Solve -1/13(30)+4/12(20)+6/1(10)

$$\frac { - 1 } { 13 } ( 30 ) + \frac { 4 } { 12 } ( 20 ) + \frac { 6 } { 1 } ( 10 )$$

Evaluate

$$\frac{2510}{39}\approx 64.358974359$$

Solution Steps

Fraction \frac{-1}{13} can be rewritten as -\frac{1}{13} by extracting the negative sign.

$$-\frac{1}{13}\times 30+\frac{4}{12}\times 20+\frac{6}{1}\times 10$$

Express -\frac{1}{13}\times 30 as a single fraction.

$$\frac{-30}{13}+\frac{4}{12}\times 20+\frac{6}{1}\times 10$$

Fraction \frac{-30}{13} can be rewritten as -\frac{30}{13} by extracting the negative sign.

$$-\frac{30}{13}+\frac{4}{12}\times 20+\frac{6}{1}\times 10$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{30}{13}+\frac{1}{3}\times 20+\frac{6}{1}\times 10$$

Multiply \frac{1}{3} and 20 to get \frac{20}{3}.

$$-\frac{30}{13}+\frac{20}{3}+\frac{6}{1}\times 10$$

Least common multiple of 13 and 3 is 39. Convert -\frac{30}{13} and \frac{20}{3} to fractions with denominator 39.

$$-\frac{90}{39}+\frac{260}{39}+\frac{6}{1}\times 10$$

Since -\frac{90}{39} and \frac{260}{39} have the same denominator, add them by adding their numerators.

$$\frac{-90+260}{39}+\frac{6}{1}\times 10$$

Add -90 and 260 to get 170.

$$\frac{170}{39}+\frac{6}{1}\times 10$$

Anything divided by one gives itself.

$$\frac{170}{39}+6\times 10$$

Multiply 6 and 10 to get 60.

$$\frac{170}{39}+60$$

Convert 60 to fraction \frac{2340}{39}.

$$\frac{170}{39}+\frac{2340}{39}$$

Since \frac{170}{39} and \frac{2340}{39} have the same denominator, add them by adding their numerators.

$$\frac{170+2340}{39}$$

Add 170 and 2340 to get 2510.

$$\frac{2510}{39}$$

Factor

$$\frac{2 \cdot 5 \cdot 251}{3 \cdot 13} = 64\frac{14}{39} = 64.35897435897436$$