Question

the simplest form of (64/729)-1/6
ans.3/2
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Answer 1

Answer:

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Answer 2

$\bf\purple{QuestioN:-}$

The simplest form of   $\sf{\dfrac{64}{729}-\dfrac{1}{6}}$ .

$\bf\blue{AnsweR:-}$

To subtract a fraction from another fraction, at first we need to find

the LCM of the denominators.

The LCM of the denominators :

$\pink{:\implies\pmb{729=3\times3\times3\times3\times3\times3}}$

$\pink{:\implies\pmb{6=2\times3}}$

LCM = 3 × 3 × 3 × 3 × 3 × 3 × 2

        = 1, 458

Next step is to convert the denominators same.

That is,

$\pink{:\implies\pmb{\dfrac{64}{729}=\dfrac{64\times2}{729\times2}}$

$\pink{:\implies\pmb{\dfrac{64\times2}{729\times2}=\dfrac{128}{1,458}}$ ----------- Eq. 1

$\pink{:\implies\pmb{\dfrac{1}{6}=\dfrac{1\times243}{6\times243}}$

$\pink{:\implies\pmb{\dfrac{1\times243}{6\times243}=\dfrac{243}{1,458}}$  ---------- Eq. 2

Now we can subtract Eq.2 from Eq.1.

$\pink{:\implies\pmb{\dfrac{128}{1,458}-\dfrac{243}{1,458}}$

$\pink{:\implies\pmb{\dfrac{-115}{1,458}}$

This fraction itself is its simplest form ! Coz both of this numbers didn't have a factor in common!

Happy Learning!