Question

How do you write a math expression for the phrase given: the sum of the quotient of p and 14 and the quotient of q and 3?

Answer 1

Hint: There are so many words that you come across when you're working on algebra problems, and these words are really code for very specific mathematical symbols. An algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.
A variable is a letter that can represent one or more numbers.
Quotient' means division with the first number as the dividend (number being divided) and the second number being the divisor (number dividing into the dividend), we can rewrite both by \[\dfrac{p}{{14}}\] and \[\dfrac{q}{3}\], and using the phrase we will add the two.

Complete step-by-step solution:
When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.
Given statement is,
The sum of the quotient of p and 14 and the quotient of q and 3.
First we will know what a quotient' means : division with the first number as the dividend (number being divided) and the second number being the divisor (number dividing into the dividend).
The sum of \[p \div 14\] and \[q \div 3\],
Division is written as a fraction. The numerator (top number) is the dividend (number being divided), and the denominator (bottom number) is the divisor (the number dividing into the dividend). In this case, p will be on top of 14 for the first term and q will be on top of 3 for the second term.
The sum of \[\dfrac{p}{{14}}\] and \[\dfrac{q}{3}\],
'Sum' indicates addition, i.e.,
\[\dfrac{p}{{14}} + \dfrac{q}{3}\],
Now finally our first term is p divided by 14. We're adding to that our second term, q divided by 3.
\[\dfrac{p}{{14}} + \dfrac{q}{3}\] is the mathematical expression for the given phrase.

The math expression for the phrase given: the sum of the quotient of p and 14 and the quotient of q and 3 will be \[\dfrac{p}{{14}} + \dfrac{q}{3}\].

Note: To write an expression, we often have to interpret a written phrase.
For example, the phrase “6 added to some number” can be written as the expression x + 6, where the variable x represents the unknown number.
Some examples of common phrases and corresponding expressions that involve the operations are:

Phrase	Expression
4 more than some number	x + 4
8 minus some number	t -8
The product of a number and 12	12w
the quotient of a number and 12	\[\dfrac{p}{{12}}\]