convert the following fraction into equivalent like fraction a)3/7 , 5/6 B)5/6 , 7/16 c) 3/4,5/6,7/8
Answers
Step-by-step explanation:
GIVEN:-
convert the following fraction into equivalent like fraction
SOLUTION:-
1)3/7,5/6
First of all eauivalent like fraction means that the given fractions must have same denominators and when put in standard form be equal to the original fraction.
So now first we need to make the denominator equal by finding L.C.M. and them dividing the L.C.M. by the original denominators respectively.After that multiplying the quotient to both numerator and denominator.
Let's get started!
\begin{gathered} = > l.c.m \: of \: denominators \: of \: \: \frac{3}{7} \: and \: \frac{5}{6} \\ \\ \\ = > 1|7 \: \: \: \: \: \: \: 6| \\ \\ \: \: \: \: \: \: \: \: \: \: |7 \: \: \: \: \: \: \: 6| \\ \\ = > 7 \times 6 = 42 |l.c.m|\end{gathered}
=>l.c.mofdenominatorsof
7
3
and
6
5
=>1∣76∣
∣76∣
=>7×6=42∣l.c.m∣
Now we will make the denominators equal to 42.
\begin{gathered} = > \frac{3}{7} = \frac{3}{42 \div 7} = \frac{3}{6} = \frac{3 \times 6}{7 \times 6} \\ \\ = > \frac{18}{42} \\ \\ \\ = > \frac{5}{6} = \frac{5}{42 \div 6} = \frac{5}{7} = \frac{5 \times 7}{6 \times 7} \\ \\ = > \frac{35}{42} \end{gathered}
=>
7
3
=
42÷7
3
=
6
3
=
7×6
3×6
=>
42
18
=>
6
5
=
42÷6
5
=
7
5
=
6×7
5×7
=>
42
35
:.3/7 and 5/6 are in equivalent like fraction in from of 18/45 and 36/45
2)5/6 , 7/16
Here also we will follow the same steps to get the fractions.
\begin{gathered} = > l.c.m \: of \: denominators = 6 \: and \: 16 \\ \\ 2|6 \: \: \: \: \: \: \: \: \: \: 16 | \\ \\ |3 \: \: \: \: \: \: \: \: \: \: \: \: \: 8| \\ \\ = > 2 \times 3 \times 8 \\ \\ = > 2 \times 24 \\ \\ = > 48\end{gathered}
=>l.c.mofdenominators=6and16
2∣616∣
∣38∣
=>2×3×8
=>2×24
=>48
Now,
\begin{gathered} \\ \\ = > \frac{5}{6} = \frac{5}{48 \div 6} = \frac{5}{8} = \frac{5 \times 8}{6 \times 8} \\ \\ = > \frac{40}{48} \\ \\ \\ = > \frac{7}{16} = \frac{7}{48 \div 16} = \frac{7}{3} = \frac{7 \times 3}{16 \times 3} \\ \\ = > \frac{21}{48} \\ \\ \\ \end{gathered}
=>
6
5
=
48÷6
5
=
8
5
=
6×8
5×8
=>
48
40
=>
16
7
=
48÷16
7
=
3
7
=
16×3
7×3
=>
48
21
:.Answer of second is 40/48 and 21/48.
3)3/4 , 5/6 , 7/8
=>L.C.M. of 4,6,8
=> 2|4,6,8|
2|2,3,4|
|1,3,2|
=>2×2×3×2
=>2×2×6
=>2×12
=>24 |L.C.M.|
=>3/4=3/24÷4
=>3/6
=>3×6/4×6
=>18/24
=>5/6=5/24÷6
=>5/4
=>5×4/6×4
=>20/24
=>7/8=7/24÷8
=>7/3
=>7×3/8×3
=>21/24
:.Third answer is 18/24 , 20/24 and 21/24
hope it helped to u
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