\frac{n^2}{2} \div \frac{3}{10}
Answer (2)
Rewrite the division as multiplication by the reciprocal: 2 n 2 ÷ 10 3 = 2 n 2 × 3 10 .
Multiply the fractions: 2 n 2 × 3 10 = 6 10 n 2 .
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 2: 6 10 n 2 = 3 5 n 2 .
The simplified expression is 3 5 n 2 .
Explanation
Understanding the Problem We are given the expression 2 n 2 ÷ 10 3 . Our goal is to simplify this expression.
Rewriting the Division To divide by a fraction, we multiply by its reciprocal. Therefore, we can rewrite the expression as: 2 n 2 ÷ 10 3 = 2 n 2 × 3 10
Multiplying the Fractions Now, we multiply the fractions: 2 n 2 × 3 10 = 6 10 n 2
Simplifying the Fraction Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 6 10 n 2 = 3 5 n 2 Thus, the simplified expression is 3 5 n 2 .
Final Answer The simplified expression is 3 5 n 2 .
Examples
Understanding how to simplify algebraic expressions like this is useful in many areas, such as physics and engineering, where you often need to manipulate formulas to solve for unknown variables. For example, if you are calculating the kinetic energy of an object, you might need to simplify an expression involving the object's mass and velocity. Simplifying expressions makes calculations easier and more accurate.
The expression 2 n 2 ÷ 10 3 simplifies to 3 5 n 2 by rewriting the division as multiplication by the reciprocal, multiplying the fractions, and then simplifying the result. This process helps in manipulating expressions in mathematics. The final answer is 3 5 n 2 .
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