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

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

Lesson 2: Comparison and Reducing Fractions

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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.

  • Earlier, we saw that fractions have two parts.

  • One part is the top number, or
    numerator
    .

  • The other is the bottom number, or

    denominator
    .

  • The denominator tells us how many
    parts
    are in a whole.

  • The numerator tells us how many of those parts we have.

  • When fractions have the same denominator, it ways they’re dissever into the same number of parts.

  • This means we can
    compare
    these fractions just past looking at the numerator.

  • Here,
    5
    is more than
    4

  • Here,
    5
    is more
    four…so we can tell that
    5/six
    is more than than
    iv/6.

  • Let’southward look at another case. Which of these is larger:
    2/eight
    or
    6/viii?

  • If you thought
    6/8
    was larger, you were right!

  • Both fractions have the same denominator.

  • And then nosotros compared the numerators.
    6
    is larger than
    2, and so
    6/8
    is more than
    two/8.

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.

  • Let’southward compare these fractions:
    5/eight
    and
    4/half dozen.

  • Earlier we compare them, we need to change both fractions and so they have the aforementioned
    denominator, or bottom number.

  • First, we’ll find the smallest number that can be divided by both denominators. We call that the
    everyman mutual denominator.

  • Our starting time footstep is to find numbers that tin exist divided evenly by
    8.

  • Using a multiplication table makes this piece of cake. All of the numbers on the
    8
    row tin can be divided evenly by
    8.

  • Now let’s expect at our second denominator:
    six.

  • We tin can utilize the multiplication table again. All of the numbers in the
    vi
    row tin can exist divided evenly by
    6.

  • Let’s compare the two rows. It looks like at that place are a few numbers that tin can exist divided evenly by both
    6
    and
    viii.

  • 24
    is the smallest number that appears on both rows, and then it’s the
    lowest common denominator.

  • At present we’re going to change our fractions so they both have the same denominator:
    24.

  • To do that, we’ll have to change the numerators the same way we inverse the denominators.

  • Let’southward look at
    five/8
    again. In order to change the denominator to
    24

  • Permit’s look at
    5/8
    again. In lodge to change the denominator to
    24…nosotros had to multiply
    8
    by
    3.

  • Since we multiplied the denominator by
    3
    , we’ll likewise multiply the numerator, or top number, by
    3.

  • 5
    times
    three
    equals
    15. So nosotros’ve changed
    v/8
    into
    15/24.

  • We tin can do that because any number over itself is equal to
    i.

  • So when we multiply
    5/8
    by
    three/3

  • So when we multiply
    5/eight
    by
    3/3…we’re really multiplying
    5/eight
    by
    1.

  • Since whatsoever number times
    1
    is equal to itself…

  • Since any number times
    1
    is equal to itself…nosotros can say that
    5/8
    is equal to
    15/24.

  • At present we’ll do the same to our other fraction:
    4/6. We too changed its denominator to
    24.

  • Our sometime denominator was
    6. To go
    24, we multiplied
    six
    past
    four
    .

  • And so we’ll likewise multiply the numerator past
    iv.

  • 4
    times
    4
    is
    16
    . And so
    iv/6
    is equal to
    16/24.

  • At present that the denominators are the same, we can compare the two fractions by looking at their numerators.

  • xvi/24
    is larger than
    xv/24

  • 16/24
    is larger than
    15/24… and so
    4/6

    is larger than
    v/8.

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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.

  • Let’s try reducing this fraction:
    16/xx.

  • Since the numerator and denominator are
    even numbers, you lot tin divide them by
    two
    to reduce the fraction.

  • Get-go, we’ll divide the numerator by
    2.
    16
    divided by
    2
    is
    8.

  • Next, we’ll divide the denominator by
    2.
    twenty
    divided by
    2
    is
    10.

  • We’ve reduced
    16/20
    to
    8/10
    . Nosotros could too say that
    16/20
    is equal to
    viii/x.

  • If the numerator and denominator tin all the same be divided by
    2, we tin continue reducing the fraction.

  • viii
    divided by
    two
    is
    4.

  • 10
    divided by
    2
    is
    5.

  • Since there’southward no number that
    four
    and
    5
    tin can be divided by, nosotros can’t reduce
    4/5
    any farther.

  • This ways
    4/v
    is the
    simplest
    grade
    of
    16/20.

  • Let’south try reducing another fraction:
    half dozen/nine.

  • While the numerator is even, the denominator is an
    odd number, and so nosotros can’t reduce past dividing by
    2.

  • Instead, we’ll need to find a number that
    6
    and
    ix
    can exist divided past. A multiplication table volition make that number easy to detect.

  • Let’southward find
    6
    and
    nine
    on the
    same
    row. As you lot tin meet,
    six
    and
    9
    can both exist divided past
    1
    and
    iii.

  • Dividing by
    1
    won’t modify these fractions, and then nosotros’ll use the
    largest
    number that
    half dozen
    and
    9
    can exist divided by.

  • That’s
    3. This is called the
    greatest common divisor, or
    GCD. (Yous tin can besides call information technology the
    greatest common factor, or
    GCF.)

  • 3
    is the
    GCD
    of
    6
    and
    nine
    considering it’s the
    largest
    number they can be divided by.

  • So we’ll separate the numerator by
    3.
    6
    divided by
    3
    is
    2.

  • Then we’ll divide the denominator by
    three.
    ix
    divided by
    3
    is
    three.

  • Now we’ve reduced
    six/9
    to
    2/3, which is its simplest course. We could also say that
    half dozen/nine
    is equal to
    2/three.

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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:

  • Allow’due south convert
    ane one/4
    into an improper fraction.

  • Kickoff, we’ll need to observe out how many
    parts
    make upward the whole number:
    1
    in this example.

  • To practise this, nosotros’ll multiply the
    whole number,
    ane, by the denominator,
    4.

  • 1
    times
    iv
    equals
    four.

  • Now, let’south add that number,
    4, to the numerator,
    i.

  • 4
    plus
    i
    equals
    5
    .

  • The denominator stays the same.

  • Our improper fraction is
    5/4,

    or
    five-fourths
    . So we could say that
    1 1/4
    is equal to
    v/iv
    .

  • This means in that location are
    five
    1/4s in
    one ane/four.

  • Let’s convert another mixed number:
    ii 2/v.

  • First, we’ll multiply the whole number by the denominator.
    2
    times
    5
    equals
    10.

  • Next, we’ll add together
    10
    to the numerator.
    10
    plus
    two
    equals
    12.

  • As always, the denominator will stay the same.

  • And then
    ii 2/5
    is equal to
    12/5.

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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.

  • Permit’s plow
    10/4
    into a mixed number.

  • Yous can think of any fraction equally a
    division
    problem. Just treat the line between the numbers like a segmentation sign (/).

  • And then we’ll
    divide
    the numerator,
    10, past the denominator,
    4.

  • 10
    divided past
    4
    equals
    2

  • ten
    divided by
    4
    equals
    2
    … with a rest of
    two.

  • The answer,
    2,
    will get our whole number because
    ten
    tin can be divided by
    4
    twice.

  • And the
    residuum,
    two, volition go the numerator of the fraction considering we have
    2
    parts left over.

  • The denominator remains the same.

  • And so
    10/4
    equals
    2 ii/iv.

  • Let’s attempt another example:
    33/iii.

  • Nosotros’ll divide the numerator,
    33, past the denominator,
    3.

  • 33
    divided by
    three

  • 33
    divided by
    3
    … equals
    11,
    with no residuum.

  • The answer,
    xi,
    will go our whole number.

  • There is no residuum, and so nosotros can see that our improper fraction was actually a whole number.
    33/3
    equals
    11.

Try This!

Try converting these improper fractions into mixed numbers.

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

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

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