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How do you write the fraction $\dfrac{{48}}{{56}}$ in simplest form?

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Last updated date: 20th Jun 2024
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Answer
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Hint: A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers. The number on the top of the line is called the numerator… it shows the total divisible number of equal parts which are there in a collection. The number below the line is called the denominator. It shows the total divisible number of equal parts the whole into or the total number of equal parts which are there in a collection.
To simplify a fraction: divide the top and bottom by the greatest number that will divide both numbers exactly (they must stay whole numbers).

Complete step-by-step solution:
To write the fraction $\dfrac{{48}}{{56}}$ in simplest form, we need to divide the numerator and denominator, by their GCD (Greatest Common Divisor)
As prime factors of $48$are
$
  48 = 2 \times 2 \times 2 \times 2 \times 3 \\
  56 = 2 \times 2 \times 2 \times 7 \\
 $
Common factors are $2 \times 2 \times 2$ and GCD is
$\Rightarrow 2 \times 2 \times 2 = 8$
$\Rightarrow \dfrac{{48}}{{56}}$
$
   \Rightarrow \dfrac{{8 \times 6}}{{8 \times 7}} \\
   \Rightarrow \dfrac{6}{7} \\
 $

Additional Information:
A fraction is not a whole number but a number in between the whole numbers. It is a part of a whole. Also, a fraction has two parts-a numerator and a denominator. When the numerator and the denominator can no longer be reduced to any smaller number separately, we get the fraction in its simplest form.

Note: To find the an accurate answer
Steps for finding the simplest form:
i) Search for common factors in the numerator and denominator.
ii) Check whether one of the numbers in the fraction is a prime number.
iii) Divide by a fraction equivalent to 1