Solve (8.4-35/6)+(51/3-2.4)

$$(8.4-3 \frac{ 5 }{ 6 } )+(5 \frac{ 1 }{ 3 } -2.4)$$

Evaluate

$$7.5$$

Solution Steps

Multiply 3 and 6 to get 18.

$$8.4-\frac{18+5}{6}+\frac{5\times 3+1}{3}-2.4$$

Add 18 and 5 to get 23.

$$8.4-\frac{23}{6}+\frac{5\times 3+1}{3}-2.4$$

Convert decimal number 8.4 to fraction \frac{84}{10}. Reduce the fraction \frac{84}{10} to lowest terms by extracting and canceling out 2.

$$\frac{42}{5}-\frac{23}{6}+\frac{5\times 3+1}{3}-2.4$$

Least common multiple of 5 and 6 is 30. Convert \frac{42}{5} and \frac{23}{6} to fractions with denominator 30.

$$\frac{252}{30}-\frac{115}{30}+\frac{5\times 3+1}{3}-2.4$$

Since \frac{252}{30} and \frac{115}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{252-115}{30}+\frac{5\times 3+1}{3}-2.4$$

Subtract 115 from 252 to get 137.

$$\frac{137}{30}+\frac{5\times 3+1}{3}-2.4$$

Multiply 5 and 3 to get 15.

$$\frac{137}{30}+\frac{15+1}{3}-2.4$$

Add 15 and 1 to get 16.

$$\frac{137}{30}+\frac{16}{3}-2.4$$

Least common multiple of 30 and 3 is 30. Convert \frac{137}{30} and \frac{16}{3} to fractions with denominator 30.

$$\frac{137}{30}+\frac{160}{30}-2.4$$

Since \frac{137}{30} and \frac{160}{30} have the same denominator, add them by adding their numerators.

$$\frac{137+160}{30}-2.4$$

Add 137 and 160 to get 297.

$$\frac{297}{30}-2.4$$

Reduce the fraction \frac{297}{30} to lowest terms by extracting and canceling out 3.

$$\frac{99}{10}-2.4$$

Convert decimal number 2.4 to fraction \frac{24}{10}. Reduce the fraction \frac{24}{10} to lowest terms by extracting and canceling out 2.

$$\frac{99}{10}-\frac{12}{5}$$

Least common multiple of 10 and 5 is 10. Convert \frac{99}{10} and \frac{12}{5} to fractions with denominator 10.

$$\frac{99}{10}-\frac{24}{10}$$

Since \frac{99}{10} and \frac{24}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{99-24}{10}$$

Subtract 24 from 99 to get 75.

$$\frac{75}{10}$$

Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{15}{2}$$

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$