Write the fractions in order of size, smallest first 11/12, 5/6 , 3/4
Answers
Step-by-step explanation:
Multiply the numerator of
A
with the denominator of
B
. The resulting product would be
A
's weighted value relative to
B
.
A
=
11
12
B
=
7
8
W
A
B
=
11
⋅
8
=
88
Similarly, multiply the numerator of
B
with the denominator of
A
. The resulting product would be
B
's weighted value relative to
A
W
B
A
=
7
⋅
12
=
84
Compare the weighted value of
A
and
B
. Whichever has the higher weighted value, is larger.
W
A
B
=
88
?
W
B
A
=
84
W
A
B
>
W
B
A
⇒
A
>
B
Note the use of the word relative. This is because the computed weighted value is only valid between the two numbers. If a third number is involved, the above steps need to be performed for each possible pairing
Do the same for
A
and
C
A
=
11
12
C
=
15
16
W
A
C
=
11
⋅
16
=
176
W
C
A
=
12
⋅
15
=
180
W
A
C
=
176
?
W
C
A
=
180
⇒
W
A
C
<
W
C
A
⇒
A
<
C
⇒
C
>
A
Since A > B, and C > A, it should follow that C > B.
Hence, we will no longer check which is bigger between B and C.
7
8
<
11
12
<
15
16
Answer link
EZ as pi
Dec 3, 2016
7
8
<
11
12
<
15
16
Explanation:
You cannot compare fractions which have different denominators.
Convert all the fractions to a common denominator.
In this case the
L
C
M
=
48
11
12
×
4
4
7
8
×
6
6
15
16
×
3
3
=
44
48
=
42
48
=
45
48
It is now possible to compare and arrange them in order:
42
48
<
44
48
<
45
48
Using the original fractions:
7
8
<
11
12
<
15
16
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Another method works in this case if you realise that each fraction is only 1 part short of being a whole number.
11
12
is
1
12
less than 1,
7
8
is
1
8
less than 1
15
16
is
1
16
less than 1.
Arranging in size
1
8
>
1
12
>
1
16
Therefore
7
8
is furthest from 1 and must be the smallest.
15
16
is closest to 1 and is therefore the biggest