Work out $1 \frac{4}{7} \times 6$
Give your answer as a fraction in its lowest terms.
Answer (1)
Convert the mixed number to an improper fraction: 1 7 4 = 7 11 .
Multiply the improper fraction by 6: 7 11 × 6 = 7 66 .
Simplify the fraction (if possible). In this case, 7 66 is already in its lowest terms.
The final answer is 7 66 .
Explanation
Problem Analysis We need to calculate 1 7 4 × 6 and express the answer as a fraction in its lowest terms.
Convert to Improper Fraction First, convert the mixed number 1 7 4 to an improper fraction. To do this, we multiply the whole number part (1) by the denominator (7) and add the numerator (4): 1 7 4 = 7 ( 1 × 7 ) + 4 = 7 7 + 4 = 7 11
Multiply by 6 Next, multiply the improper fraction 7 11 by 6: 7 11 × 6 = 7 11 × 6 = 7 66
Simplify the Fraction Now, we need to check if the fraction 7 66 can be simplified. To do this, we find the greatest common divisor (GCD) of the numerator (66) and the denominator (7). Since 7 is a prime number, we only need to check if 7 divides 66. 66 ÷ 7 = 9 with a remainder of 3. Since the remainder is not 0, the GCD of 66 and 7 is 1, which means the fraction is already in its lowest terms.
Final Answer Therefore, the answer is 7 66 .
Examples
Imagine you are baking a cake and the recipe calls for 1 7 4 cups of flour per cake. If you want to bake 6 cakes, you need to calculate the total amount of flour required. This problem is equivalent to calculating 1 7 4 × 6 , which we found to be 7 66 cups of flour. This means you would need 7 66 cups of flour to bake 6 cakes. Converting this improper fraction to a mixed number gives you 9 7 3 cups.
