Question

Salil wants to put a picture in a frame. The picture is $$7{\displaystyle \frac{3}{5}}\mathrm{c}\mathrm{m}$$ wide. To fit in the frame the picture cannot be more than $$7{\displaystyle \frac{3}{10}}\mathrm{c}\mathrm{m}$$wide. How much should the picture be trimmed?

Answer 1

Hint: Here, we can find the width of the picture that has to be trimmed by using the concept of subtraction.. For that, we will first convert the width from mixed to improper fraction, then subtract the picture’s width from frame’s width to get the required answer.

Complete step-by-step answer:
It is clear from the question that the picture’s width is greater than the frame’s width.
Now, we have to find the width of the picture that has to be trimmed.
Width of the Picture that has to be trimmed $$=$$ Picture’s width $$-$$ Frame’s width
$$\Rightarrow$$ Width of the Picture that has to be trimmed $$=7{\displaystyle \frac{3}{5}}-7{\displaystyle \frac{3}{10}}$$cm
Now, we have to convert the mixed fraction into an improper fraction. Therefore, we get
$$\Rightarrow$$ Width of the Picture that has to be trimmed$$=$$$${\displaystyle \frac{38}{5}}-{\displaystyle \frac{73}{10}}$$cm
Now, we will convert the improper fraction into like fraction by taking LCM. Here, the L.C.M of $$\left(5,10\right)$$ is 10.
So, we have
$$\Rightarrow$$ Width of the Picture that has to be trimmed$$=$$$${\displaystyle \frac{38}{5}}\times {\displaystyle \frac{2}{2}}-{\displaystyle \frac{73}{10}}$$cm
$$\Rightarrow$$ Width of the Picture that has to be trimmed $$=$$$${\displaystyle \frac{76}{10}}-{\displaystyle \frac{73}{10}}$$cm
Subtracting the like terms, we have
$$\Rightarrow$$ Width of the Picture that has to be trimmed $$=$$$${\displaystyle \frac{3}{10}}$$cm
Therefore, the picture has to be trimmed $${\displaystyle \frac{3}{10}}$$cm.

Note: We should be clear about the mixed fraction and the improper fraction. Since the given value is in mixed fraction it has to be converted improper fraction. To convert the mixed fraction into an improper fraction, we have to multiply the whole number by the denominator of a fraction, and then add the obtained value with the numerator value. This should be the new numerator value of a fraction.