Solve -1010/4+143/4+3*371/4varphi-9*286/4

$$- \frac { 1010 } { 4 } + \frac { 143 } { 4 } + \frac { 3 \times 371 } { 4 } \varphi - \frac { 9 \times 286 } { 4 }$$

Evaluate

$$\frac{1113\phi -3441}{4}$$

Solution Steps

Since -\frac{1010}{4} and \frac{143}{4} have the same denominator, add them by adding their numerators.

$$\frac{-1010+143}{4}+\frac{3\times 371}{4}\phi -\frac{9\times 286}{4}$$

Add -1010 and 143 to get -867.

$$-\frac{867}{4}+\frac{3\times 371}{4}\phi -\frac{9\times 286}{4}$$

Multiply 3 and 371 to get 1113.

$$-\frac{867}{4}+\frac{1113}{4}\phi -\frac{9\times 286}{4}$$

Multiply 9 and 286 to get 2574.

$$-\frac{867}{4}+\frac{1113}{4}\phi -\frac{2574}{4}$$

Since -\frac{867}{4} and \frac{2574}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-867-2574}{4}+\frac{1113}{4}\phi$$

Subtract 2574 from -867 to get -3441.

$$-\frac{3441}{4}+\frac{1113}{4}\phi$$

Factor

$$\frac{3\left(371\phi -1147\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{-3441+1113\phi }{4}$$

Consider -1010+143+1113\phi -2574. Multiply and combine like terms.

$$1113\phi -3441$$

Consider 1113\phi -3441. Factor out 3.

$$3\left(371\phi -1147\right)$$

Rewrite the complete factored expression.

$$\frac{3\left(371\phi -1147\right)}{4}$$