Divide these two fractions: [tex]$\frac{1}{6} \div \frac{3}{7}=?$[/tex]
Answer (1)
To divide fractions, multiply by the reciprocal: 6 1 ÷ 7 3 = 6 1 × 3 7 .
Multiply the numerators: 1 × 7 = 7 .
Multiply the denominators: 6 × 3 = 18 .
The result is: 18 7 .
Explanation
Understanding the Problem We are asked to divide two fractions: 6 1 and 7 3 . The expression is 6 1 ÷ 7 3 .
Dividing Fractions To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 7 3 is 3 7 . Therefore, 6 1 ÷ 7 3 = 6 1 × 3 7 .
Multiplying Numerators and Denominators Now, we multiply the numerators and the denominators separately. The product of the numerators is 1 × 7 = 7 , and the product of the denominators is 6 × 3 = 18 .
Final Result Thus, the result of the division is 18 7 .
Examples
In baking, if a recipe calls for 6 1 cup of flour and you only have a 7 3 cup measuring spoon, dividing 6 1 by 7 3 tells you what fraction of the 7 3 cup measuring spoon you need to use. This ensures you get the correct amount of flour for your recipe, maintaining the right consistency and taste in your baked goods. Understanding fraction division helps in accurately scaling recipes and measuring ingredients.
