  # Find the missing numerator or denominator (equivalent fractions)

?/3=12/9

## Equivalent fractions

Equivalent fractions are equal in value, even though they look different.

E.g.: \$\;1/2=2/4\$
We can draw it:

When we multiply or divide the numerator (the top number) and the denominator (the bottom number) of a fraction by another fraction with the same numerator or denominator, it keeps the same value. A fraction with the same numerator and denominator is actually equal to 1 and by multiplying or dividing by 1 we won't change the value of original fraction.
E.g.:

\$\$2/3×2/2=4/6=4/6×2/2=8/12=\$\$
\$\$=8/12×3/3=24/36 ...\$\$
\$\$12/16={12÷4}/{16÷4}=3/4\$\$

If there is a missing part of a fraction in an equation, we need to find the equivalent fraction:

\$\$1/3=2/x\$\$

We need to multiply 1 by 2 to get 2. We need to do the same with the denominator (3). And 3×2=6

\$\$1/3=2/x\;→\;{1×2}/{3×2}\$\$
\$\$→\;{3×2}=6\;→\;x=6\$\$

If there is a missing part of a fraction in an inequality, we need to find the equivalent fraction at first and then decrease/increase it to have it greater or smaller. E.g.:

\$\$3/8>6/x\;→\;{3×2}/{8×2}=6/16\;→\;3/8=6/16\$\$

Since \$3/8\$ are equivalent to \$6/16\$, we need to find a fraction that has 6 as a numerator (top number) and at the same time it is smaller than \$6/16\$. This is any fraction with a denominator greater than 16, e.g. \$6/17 ; 6/18 ; 6/19\$

\$\$x={17\;;\;18\;;\;19\;;\;20...}\$\$ 