Solve 313/15-29/14+52/15-15/14

$$3 \frac { 13 } { 15 } - 2 \frac { 9 } { 14 } + 5 \frac { 2 } { 15 } - 1 \frac { 5 } { 14 }$$

Evaluate

$$5$$

Solution Steps

Multiply 3 and 15 to get 45.

$$\frac{45+13}{15}-\frac{2\times 14+9}{14}+\frac{5\times 15+2}{15}-\frac{1\times 14+5}{14}$$

Add 45 and 13 to get 58.

$$\frac{58}{15}-\frac{2\times 14+9}{14}+\frac{5\times 15+2}{15}-\frac{1\times 14+5}{14}$$

Multiply 2 and 14 to get 28.

$$\frac{58}{15}-\frac{28+9}{14}+\frac{5\times 15+2}{15}-\frac{1\times 14+5}{14}$$

Add 28 and 9 to get 37.

$$\frac{58}{15}-\frac{37}{14}+\frac{5\times 15+2}{15}-\frac{1\times 14+5}{14}$$

Least common multiple of 15 and 14 is 210. Convert \frac{58}{15} and \frac{37}{14} to fractions with denominator 210.

$$\frac{812}{210}-\frac{555}{210}+\frac{5\times 15+2}{15}-\frac{1\times 14+5}{14}$$

Since \frac{812}{210} and \frac{555}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{812-555}{210}+\frac{5\times 15+2}{15}-\frac{1\times 14+5}{14}$$

Subtract 555 from 812 to get 257.

$$\frac{257}{210}+\frac{5\times 15+2}{15}-\frac{1\times 14+5}{14}$$

Multiply 5 and 15 to get 75.

$$\frac{257}{210}+\frac{75+2}{15}-\frac{1\times 14+5}{14}$$

Add 75 and 2 to get 77.

$$\frac{257}{210}+\frac{77}{15}-\frac{1\times 14+5}{14}$$

Least common multiple of 210 and 15 is 210. Convert \frac{257}{210} and \frac{77}{15} to fractions with denominator 210.

$$\frac{257}{210}+\frac{1078}{210}-\frac{1\times 14+5}{14}$$

Since \frac{257}{210} and \frac{1078}{210} have the same denominator, add them by adding their numerators.

$$\frac{257+1078}{210}-\frac{1\times 14+5}{14}$$

Add 257 and 1078 to get 1335.

$$\frac{1335}{210}-\frac{1\times 14+5}{14}$$

Reduce the fraction \frac{1335}{210} to lowest terms by extracting and canceling out 15.

$$\frac{89}{14}-\frac{1\times 14+5}{14}$$

Multiply 1 and 14 to get 14.

$$\frac{89}{14}-\frac{14+5}{14}$$

Add 14 and 5 to get 19.

$$\frac{89}{14}-\frac{19}{14}$$

Since \frac{89}{14} and \frac{19}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{89-19}{14}$$

Subtract 19 from 89 to get 70.

$$\frac{70}{14}$$

Divide 70 by 14 to get 5.

$$5$$

Factor

$$5$$