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

Mar 11, 2018

Convert to fractions, multiply to get a common denominator, divide, giving you $\frac{6}{7}$ .

Explanation:

Start by writing the problem as fractions.

$\frac{2 \frac{1}{7}}{2 \frac{1}{2}} = \frac{\frac{2}{1} + \frac{1}{7}}{\frac{2}{1} + \frac{1}{2}}$

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 $\frac{1}{1}$ using factors from the other fraction, so that you don't change the equation from the original value. Since our denominator in $\frac{2}{1}$ 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.

$\frac{\left(\frac{2}{1} \cdot \frac{7}{7}\right) + \frac{1}{7}}{\frac{2}{1} + \frac{1}{2}} = \frac{\frac{14}{7} + \frac{1}{7}}{\frac{2}{1} + \frac{1}{2}}$

Then we'll do the denominator of the original, multiplying $\frac{2}{1}$ by $\frac{2}{2}$, which we got from the other fraction's denominator.

$\frac{\frac{14}{7} + \frac{1}{7}}{\left(\frac{2}{1} \cdot \frac{2}{2}\right) + \frac{1}{2}} = \frac{\frac{14}{7} + \frac{1}{7}}{\frac{4}{2} + \frac{1}{2}}$

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.

$\frac{\frac{14 + 1}{7}}{\frac{4 + 1}{2}} = \frac{\frac{15}{7}}{\frac{5}{2}}$

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.

$\left(\frac{15}{7}\right) \cdot \left(\frac{2}{5}\right)$

Multiply numerators by numerators and denominators by denominators.

$\left(\frac{15}{7}\right) \cdot \left(\frac{2}{5}\right) = \frac{30}{35}$

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 $\frac{6}{7}$ .

$\frac{30}{35} = \frac{5}{5} \cdot \frac{6}{7} = 1 \cdot \frac{6}{7} = \frac{6}{7}$

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.

$\frac{15}{7} \cdot \frac{2}{5} = \frac{3}{7} \cdot \frac{2}{1} = \frac{6}{7}$

Mar 11, 2018

$\frac{6}{7}$

Explanation:

First change the mixed numbers into improper fractions.

$2 \frac{1}{7} \div 2 \frac{1}{2}$

$= \frac{15}{7} \times \frac{5}{2}$

Multiply by the reciprocal:

$\frac{15}{7} \times \frac{2}{5}$

${\cancel{15}}^{3} / 7 \times \frac{2}{\cancel{5}}$

$= \frac{6}{7}$

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