Solve 2/5(a/3+2b/5)-5/1(frac{3a}{4}+frac{2b}{3})-(a+5b-4c)=

$$\frac { 2 } { 5 } ( \frac { a } { 3 } + \frac { 2 b } { 5 } ) - \frac { 5 } { 1 } ( \frac { 3 a } { 4 } + \frac { 2 b } { 3 } ) - ( a + 5 b - 4 c ) =$$

Evaluate

$$-\frac{277a}{60}-\frac{613b}{75}+4c$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{a}{3} times \frac{5}{5}. Multiply \frac{2b}{5} times \frac{3}{3}.

$$\frac{2}{5}\left(\frac{5a}{15}+\frac{3\times 2b}{15}\right)-\frac{5}{1}\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

Since \frac{5a}{15} and \frac{3\times 2b}{15} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}\times \frac{5a+3\times 2b}{15}-\frac{5}{1}\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

Do the multiplications in 5a+3\times 2b.

$$\frac{2}{5}\times \frac{5a+6b}{15}-\frac{5}{1}\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

Multiply \frac{2}{5} times \frac{5a+6b}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(5a+6b\right)}{5\times 15}-\frac{5}{1}\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

Anything divided by one gives itself.

$$\frac{2\left(5a+6b\right)}{5\times 15}-5\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{3a}{4} times \frac{3}{3}. Multiply \frac{2b}{3} times \frac{4}{4}.

$$\frac{2\left(5a+6b\right)}{5\times 15}-5\left(\frac{3\times 3a}{12}+\frac{4\times 2b}{12}\right)-\left(a+5b-4c\right)$$

Since \frac{3\times 3a}{12} and \frac{4\times 2b}{12} have the same denominator, add them by adding their numerators.

$$\frac{2\left(5a+6b\right)}{5\times 15}-5\times \frac{3\times 3a+4\times 2b}{12}-\left(a+5b-4c\right)$$

Do the multiplications in 3\times 3a+4\times 2b.

$$\frac{2\left(5a+6b\right)}{5\times 15}-5\times \frac{9a+8b}{12}-\left(a+5b-4c\right)$$

Express 5\times \frac{9a+8b}{12} as a single fraction.

$$\frac{2\left(5a+6b\right)}{5\times 15}-\frac{5\left(9a+8b\right)}{12}-\left(a+5b-4c\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\times 15 and 12 is 300. Multiply \frac{2\left(5a+6b\right)}{5\times 15} times \frac{4}{4}. Multiply \frac{5\left(9a+8b\right)}{12} times \frac{25}{25}.

$$\frac{4\times 2\left(5a+6b\right)}{300}-\frac{25\times 5\left(9a+8b\right)}{300}-\left(a+5b-4c\right)$$

Since \frac{4\times 2\left(5a+6b\right)}{300} and \frac{25\times 5\left(9a+8b\right)}{300} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 2\left(5a+6b\right)-25\times 5\left(9a+8b\right)}{300}-\left(a+5b-4c\right)$$

Do the multiplications in 4\times 2\left(5a+6b\right)-25\times 5\left(9a+8b\right).

$$\frac{40a+48b-1125a-1000b}{300}-\left(a+5b-4c\right)$$

Combine like terms in 40a+48b-1125a-1000b.

$$\frac{-1085a-952b}{300}-\left(a+5b-4c\right)$$

To find the opposite of a+5b-4c, find the opposite of each term.

$$\frac{-1085a-952b}{300}-a-5b-\left(-4c\right)$$

The opposite of -4c is 4c.

$$\frac{-1085a-952b}{300}-a-5b+4c$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -a-5b+4c times \frac{300}{300}.

$$\frac{-1085a-952b}{300}+\frac{300\left(-a-5b+4c\right)}{300}$$

Since \frac{-1085a-952b}{300} and \frac{300\left(-a-5b+4c\right)}{300} have the same denominator, add them by adding their numerators.

$$\frac{-1085a-952b+300\left(-a-5b+4c\right)}{300}$$

Do the multiplications in -1085a-952b+300\left(-a-5b+4c\right).

$$\frac{-1085a-952b-300a-1500b+1200c}{300}$$

Combine like terms in -1085a-952b-300a-1500b+1200c.

$$\frac{-1385a-2452b+1200c}{300}$$

Expand

$$-\frac{277a}{60}-\frac{613b}{75}+4c$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{a}{3} times \frac{5}{5}. Multiply \frac{2b}{5} times \frac{3}{3}.

$$\frac{2}{5}\left(\frac{5a}{15}+\frac{3\times 2b}{15}\right)-\frac{5}{1}\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

Since \frac{5a}{15} and \frac{3\times 2b}{15} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}\times \frac{5a+3\times 2b}{15}-\frac{5}{1}\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

Do the multiplications in 5a+3\times 2b.

$$\frac{2}{5}\times \frac{5a+6b}{15}-\frac{5}{1}\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

Multiply \frac{2}{5} times \frac{5a+6b}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(5a+6b\right)}{5\times 15}-\frac{5}{1}\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

Anything divided by one gives itself.

$$\frac{2\left(5a+6b\right)}{5\times 15}-5\left(\frac{3a}{4}+\frac{2b}{3}\right)-\left(a+5b-4c\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{3a}{4} times \frac{3}{3}. Multiply \frac{2b}{3} times \frac{4}{4}.

$$\frac{2\left(5a+6b\right)}{5\times 15}-5\left(\frac{3\times 3a}{12}+\frac{4\times 2b}{12}\right)-\left(a+5b-4c\right)$$

Since \frac{3\times 3a}{12} and \frac{4\times 2b}{12} have the same denominator, add them by adding their numerators.

$$\frac{2\left(5a+6b\right)}{5\times 15}-5\times \frac{3\times 3a+4\times 2b}{12}-\left(a+5b-4c\right)$$

Do the multiplications in 3\times 3a+4\times 2b.

$$\frac{2\left(5a+6b\right)}{5\times 15}-5\times \frac{9a+8b}{12}-\left(a+5b-4c\right)$$

Express 5\times \frac{9a+8b}{12} as a single fraction.

$$\frac{2\left(5a+6b\right)}{5\times 15}-\frac{5\left(9a+8b\right)}{12}-\left(a+5b-4c\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\times 15 and 12 is 300. Multiply \frac{2\left(5a+6b\right)}{5\times 15} times \frac{4}{4}. Multiply \frac{5\left(9a+8b\right)}{12} times \frac{25}{25}.

$$\frac{4\times 2\left(5a+6b\right)}{300}-\frac{25\times 5\left(9a+8b\right)}{300}-\left(a+5b-4c\right)$$

Since \frac{4\times 2\left(5a+6b\right)}{300} and \frac{25\times 5\left(9a+8b\right)}{300} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 2\left(5a+6b\right)-25\times 5\left(9a+8b\right)}{300}-\left(a+5b-4c\right)$$

Do the multiplications in 4\times 2\left(5a+6b\right)-25\times 5\left(9a+8b\right).

$$\frac{40a+48b-1125a-1000b}{300}-\left(a+5b-4c\right)$$

Combine like terms in 40a+48b-1125a-1000b.

$$\frac{-1085a-952b}{300}-\left(a+5b-4c\right)$$

To find the opposite of a+5b-4c, find the opposite of each term.

$$\frac{-1085a-952b}{300}-a-5b-\left(-4c\right)$$

The opposite of -4c is 4c.

$$\frac{-1085a-952b}{300}-a-5b+4c$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -a-5b+4c times \frac{300}{300}.

$$\frac{-1085a-952b}{300}+\frac{300\left(-a-5b+4c\right)}{300}$$

Since \frac{-1085a-952b}{300} and \frac{300\left(-a-5b+4c\right)}{300} have the same denominator, add them by adding their numerators.

$$\frac{-1085a-952b+300\left(-a-5b+4c\right)}{300}$$

Do the multiplications in -1085a-952b+300\left(-a-5b+4c\right).

$$\frac{-1085a-952b-300a-1500b+1200c}{300}$$

Combine like terms in -1085a-952b-300a-1500b+1200c.

$$\frac{-1385a-2452b+1200c}{300}$$