FRACTIONS LESSON
Equivalent and Comparing Fractions
Equivalent Fractions
Equivalent fractions are equal
in value. When we reduce them to lowest terms, they are identical. For instance,
if you were holding 5 dimes, you wouldn't say I have 5 tenths of a dollar.
You'd probably say I have ½ a dollar – because you know that 5
tenths equals or is equivalent to
half of a dollar.
Example:
When we cut a pizza into two pieces, each piece is one-half of the pizza.
If we cut it into 4 pieces, then it
takes 2 such pieces or 2 quarters, to make half of a pizza,
and 4 such pieces or quarters to get back the whole pie.
So, we see that ½ is exactly equal or equivalent
to
A whole pizza is equivalent to 2 halves of a pizza or 4 quarters of a pizza.
Think money! You know 2 quarters
(¼ 's) make a half-dollar and 4 quarters (¼ 's) make a buck.
To create a fraction that is
equivalent to a given fraction, we multiply both its numerator and denominator
by the same number – so we're multiplying by one (1) and we're not changing the
value, just the form.
Remember
there's no prejudice in math!!! --
what you do to the top, you do to the bottom!
So,
to change ½ into
We have twice
as many pieces but they're half as big
as before.
Example: Fill in the blank space to create an
equivalent fraction:
Since we multiplied 7 (the
denominator) by 6 to get 42, we do
the same to the 5.
The solution is
But, 6 over 6 = 1, so we haven't changed
the value of the original fraction.
We just multiplied it by one – to change its form, not its value.
Equivalent
Fractions Exercise #1:
Fill
in the blanks to create an equivalent fraction.
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e)
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Just
as we can get equivalent fractions when we multiply by one, we can do the same
when we divide by one. In this case
we reduce the fraction to lowest terms.
So an answer of 15/20 would reduce to 3/4, since
In
the same way,
Equivalent
Fractions Exercise #2:
Now
we divide top and bottom by the same value
Factor these fractions as in the examples, then Reduce them to lowest
terms.
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John and Don, a pair of quarrelsome twins, were arguing
one day. Seems their Mom asked them to choose between two pieces of chocolate
candy. One piece was three quarters of a whole candy bar; the other was five
eighths of a bar. Since they both loved candy, they had to figure out which
piece was bigger. John said 5 eighths must be bigger than 3 quarters because 5
is bigger than 3. But Don said that 4 was smaller than 8 so 3 big pieces might
be bigger than 5 smaller ones.
They decided to figure it
out! They
wrote the two fractions like this:
themselves which symbol: < (less than), > (greater than), or = (equal to) made sense between them. Then
Don got a brilliant idea. He decided to turn the 3-quarter-sized-pieces into
6-eighth-sized-pieces by cutting each one of them in half – like
we did before with the pizza – remember? – This, of course, doubled the number of pieces to create
6 pieces from the 3 – but now each one was only one-eighth of a candy bar – no
longer a quarter. Both twins quickly concluded that 6-eighths is more candy than 5-eighths – so
they chose the bigger piece – the one that was 3 quarters of the bar.
What our twins did was find a common
denominator
for the two fractions.
They cut the two pieces of candy into the same sized pieces.
They found that
When fractions have the same
denominators they are easy to compare.
We look at their numerators and compare them.
When fractions
have the same denominators, the biggest
fraction is the one with the biggest numerator.
Ex:
When fractions
have the same numerators they are
also easy to compare. We just have to know into how many pieces the whole pie,
candy bar, whatever – was cut.
As we just learned, eighth-sized-pieces are half the size of quarter-sized-pieces,
and so on.
When the numerators are the same, the biggest fraction
is the one with the smallest denominator.
Ex:
Equivalent
Fractions Exercise #3:
Change these into equivalent fractions. Write < (less
than), > (greater than), or = (equal
to)
between them to indicate the relation.
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b) |
c) |
d) |
e) |
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Factor these fractions then Reduce
to lowest terms.
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b) |
c) |
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e) |
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