same thing, even though they’re written differently.

If

4/8

means the aforementioned matter every bit

1/two, why not just phone call it that?

**Half**

is easier to say than

**four-eighths**, and for most people it’s also easier to understand. After all, when you lot eat out with a friend, you lot split the neb in

**half**, not in

**eighths**.

If you write

4/8

as

one/ii, yous’re

**reducing**

it. When nosotros

**reduce**

a fraction, nosotros’re writing it in a simpler form. Reduced fractions are e’er

**equal**

to the original fraction.

We already reduced

4/8

to

1/ii. If you expect at the examples beneath, you lot tin can run into that other numbers tin can be reduced to

1/two

as well. These fractions are all

**equal**.

**5/10 = i/ii**

11/22 = 1/2

36/72 = 1/2

** **

These fractions take all been reduced to a simpler form as well.

**4/12 = 1/3**

14/21 = 2/3

35/50 = 7/10

** **

Click through the slideshow to learn how to reduce fractions past

**dividing**.

#### Irreducible fractions

Not all fractions can exist reduced. Some are already as simple as they tin can be. For example, you can’t reduce

1/ii

considering there’s no number other than

1

that both

1

and

2

can be divided by. (For that reason, you tin can’t reduce

**any**

fraction that has a

numerator

of

i.)

Some fractions that have larger numbers tin’t exist reduced either. For instance,

17/36

can’t be reduced because there’s no number that both

17

and

36

can be divided past. If yous can’t detect any

**common multiples**

for the numbers in a fraction, chances are information technology’due south

**
irreducible
**.

#### Endeavor This!

Reduce each fraction to its simplest course.

### Mixed numbers and improper fractions

In the previous lesson, you learned about

**mixed numbers**. A mixed number has both a

**fraction
**and a

**whole number**. An example is

1 2/3. You’d read

1 2/iii

similar this:

**i and two-thirds**.

Another way to write this would be

5/three, or

**five-thirds**. These two numbers look unlike, but they’re really the same.

v/3

is an

**improper fraction**. This but means the numerator is

**larger**

than the denominator.

In that location are times when you may prefer to employ an improper fraction instead of a mixed number. It’s easy to change a mixed number into an improper fraction. Let’s learn how:

#### Attempt This!

Try converting these mixed numbers into improper fractions.

####

Converting improper fractions into mixed numbers

Improper fractions are useful for math problems that use fractions, equally you’ll acquire afterward. However, they’re also more hard to read and understand than

**mixed**

**numbers**. For example, it’s a lot easier to picture

2 4/seven

in your head than

18/7.

Click through the slideshow to learn how to modify an improper fraction into a mixed number.

#### Try This!

Try converting these improper fractions into mixed numbers.

/en/fractions/adding-and-subtracting-fractions/content/

## 5/4 Inches to 2/3 Inch in Simplest Form

Source: https://edu.gcfglobal.org/en/fractions/comparing-and-reducing-fractions/1/