Solve 4.2div4+0.2(42/3-41/6)=

$$4.2 \div 4+0.2( 4 \frac { 2 } { 3 } - 4 \frac { 1 } { 6 } )=$$

Evaluate

$$1.15$$

Solution Steps

Expand \frac{4.2}{4} by multiplying both numerator and the denominator by 10.

$$\frac{42}{40}+0.2\left(\frac{4\times 3+2}{3}-\frac{4\times 6+1}{6}\right)$$

Reduce the fraction \frac{42}{40} to lowest terms by extracting and canceling out 2.

$$\frac{21}{20}+0.2\left(\frac{4\times 3+2}{3}-\frac{4\times 6+1}{6}\right)$$

Multiply 4 and 3 to get 12.

$$\frac{21}{20}+0.2\left(\frac{12+2}{3}-\frac{4\times 6+1}{6}\right)$$

Add 12 and 2 to get 14.

$$\frac{21}{20}+0.2\left(\frac{14}{3}-\frac{4\times 6+1}{6}\right)$$

Multiply 4 and 6 to get 24.

$$\frac{21}{20}+0.2\left(\frac{14}{3}-\frac{24+1}{6}\right)$$

Add 24 and 1 to get 25.

$$\frac{21}{20}+0.2\left(\frac{14}{3}-\frac{25}{6}\right)$$

Least common multiple of 3 and 6 is 6. Convert \frac{14}{3} and \frac{25}{6} to fractions with denominator 6.

$$\frac{21}{20}+0.2\left(\frac{28}{6}-\frac{25}{6}\right)$$

Since \frac{28}{6} and \frac{25}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21}{20}+0.2\times \frac{28-25}{6}$$

Subtract 25 from 28 to get 3.

$$\frac{21}{20}+0.2\times \frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{21}{20}+0.2\times \frac{1}{2}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{21}{20}+\frac{1}{5}\times \frac{1}{2}$$

Multiply \frac{1}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21}{20}+\frac{1\times 1}{5\times 2}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 2}.

$$\frac{21}{20}+\frac{1}{10}$$

Least common multiple of 20 and 10 is 20. Convert \frac{21}{20} and \frac{1}{10} to fractions with denominator 20.

$$\frac{21}{20}+\frac{2}{20}$$

Since \frac{21}{20} and \frac{2}{20} have the same denominator, add them by adding their numerators.

$$\frac{21+2}{20}$$

Add 21 and 2 to get 23.

$$\frac{23}{20}$$

Factor

$$\frac{23}{5 \cdot 2 ^ {2}} = 1\frac{3}{20} = 1.15$$