Question

How do you define a variable and write an expression for each phrase: the quotient of 11 and a number?

Answer 1

In this question we have to write the phrase “the quotient of 11 and a number” as a mathematical operation, so for doing it we must know what a quotient is how to find it. The quotient is defined as a number obtained by dividing one number by another number. The number that is being divided is known as the dividend and the number by which another number is divided is known as the divisor.
Thus quotient can be defined in simple words as the result obtained on dividing the dividend by the divisor.
Now, according to Euclid’s division lemma, the dividend is equal to the product of the divisor and the quotient plus the denominator, that is, $a = bq + r$ . Using the above-mentioned information we can find out the correct answer.

Complete step by step answer:
A variable is defined as a quantity that doesn’t have a fixed value and can take many different values. It is represented by an alphabet.
Let “a number” be represented by an unknown variable quantity n,
Hence this phrase can be written in the expression form as $11 \div n\,\,or\,\,\dfrac{{11}}{n}$ .

Note: The expression obtained is an algebraic expression that is defined as a combination of the numerical values and the alphabets representing an unknown quantity. We have to express the phrase “the quotient of 11 and a number” as a mathematical operation. As we know that the quotient is the ratio of the dividend and the divisor. From the given phrase, we get that the numerator is equal to 11 and the denominator is “a number”.