Question

simplify:3/4 + 1/2 -2 1/2 - 2/3 × 7/8 -1 1/4​

Answer 1

The value of the expression is -37/12

Step-by-step explanation:

Given:

3/4 + 1/2 -2 1/2 - 2/3 × 7/8 -1 1/4​

To find:

simplify the expression given

Solution:

The expression will be solved using the BODMAS rule

So we solve the multiplication in the expression

$\frac{3}{4} +\frac{1}{2} -2\frac{1}{2} -\frac{2}{3} \ .\ \frac{7}{8} -1\frac{1}{4}$

Solving the part -2/3 X 7/8 we get

= $\frac{3}{4} +\frac{1}{2} -2\frac{1}{2} -\frac{14}{24} -1\frac{1}{4}$

Solving all the mixed fractions if any

= $\frac{3}{4} +\frac{1}{2} -\frac{4+1}{2} -\frac{14}{24} -\frac{4+1}{4}$

= $\frac{3}{4} +\frac{1}{2} -\frac{5}{2} -\frac{14}{24} -\frac{5}{4}$

Adding the fractions one by one

Since the denominators are not equal we use the cross multiplication method

= $\frac{3(2)+4(1)}{4(2)} -\frac{5}{2} -\frac{14}{24} -\frac{5}{4}$

= $\frac{6+4}{8} -\frac{5}{2} -\frac{14}{24} -\frac{5}{4}$

= $\frac{10}{8} -\frac{5}{2} -\frac{14}{24} -\frac{5}{4}$

Solving through the expression

= $\frac{10(2)-5(8)}{8(2)} -\frac{14}{24} -\frac{5}{4}$

= $\frac{20-40}{16} -\frac{14}{24} -\frac{5}{4}$

= $\frac{-20}{16} -\frac{14}{24} -\frac{5}{4}$

= $\frac{-20(24)-14 (16)}{16(24)} -\frac{5}{4}$

= $\frac{(-480)-224}{384} -\frac{5}{4}$

= $\frac{-704}{384} -\frac{5}{4}$

Finally, simplify the last two terms as

= $\frac{-704(4)-5(384)}{384(4)}$

= $\frac{(-2816)-1920}{1536}$

= $\frac{-4736}{1536}$

Simplifying further

= $-\frac{37}{12}$

∴ $\frac{3}{4} +\frac{1}{2} -2\frac{1}{2} -\frac{2}{3} \ .\ \frac{7}{8} -1\frac{1}{4}= -\frac{37}{12}$

Therefore the value of the expression 3/4 + 1/2 -2 1/2 - 2/3 × 7/8 -1 1/4​ is -37/12

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