Work out $1 \frac{4}{7} \times 6$ Give your answer as a fraction in its lowest terms.
Answer (2)
The answer to 1 7 4 × 6 is 7 66 , which is in its lowest terms. This was obtained by converting the mixed number to an improper fraction and then multiplying. The fraction 7 66 cannot be simplified further.
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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 are asked to calculate 1 7 4 × 6 and express the answer as a fraction in its lowest terms.
Convert to Improper Fraction First, we need to convert the mixed number 1 7 4 into an improper fraction. To do this, we multiply the whole number part (1) by the denominator (7) and add the numerator (4). This gives us 1 × 7 + 4 = 7 + 4 = 11 . So, the improper fraction is 7 11 .
Multiply by 6 Now, we multiply the improper fraction 7 11 by 6. This gives us 7 11 × 6 = 7 11 × 6 = 7 66 .
Check for Simplification To express the fraction in its lowest terms, we need to check if the numerator and denominator have any common factors other than 1. The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. The factors of 7 are 1 and 7. The only common factor is 1, so the fraction is already in its lowest terms.
Final Answer Therefore, the answer is 7 66 .
Examples
Suppose 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 is done by multiplying 1 7 4 by 6, which gives you 7 66 cups of flour. This type of calculation is useful in many real-life situations involving scaling quantities.
