Divide these two fractions: [tex]$\frac{1}{3} \div \frac{2}{5}=?$[/tex]
Answer (1)
To divide fractions, multiply by the reciprocal of the second fraction.
The reciprocal of 5 2 is 2 5 .
Multiply 3 1 by 2 5 to get 3 × 2 1 × 5 .
Simplify the fraction to get the final answer: 6 5 .
Explanation
Understanding the Problem We are asked to divide two fractions: 3 1 and 5 2 . The problem is 3 1 ÷ 5 2 .
Finding the Reciprocal To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 5 2 is 2 5 .
Rewriting the Division as Multiplication Therefore, 3 1 ÷ 5 2 = 3 1 × 2 5 .
Multiplying the Fractions Now, we multiply the numerators and the denominators: 3 × 2 1 × 5 = 6 5 .
Final Answer The result of dividing 3 1 by 5 2 is 6 5 .
Examples
Dividing fractions is a fundamental concept that appears in various real-life situations. For instance, imagine you are baking a cake and the recipe calls for 5 2 of a cup of sugar, but you only want to make 3 1 of the recipe. To find out how much sugar you need, you would divide 3 1 by 5 2 . This gives you 6 5 of the original amount of sugar, which is 6 5 × 5 2 = 3 1 cup of sugar. Understanding fraction division helps in scaling recipes, calculating proportions, and many other everyday tasks.
