Question

How do you express the phrase “Five more than the product of $7$ and $a$” as an algebraic expression?

Answer 1

Hint:Algebraic operation or term for the phrase “more than” is “+” that is additional operation and the operation for the phrase “product” is “$ \times $” that is multiplication. Use this information to express the given phrase as an algebraic expression.

Complete step by step solution:
In order to express the phrase “Five more than the product of $7$ and $a$” as an algebraic expression, we should have the information about what algebraic operations are occurring in the phrase. From the given phrase
“Five more than the product of $7$ and $a$”
We can see that there are two algebraic operations going on, but what they actually mean in algebra.
Let us see some general phrases and their algebraic expressions in order to express the given phrase
“a” more than “b” represents the algebraic expression: $a + b$
“a” minus “b” represents the algebraic expression: $a - b$
“b” divided by “a” represents the algebraic expression: $\dfrac{b}{a}\;{\text{or}}\;b \div a$
Product of “a” and “b” represents the same algebraic expression: $a \times b$
With the help of above information we can express the given phrase into algebraic expression
“Five more than the product of $7$ and $a$” $ = 7 \times a + 5$
Phrase “more than” stands for addition and “product of” stands for multiplication.

Note: Learning about the phrases and their algebraic meanings are very helpful in solving word problems. If you know the phrases and their meanings then you can easily elaborate and solve the word problems but if you don’t then it will be harder for you to elaborate word problems.