How do you multiply #1 1/4 div 7#?

1 Answer
Jun 8, 2016

Answer:

#5/28#

Explanation:

Firs, rewrite #1 1/4# as an improper fraction. Do this by recognizing that

#1 1/4=1+1/4#

Now, to add these fractions, we need a common denominator. Note that:

#1+1/4=1/1+1/4#

The common denominator will be #4#, since it is the least common multiple of #1# and #4#.

#1/1+1/4=(1xx4)/(1xx4)+1/4=4/4+1/4#

We can do #4/4+1/4# since the fractions have the same denominator: add the numerators, #1# and #4#, and leave the denominators the same. Thus

#4/4+1/4=(4+1)/4=5/4#

So, instead of the original equation #1 1/4-:7#, we have the new equation

#5/4-:7#

The next step is to note that dividing by #7# is the same as multiplying by the reciprocal of #7#.

You may be confused, since #7# doesn't seem to be a fraction, so how can it have a reciprocal?

However, note that #7=7/1#. Thus, the reciprocal of #7# is the same as saying the reciprocal of #7/1#, which is #1/7#.

So, saying #5/4-:7# is equal to #5/4xx1/7#.

To multiply fractions, multiply the numerators straight across and the denominators straight across.

#5/4xx1/7=(5xx1)/(4xx7)=5/28#

#5/28# cannot be simplified since #5# and #28# share no common factors other than #1#.