Divide these two fractions: [tex]$\frac{3}{8} \div \frac{1}{6}=?$[/tex]
Answer (1)
To divide 8 3 by 6 1 , multiply 8 3 by the reciprocal of 6 1 , which is 1 6 .
Multiply the numerators and denominators: 8 × 1 3 × 6 = 8 18 .
Simplify the fraction 8 18 by dividing both numerator and denominator by their greatest common divisor, which is 2: 8 ÷ 2 18 ÷ 2 = 4 9 .
The simplified fraction is 4 9 .
Explanation
Understanding the Problem We are asked to divide two fractions, 8 3 and 6 1 , and simplify the result to its simplest form.
Dividing Fractions To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 6 1 is 1 6 . So, we have: 8 3 ÷ 6 1 = 8 3 × 1 6
Multiplying Numerators and Denominators Now, we multiply the numerators and the denominators: 8 × 1 3 × 6 = 8 18
Finding the Greatest Common Divisor (GCD) Next, we simplify the fraction 8 18 by finding the greatest common divisor (GCD) of 18 and 8. The GCD of 18 and 8 is 2.
Simplifying the Fraction We divide both the numerator and the denominator by the GCD, which is 2: 8 ÷ 2 18 ÷ 2 = 4 9
Final Answer The fraction 4 9 is now in its simplest form, as 9 and 4 have no common factors other than 1.
Examples
In cooking, if a recipe calls for 8 3 of a cup of flour and you only have a 6 1 cup measuring spoon, you need to know how many 6 1 cup portions make up 8 3 of a cup. Dividing 8 3 by 6 1 tells you that you need 2 4 1 portions of the 6 1 cup to get the required amount of flour. This ensures accurate measurements and better cooking results.
