Solve (2/3+7/10)div1/4-1.3

$$( \frac{ 2 }{ 3 } + \frac{ 7 }{ 10 } ) \div \frac{ 1 }{ 4 } -1.3$$

Evaluate

$$\frac{25}{6}\approx 4.166666667$$

Solution Steps

Least common multiple of 3 and 10 is 30. Convert \frac{2}{3} and \frac{7}{10} to fractions with denominator 30.

$$\frac{\frac{20}{30}+\frac{21}{30}}{\frac{1}{4}}-1.3$$

Since \frac{20}{30} and \frac{21}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20+21}{30}}{\frac{1}{4}}-1.3$$

Add 20 and 21 to get 41.

$$\frac{\frac{41}{30}}{\frac{1}{4}}-1.3$$

Divide \frac{41}{30} by \frac{1}{4} by multiplying \frac{41}{30} by the reciprocal of \frac{1}{4}.

$$\frac{41}{30}\times 4-1.3$$

Express \frac{41}{30}\times 4 as a single fraction.

$$\frac{41\times 4}{30}-1.3$$

Multiply 41 and 4 to get 164.

$$\frac{164}{30}-1.3$$

Reduce the fraction \frac{164}{30} to lowest terms by extracting and canceling out 2.

$$\frac{82}{15}-1.3$$

Convert decimal number 1.3 to fraction \frac{13}{10}.

$$\frac{82}{15}-\frac{13}{10}$$

Least common multiple of 15 and 10 is 30. Convert \frac{82}{15} and \frac{13}{10} to fractions with denominator 30.

$$\frac{164}{30}-\frac{39}{30}$$

Since \frac{164}{30} and \frac{39}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{164-39}{30}$$

Subtract 39 from 164 to get 125.

$$\frac{125}{30}$$

Reduce the fraction \frac{125}{30} to lowest terms by extracting and canceling out 5.

$$\frac{25}{6}$$

Factor

$$\frac{5 ^ {2}}{2 \cdot 3} = 4\frac{1}{6} = 4.166666666666667$$