Divide. A) (-3/5)(-15/11)

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mariloucortez's profile pic

mariloucortez | High School Teacher | (Level 3) Adjunct Educator

Posted on

To divide (-3/5) by (-15/11), there are two rules that apply. First, the rule in dividing signed numbers (same applies in multiplication): if the dividend (first number) and divisor (second number) have the same sign, the quotient is positive, otherwise, the quotient is negative. Second, the rule in dividing fractions: take first the reciprocal or inverse of the divisor, then apply multiplication.

Now, let's apply those rule. Notice that both given are negative, so we are expecting a positive answer.

Then, get the reciprocal of the divisor, `(-15)/(11)`

which results to `(-11)/(15)`

then apply multiplication: `(-3)/(5) * (-11)/(15) .`

In multiplying fractions, just multiply numerators together and the denominators together. That would be:

`(-3*-11)/(5*15)`

so -3 * -11 = 33 (positive, since both factors are negative) and

     5 * 15 = 75.

The fraction is   `(33)/(75).`

You can simplify that answer into smaller fraction by dividing top ang bottom by the the GCF of 33 and 75, that is 3. You can get 3 by listing the prime factors of each.

33 = 3 *11   (both 3 and 11 are prime numbers)

75 = 3  * 5 * 5 (5 is also a prime number)

Get the factor/factors that is/are common to both. In this case, 3 is only the number that is common to both. In case that there are multiple common numbers, you just multiply those numbers to get GCF. So GCF is 3 in here. 

`(33/3)/(75/3) =(11/25)`

Therefore, your answer should be 11/25. Remember always reduce your answer to lowest term. :)

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

(-3/5) / (-15/11) 

Dividing by a fraction is the same multiplying by its reciprocal. The reciprocal of -15/11 is -11/15

So the problem can be rewritten as 

-3/5  x -11/15

When multiplying fractions, do the numerators and denominators separately: 

33/75 is the simplified answer. 

To simplify, divide by a common multiple like 3: 

11/25

zumba96's profile pic

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on

Divide. A) (-3/5)/(-15/11) 

You would simply multiple across after you flip the second part of the equation

`(-3/5)` `(11/-15)` = 33/75

Since there are two negatives in the problem they both get cancelled out

Since 33 and 75 are both divisible by 3 you can divide 33/75 divided by 3 and get 11/25

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`(-3/5)(-15/11)`

Flip the divider

`(-3/5)(-11/15)`

Multiply straight across

`-3/5xx-11/15 = 33/75`

33/75 is the answer but you can simplify it because both 33 and 75 have a common fact of 3

`33/75 -: 3 = 11/25`

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