Two-fifths of the square of the number j in algebraic expression.
The Correct Answer and Explanation is:
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Algebraic Expression:
The expression for two-fifths of the square of the number j is:25j2\frac{2}{5}j^252j2
Explanation
To form an algebraic expression from a verbal statement, you need to interpret the language of mathematics carefully. Let us break down the phrase “two-fifths of the square of the number j” step by step:
- “The number j” refers to the variable j, which represents an unknown or general number.
- “The square of the number j” means raising j to the power of 2, or multiplying j by itself. Mathematically, this is written as: j2j^2j2
- “Two-fifths of the square” tells us to take a fraction of that squared value. The phrase “of” in mathematics usually indicates multiplication. So, we are multiplying the squared value, j², by the fraction 2⁄5: 25×j2\frac{2}{5} \times j^252×j2
Putting these parts together, we arrive at the complete algebraic expression:25j2\frac{2}{5}j^252j2
This expression means that we are taking two-fifths of the quantity j². This is a common way to express a fraction of a power in algebra.
This type of expression is useful in real-world scenarios as well. For instance, if j represents a measurement such as the length of a side of a square, then j² represents the area of that square. Taking two-fifths of that area might be useful when calculating proportions, such as shaded regions, resource usage, or financial distributions.
Understanding how to convert between verbal phrases and algebraic expressions is key in algebra. It helps in forming equations, solving word problems, and communicating mathematical ideas precisely.
