Question

How do you write the phrase “four-fifths of the sum of \[ - 20\] and \[5\]” as a mathematical expression?

Answer 1

Hint: Here, we will use the keyword of the given phrase to write the expression in parts. Then we will combine all the parts to get the required answer. The arithmetic expression or Mathematical expression is defined as an expression with the numbers and the arithmetic operators like plus, minus etc.

Complete Step by Step Solution:
We are given the phrase four-fifths of the sum of \[ - 20\] and \[5\].
We know that the four-fifths can be represented as a fraction with four in the numerator and five in the denominator.
So, four-fifths can be written as \[\dfrac{4}{5}\].
We know that the sum of \[ - 20\] and \[5\] represents the arithmetic operation of addition.
So the sum of \[ - 20\] and \[5\] can be written as \[ - 20 + 5\].
We know that the preposition “of” represents the arithmetic operation of multiplication.
Four-fifths of the sum of \[ - 20\] and \[5\] \[ = \dfrac{4}{5} \times \left( { - 20 + 5} \right)\]

Therefore, the phrase four-fifths of the sum of \[ - 20\] and \[5\] can be written as a mathematical expression \[\dfrac{4}{5} \times \left( { - 20 + 5} \right)\].

Additional Information:
We should know that there is no single strategy for converting an algebraic expression into a word phrase and vice versa. We have many keywords to represent the arithmetic operation where some of the keywords are listed here. The key words to represent addition are plus, added to, increased by, more than, total of, the sum of. The key words to represent subtraction are minus, the difference of, subtracted from, decreased by, less than. The key words to represent multiplication are times, the product of two terms. The key words to represent division are divided by, the quotient of, the ratio of, divided into.

Note:
We know that Algebraic expression is defined as an expression with both the numbers and the variables and the arithmetic operators like plus, minus, etc. We have many ways to represent an algebraic expression into the word phrase. Word phrase is a way of representing the algebraic expression or mathematical expression in the form of sentences using the keywords. We should remember it is enough for us to write only the expression rather than evaluating the expression.