Multiply −1 1/6 by 7. Write the answer as a mixed number.(
To multiply a mixed number by a whole number, we can multiply the whole number by the whole part of the mixed number and then multiply the whole number by the fractional part of the mixed number and add those products together.
First, we multiply 7 by -1. The product is -7.
Next, we multiply 7 by 1/6. To do this, we can rewrite 1/6 as a fraction with 7 as the denominator: 1/6 = 7/42.
Now we can multiply 7 by 7/42: 7 * 7/42 = 49/42.
Finally, we add the two products together: -7 + 49/42.
To write this as a mixed number, we need to convert the fraction to a mixed number.
First, we divide the numerator (49) by the denominator (42).
49 ÷ 42 = 1 remainder 7
So, the mixed number is 1 and 7/42.
To multiply a mixed number by a whole number, we first need to convert the mixed number into an improper fraction.
The improper fraction form of −1 1/6 is -7/6 because the negative sign applies to the whole number part as well.
Now we can multiply -7/6 by 7:
-7/6 * 7 = -49/6
To write the answer as a mixed number, we divide the numerator (-49) by the denominator (6) which gives us a quotient of -8 with a remainder of -1.
Since the remainder is negative, we use the negative sign for the whole number part and keep the remainder as the numerator.
Therefore, the answer as a mixed number is -8 1/6.