Solve 4.4-|(-0.9)-(71/7)+(-36/7)|

$$4.4 - | ( - 0.9 ) - ( 7 \frac { 1 } { 7 } ) + ( - 3 \frac { 6 } { 7 } ) |$$

Evaluate

$$-7.5$$

Solution Steps

Multiply 7 and 7 to get 49.

$$4.4-|-0.9-\frac{49+1}{7}-\frac{3\times 7+6}{7}|$$

Add 49 and 1 to get 50.

$$4.4-|-0.9-\frac{50}{7}-\frac{3\times 7+6}{7}|$$

Convert decimal number -0.9 to fraction -\frac{9}{10}.

$$4.4-|-\frac{9}{10}-\frac{50}{7}-\frac{3\times 7+6}{7}|$$

Least common multiple of 10 and 7 is 70. Convert -\frac{9}{10} and \frac{50}{7} to fractions with denominator 70.

$$4.4-|-\frac{63}{70}-\frac{500}{70}-\frac{3\times 7+6}{7}|$$

Since -\frac{63}{70} and \frac{500}{70} have the same denominator, subtract them by subtracting their numerators.

$$4.4-|\frac{-63-500}{70}-\frac{3\times 7+6}{7}|$$

Subtract 500 from -63 to get -563.

$$4.4-|-\frac{563}{70}-\frac{3\times 7+6}{7}|$$

Multiply 3 and 7 to get 21.

$$4.4-|-\frac{563}{70}-\frac{21+6}{7}|$$

Add 21 and 6 to get 27.

$$4.4-|-\frac{563}{70}-\frac{27}{7}|$$

Least common multiple of 70 and 7 is 70. Convert -\frac{563}{70} and \frac{27}{7} to fractions with denominator 70.

$$4.4-|-\frac{563}{70}-\frac{270}{70}|$$

Since -\frac{563}{70} and \frac{270}{70} have the same denominator, subtract them by subtracting their numerators.

$$4.4-|\frac{-563-270}{70}|$$

Subtract 270 from -563 to get -833.

$$4.4-|\frac{-833}{70}|$$

Reduce the fraction \frac{-833}{70} to lowest terms by extracting and canceling out 7.

$$4.4-|-\frac{119}{10}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{119}{10} is \frac{119}{10}.

$$4.4-\frac{119}{10}$$

Convert decimal number 4.4 to fraction \frac{44}{10}. Reduce the fraction \frac{44}{10} to lowest terms by extracting and canceling out 2.

$$\frac{22}{5}-\frac{119}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{22}{5} and \frac{119}{10} to fractions with denominator 10.

$$\frac{44}{10}-\frac{119}{10}$$

Since \frac{44}{10} and \frac{119}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{44-119}{10}$$

Subtract 119 from 44 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

$$-7.5$$