Simplify the expression: [tex]$\frac{18 m \cdot 24}{60}$[/tex]
Answer (2)
To simplify the expression 60 18 m ⋅ 24 , first multiply to get 60 432 m . Then find the GCD of 432 and 60, which is 12, and divide both numerator and denominator by 12 to yield 5 36 m . Therefore, the simplified expression is 5 36 m .
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Multiply the constants in the numerator: 18 \t ⋅ 24 = 432 .
Simplify the fraction 60 432 by finding the GCD of 432 and 60, which is 12.
Divide both the numerator and the denominator by the GCD: 60 \t ÷ 12 432 \t ÷ 12 = 5 36 .
The simplified expression is 5 36 m .
Explanation
Understanding the Expression We are asked to simplify the expression 60 18 m \t ⋅ 24 . This involves multiplying the numbers in the numerator and then dividing by the denominator. The variable m will remain as a factor in the simplified expression.
Multiplying the Numerator First, let's multiply the constants in the numerator: 18 \t ⋅ 24 = 432 . So the expression becomes 60 432 m .
Finding the GCD Now, we need to simplify the fraction 60 432 . We can divide both the numerator and the denominator by their greatest common divisor (GCD). Let's find the GCD of 432 and 60. The prime factorization of 432 is 2 4 \t ⋅ 3 3 , and the prime factorization of 60 is 2 2 \t ⋅ 3 \t ⋅ 5 . The GCD is 2 2 \t ⋅ 3 = 12 .
Simplifying the Fraction Divide both the numerator and the denominator by 12: 60 \t ÷ 12 432 \t ÷ 12 = 5 36 . Therefore, the simplified expression is 5 36 m .
Final Answer The simplified expression is 5 36 m .
Examples
Understanding how to simplify algebraic expressions like this is useful in many real-world scenarios. For example, if you are calculating the total cost of items where the price per item is given by an expression, simplifying that expression can make the calculation easier. Imagine you are buying m items, and the price per item is 60 18 \t ⋅ 24 dollars. Simplifying this to 5 36 m or 7.2 m dollars makes it easier to calculate the total cost for any number of items. This is also applicable in physics, where formulas often need simplification before calculations.
