Question

A piece of fabric is cut into three sections so that the first is three times as long as the second and the second section is three times as long as the third. What part of the entire piece is the smallest section?​

Answer 1

Let the total length of the fabric be x

Length of the first section = a

Length of the second section = b

Length of the third section = c

By the given conditions,

a = 3b

b = 3c

a + b + c = x

a = 3*3c = 9c

Hence, a > b > c    (9c > 3c > c)

Fraction of the fabric which is the the smallest ie, c

= $\frac{c}{x} = \frac{c}{a + b +c} =\frac{c}{9c+3c+c} =\frac{c}{13c} =\frac{1}{13}$$\frac{c}{x} =\frac{c}{a+b+c} =\frac{c}{9c+3c+c} =\frac{c}{13c} =\frac{1}{13}$

Hence, the smallest section is 1/13 th of the fabric

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Answer 2

The answer is 1/13

GIVEN

A piece of fabric is cut into three sections so that the first is three times as long as the second and the second section is three times as long as the third.

TO FIND

What part of the entire piece is the smallest section.

SOLUTION

We can simply solve the above problem as follows;

Let the smallest piece of the fabrice = x

Therefore,

Second piece = 3x

Largest piece of the fabrice = 3 × 3x = 9x

Total length = x + 3x + 9x

= 13x

Measure of the smallest part = Length of the smallest part/Total length

= x/13x

= 1/13

Hence, The answer is 1/13

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