Multiply these two fractions: [tex]$\frac{3}{8} \times \frac{1}{6}=?$[/tex]
Answer (1)
Multiply the numerators: 3 × 1 = 3 .
Multiply the denominators: 8 × 6 = 48 .
Form the fraction: 48 3 .
Simplify the fraction: 48 3 = 16 1 .
16 1
Explanation
Understanding the Problem We are asked to multiply two fractions, 8 3 and 6 1 . To do this, we multiply the numerators together and the denominators together.
Multiplying Numerators First, we multiply the numerators: 3 × 1 = 3 .
Multiplying Denominators Next, we multiply the denominators: 8 × 6 = 48 .
Forming the Fraction So, the result of the multiplication is 48 3 . Now we need to simplify this fraction.
Finding the Greatest Common Divisor (GCD) To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 3 and 48 is 3.
Simplifying the Fraction Now we divide both the numerator and the denominator by the GCD: 48 ÷ 3 3 ÷ 3 = 16 1 .
Final Answer Therefore, the product of the two fractions is 16 1 .
Examples
Understanding fraction multiplication is essential in many real-life situations. For instance, if you are baking a cake and the recipe calls for 2 1 cup of sugar, but you only want to make 4 1 of the recipe, you need to multiply 2 1 × 4 1 to find out how much sugar you need. This gives you 8 1 cup of sugar. Similarly, in construction or engineering, multiplying fractions is crucial for scaling measurements and calculating material quantities.
