Question

How do you write $\dfrac{8}{{74}}$ in simplest form?

Answer 1

Hint:Here we will solve this problem by dividing the common factor of the numerator and the denominator. This kind of dividing process is also called reducing the terms by one common term.

Complete step by step answer:Given term $\dfrac{8}{{74}}$, This is a proper fraction once the absolute value of the top number or numerator is smaller than the absolute value of the bottom number or denominator, the fraction can be reduced.
Now first we can find the common factor of the denominator and the numerator,
Both terms are divided by one common term, that term helps us to reduce this term into the simplest form.
To find the greatest common factor, we first list the factors of $8$ and $74$ and then we find the largest factor they have in common. The factors of any number are all the numbers that we can evenly divide into that number.
In other words, the factors of $8$ are all the numbers that can evenly divide into $8$ and the factors of $74$ are all the numbers that can evenly divide into $74$.
Here are the factors for $8$ and $74$,
Factors of $8$ : $1,2,4,8$
Factors of $74$: $1,2,37,74$
The greatest factor on the two lists that they have in common is the GCF of $8$ and$74$.
Therefore, the GCF of $8$ and $74$ is $2$.
We can see that the GCF is $2$ because it is the largest number by which $8$ and $74$ can be divided without leaving any residue.
To reduce this fraction, simply divide the numerator and denominator by $2$
So,$\dfrac{8}{{74}} = \dfrac{{8 \div 2}}{{74 \div 2}} = \dfrac{4}{{37}}$
Thus, $\dfrac{8}{{74}}$ is equivalent to $\dfrac{4}{{37}}$ in the reduced form.

Note:
The factors are numbers that multiply each other to get another number.
For example $2$ and $3$ are factors of $6$ because by multiplying them you get $6$.
The fraction $\dfrac{8}{{74}}$ means $8 \div 74$ .
And it can also be expressed as a decimal as $0.108108$ and expressed as a percentage as $10.81\% $