Question

Find the quotient.1. 3/4 divided by 1 1/10.2. 5 1/2 divided by 6.3. 1 2/15 divided by 1/5.

Answer 1

In order to find those quotients, we can use the following rules for multiplying two fractions:

We keep the first fraction and multiply it by the inverse of the second fraction:

`(a)/(b)\colon(c)/(d)=(a)/(b)\cdot(d)/(c)`

Then, the numerator of the result will equal the product of the new numerators, and the denominator of the result will equal the product of the new denominators:

`(a)/(b)\cdot(d)/(c)=(ad)/(bc)`

Writing both rules together, we obtain:

`(a)/(b)\colon(c)/(d)=(ad)/(bc)`

Now, using the given fractions, we have:

1. We keep the first fraction (3/4) as it is, change the sign of division (:) by the sign of multiplication (.), and exchange the numerator and the denominator of the second fraction (11/10), so it becomes 10/11:

`(3)/(4)\colon(11)/(10)=(3)/(4)\cdot(10)/(11)=(3\cdot10)/(4\cdot11)=(30)/(44)`

Notice we can simplify this result by dividing both the numerator and the denominator by the factor 2:

`(30)/(44)=(15)/(22)`

2. Now, we can use the same steps. First, though, let's rewrite the mixed number 5 1/2 as a fraction:

`5(1)/(2)=5+(1)/(2)=(2\cdot5+1)/(2)=(10+1)/(2)=(11)/(2)`

Now, we can proceed with the division:

`(11)/(2)\colon6=(11)/(2)\cdot(1)/(6)=(11\cdot1)/(2\cdot6)=(11)/(12)`

3. Again, we need to rewrite the mixed number 1 2/15 as a fraction:

`1(2)/(15)=(1\cdot15+2)/(15)=(15+2)/(15)=(17)/(15)`

Now, we need to divide this by 1/5:

`(17)/(15)\colon(1)/(5)=(17)/(15)\cdot(5)/(1)=(17\cdot5)/(15\cdot1)=(17\cdot5)/(15)`

Notice that both the factor 5 in the numerator and 15 in the denominator are multiples of the number 5. So, we can divide them both by 5 in order to simplify the fraction:

`(17\cdot5)/(15)=(17)/(3)`