Final answer:
To find the product of -11 and 7 6/7, one can either rewrite the mixed number as an improper fraction and apply the distributive property, or multiply the fractions directly after converting the mixed number to an improper fraction. Both methods will yield the same negative product: -605/7.
Step-by-step explanation:
The student is asking how to find the product of an integer and a mixed number. There are two methods for calculating this product:
- Rewriting the mixed number and applying the distributive property: First, convert 7 6/7 to an improper fraction by multiplying the whole number 7 by the denominator 7 and adding the numerator 6, which gives 55/7. Then, the product can be found by multiplying -11 by 55/7. Applying the distributive property, we get (-11 * 55) / 7.
- Multiplying the integer and mixed number by multiplying fractions: Here, we do a similar conversion of 7 6/7 to 55/7. Then, we multiply -11 (which is the same as -11/1) by 55/7. The product is again the multiplication of numerators (-11 * 55) divided by the multiplication of denominators (1 * 7).
For both methods, we follow the rule that when two numbers multiplied have opposite signs, the answer has a negative sign. Thus, multiplying an integer -11 by a positive fraction 55/7 will result in a negative product.
The steps for calculating the product include:
- Conversion of the mixed number to an improper fraction.
- Multiplication of the numerators.
- Division of the result by the denominator.
- Ensuring that the sign of the final product is negative due to the initial negative integer.
The final answer for the product using both methods will be the same: -605/7.