Which expression represents, five times the quotient of two numbers
The Correct Answer and Explanation is:
Correct Expression:
The expression that represents five times the quotient of two numbers is:5×(ab)or simply5(ab)5 \times \left(\frac{a}{b}\right) \quad \text{or simply} \quad 5\left(\frac{a}{b}\right)5×(ba)or simply5(ba)
Explanation:
In mathematics, translating verbal phrases into algebraic expressions is a fundamental skill. Let’s break down the phrase “five times the quotient of two numbers” into its parts to understand how we arrive at the expression:
- Quotient of two numbers:
The word quotient refers to the result of a division. When the phrase says “the quotient of two numbers,” it means one number is being divided by another. If we call these two numbers a and b, then the quotient is written as: ab\frac{a}{b}ba - Five times the quotient:
The phrase “five times” means to multiply by 5. So, when we are asked for “five times the quotient,” we multiply the quotient ab\frac{a}{b}ba by 5. That gives us: 5×(ab)5 \times \left(\frac{a}{b}\right)5×(ba)
Putting both parts together, the full expression becomes:5(ab)5\left(\frac{a}{b}\right)5(ba)
This expression shows that we first take the quotient of two numbers and then multiply that result by 5. The parentheses help clarify the order of operations, ensuring that the division happens before the multiplication.
This type of algebraic translation is essential in solving real-world problems, especially in word problems involving ratios, rates, and proportions. Understanding how to interpret terms like sum, difference, product, and quotient—and how to combine them with multipliers like “five times”—makes it easier to set up and solve equations.
To summarize, the correct expression for “five times the quotient of two numbers” is:5(ab)5\left(\frac{a}{b}\right)5(ba)
where a and b represent any two numbers, with b ≠ 0 (since division by zero is undefined).
