Mathematik Übungen

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:

2412

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. $6/17 ; 6/18 ; 6/19$

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

   
   

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