What is 2 1/7 div 2 1/2?

2 Answers
Mar 11, 2018

Convert to fractions, multiply to get a common denominator, divide, giving you 6/7 .

Explanation:

Start by writing the problem as fractions.

(2 1/7) / (2 1/2) = (2/1+1/7)/(2/1 + 1/2)

Working with one set of numbers at a time, multiply to get a common denominator. The easiest and fastest route is usually to multiply one of your fractions by 1/1 using factors from the other fraction, so that you don't change the equation from the original value. Since our denominator in 2/1 is 1, we can multiply that denominator by the other fraction's denominator, to get our common denominator.

First the numerator of the original problem.

((2/1*7/7)+1/7)/(2/1 + 1/2)=(14/7+1/7)/(2/1 + 1/2)

Then we'll do the denominator of the original, multiplying 2/1 by 2/2, which we got from the other fraction's denominator.

(14/7+1/7)/((2/1*2/2) + 1/2)=(14/7+1/7)/(4/2 + 1/2)

Now that all the addition fractions are over a common denominator and are all equal slices of the same pie, we can add numerators together.

((14+1)/7)/((4+1)/2)=(15/7)/(5/2)

Dividing by a fraction is the same as multiplying by the inverse of that fraction. Flip the numerator and denominator of the original denominator and multiply that against the original numerator.

(15/7)*(2/5)

Multiply numerators by numerators and denominators by denominators.

(15/7)*(2/5) = 30/35

From there you could see both top and bottom are divisible by 5, so you can pull out 5 from the top and bottom, which is just one, and simplifying your problem to 6/7 .

30/35=5/5*6/7=1*6/7=6/7

Alternatively, you can cancel: 15 divided by 5 from the second fraction which leaves 3 in the numerator of the first, and then multiply numerators and denominators.

15/7*2/5=3/7*2/1=6/7

Mar 11, 2018

6/7

Explanation:

First change the mixed numbers into improper fractions.

2 1/7 div2 1/2

=15/7 xx 5/2

Multiply by the reciprocal:

15/7 xx2/5

cancel15^3/7 xx2/cancel5

=6/7

Note that by multiplying by 2/5, you are first finding how many 'halves' there are in 2 1/7 and then by dividing by 5, you are finding how many 'groups of '5 halves' there are .... which is what div 2 1/2 actually means,