negative one third divided by twenty-one

Question

we are studying subtracting integers with fractions but i am not getting it. Even with the negatives

 

Answer 1

For this problem, you are dividing a negative fraction by a whole number. The main thing is to think of both numbers as fractions so it might seem recognizable to you.

 

Using numbers, the equation is: -1/3÷21. -1/3 is the same as -1÷3 because a fraction is division and division is a fraction. When you input -1/3 and -1÷3 into a calculator, they will both be equal to -0.333333.... showing that they are indeed the same.

 

Getting back to the problem, you can represent the whole number as a fraction using the same principle. Think to yourself if a fraction is division and division is a fraction, then what division could I use for 21 so that it becomes a fraction? In other words, 21 divided by what would give 21? It would be one because anything divided by one would be itself (21÷1=21). So 21 written as a fraction becomes 21/1.

 

Now that both numbers are fractions and they are being divided, you must multiply the first number by the reciprocal ("flip") of the second number. This means the denominator and numerator switch places and in the problem it would be: -1/3 ÷ 21/1= -1/3 • 1/21. When multiplying by negative numbers, the negative is present if there is an odd number of fractions or integers etc. Here there is a negative times a positive so the answer is negative (only one out of the two numbers multiplied were negative).

 

Multiplying the numerators together and the denominators together, the answer is -1/63: -1/3 • 1/21 = (-1 •1) / (3•21)= -1/63.

 

I hope this helps! Feel free to contact me if you need would like more help.

Answer 2

Hi Emma!

 

So, if I'm understanding this problem correctly, you are being asked to find the answer to the problem

 

-1/3 divided by 21  ?

 

First, I would make everything a fraction, just for consistency

 

-1/3  /  21/1

 

and if I remember the rules for dividing fractions correctly, you just multiply by the reciprocal of the second fraction, or

 

-1/3 x 1/21 = -1/63

 

 

I hope I got this right! And I hope it helps! Best of luck to you with your fraction homework.

 

Debra