\frac{2}{6} \div \frac{4}{10}
Answer (2)
Rewrite the division as multiplication by the reciprocal: 6 2 ÷ 10 4 = 6 2 × 4 10 .
Multiply the fractions: 6 2 × 4 10 = 24 20 .
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 4: 24 20 = 6 5 .
The final answer is 6 5 .
Explanation
Rewrite the division as multiplication We are asked to evaluate the expression 6 2 ÷ 10 4 . Dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the expression as 6 2 × 4 10 .
Multiply the fractions Now, we multiply the fractions: 6 2 × 4 10 = 6 × 4 2 × 10 = 24 20 .
Simplify the fraction Next, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 20 and 24 is 4. We divide both the numerator and the denominator by 4: 24 20 = 24 ÷ 4 20 ÷ 4 = 6 5 .
Final Answer Therefore, the simplified fraction is 6 5 .
Examples
In baking, if a recipe calls for 6 2 of a cup of flour and you only want to make 10 4 of the recipe, you would calculate 6 2 ÷ 10 4 to find out how much flour you need. This calculation ensures you maintain the correct proportions for your adjusted recipe, preventing it from being too dry or too wet. Understanding fraction division is crucial for scaling recipes accurately.
To evaluate 6 2 ÷ 10 4 , first, we rewrite it as multiplication with the reciprocal, resulting in 6 5 after simplification. The process involves multiplying the two fractions together and simplifying by dividing by their GCD. The final answer is 6 5 .
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