Question

How do you solve $ \dfrac{{40}}{{56}} = \dfrac{k}{7}? $

Answer 1

Hint: Take the given expression and perform cross multiplication and make the simplified in terms of “k” subject and on the end find the common factors from the numerator and the denominator and cancel them and then simplify the expression for the resultant required value for “k”

Complete step by step solution:
Take the given expression: $ \dfrac{{40}}{{56}} = \dfrac{k}{7} $
Perform cross multiplication where the numerator of one side is multiplied with the denominator of the opposite side and similarly the denominator of one side is multiplied with the numerator of the opposite side.
 $ 40 \times 7 = k \times 56 $
The above equation can be re-written as: $ k \times 56 = 40 \times 7 $
Make “k” the subject in the above expression. The term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ k = \dfrac{{40 \times 7}}{{56}} $
Find the factors for the expression on the right hand side of the equation.
 $ k = \dfrac{{8 \times 5 \times 7}}{{8 \times 7}} $
Common multiple from the numerator and the denominator cancel each other. Therefore, remove from the above expression.
 $ \Rightarrow k = 5 $
This is the required solution.
So, the correct answer is “k = 5”.

Note: Be careful while simplifying the equation from the given expression while doing cross multiplication. Be good in multiples and finding the factors, remember multiples of the numbers at least till twenty for the efficient and the accurate solution. Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $ 1 $ and which are not the product of any two smaller natural numbers. For Example: $ 2,{\text{ 3, 5, 7,}}...... $ $ 2 $ is the prime number as it can have only $ 1 $ factor.