Question

evaluate 8 7/8+(7 5/6-2 1/3)

Answer 1

Answer:

$14 \frac{3}{8}$

Step-by-step explanation:

I assume you mean this:

$8 \frac{7}{8} +(7 \frac{5}{6} -2\frac{1}{3} )$

Lets begin with the parentheses. When operating with fractions, we need them to have the same denominator. Looking at the expression in the parenthesis, we can see that the denominator of 5/6, that being 6, is twice that of 1/3, that being 3. Thus, if we multiply the numerator and denominator of 1/3 by 2, the result will be a fraction of same value, but with denominator 6, which we can work with.

$\frac{1*2}{3*2}$

$\frac{2}{6}$

Now we can replace this in the original parenthesis

$(7 \frac{5}{6} -2\frac{2}{6})$

We can now evaluate the parenthesis. 7-2=5, which leaves us with 5 5/6 - 2/6. Since the two fractions have the same denominator, we can subtract the numerator of 2/6 from 5/6. This gives us with 3/6, which we add to the 5 from before.

$5\frac{3}{6}$

The numerator and denominator of 3/6 are both divisible by three, so we can simply the fraction.

$5\frac{1}{2}$

Now that we have solved the parenthesis, we can plug our solution back into the original expression.

$8 \frac{7}{8} +5\frac{1}{2}$

We now have a similar problem to the parenthesis, where our fractions have different denominators. However, you may notice that the denominator of 7/8 (8) is four times larger than the denominator of 1/2 (2). Thus, if we multiply the numerator and denominator of 1/2 by four, we will have a new fraction of equal value, but with denominator 8.

$\frac{1*4}{2*4}$

$\frac{4}{8}$

Now lets update our expression with this information.

$8 \frac{7}{8} +5 \frac{4}{8}$

8+5=13$13\frac{7}{8} +\frac{4}{8}$, so we can further simplify the expression.

Since the denominators of the fractions are the same, we can combine the numerators. 7+4=11

$13 \frac{11}{8}$

We can simplify the fraction by taking one whole out of it (8/8) and adding it as 1 instead. 11-8=3, thus the fraction that remains is 3/8.

$14 \frac{3}{8}$