Evaluate negative five-thirds divided by seven, giving the answer in its simplest form.
We can begin this question by recalling that any integer or whole number can be written as that number over one. In this case, seven is equal to seven over one. When dividing two fractions, we multiply the first fraction by the reciprocal of the second fraction. This is sometimes known as keep, change, flip. We keep the first fraction the same, we change the division sign to a multiplication, and we flip the second fraction. We can then multiply our two numerators and multiply the denominators separately.
This means that, in our question, negative five-thirds divided by seven is the same as negative five-thirds multiplied by one-seventh. Multiplying a negative number by a positive number gives us a negative answer. This means that our fraction will be negative. Five multiplied by one is equal to five, and three multiplied by seven is 21. Negative five-thirds multiplied by one-seventh is equal to negative five over 21.
There is a quicker way of dividing a fraction by a whole number. We just multiply the denominator of the fraction by the whole number. In this case, three multiplied by seven is 21. This becomes the denominator of the fraction, and the numerator stays the same. Negative five-thirds divided by seven is equal to negative five over 21.