Question

How do you express the phrase “45 divided into a number b” as an algebraic expression?

Answer 1

Hint: We start solving the problem by recalling the fact that the phrase “a divided into a number c” means that the number c is divided with a. We then make use of the fact that the division operation is represented by the symbol \[\div \] to proceed through the problem. We then use both of these definitions and symbols to get the required algebraic expression of the given phrase in the problem.

Complete step by step answer:
According to the problem, we are asked to express the phrase “45 divided into a number b” as an algebraic expression.
We know that the phrase “a divided into a number c” means that the number c is divided with a.
We know that the division operation is represented by the symbol \[\div \].
So, the algebraic expression for representing the phrase “45 divided into a number b” is $b\div 45$.

$\therefore $ The algebraic expression for representing the given phrase “45 divided into a number b” is $b\div 45$.

Note: We should not confuse that “a divided into a number c” with $a\div c$ which is the common mistake done by students. We can also represent the given phrase as $\dfrac{b}{45}$ which is the same as representing $b\div 45$. Similarly, we can exponentially solve problems to write the algebraic expression for the phrase “multiplication of 8 with the quotient of 35 with c”.