Solve 1/4=12/20+5/20=17/20+frac{1}{2}

$$\frac { 1 } { 4 } = \frac { 12 } { 20 } + \frac { 5 } { 20 } = \frac { 17 } { 20 } + \frac { 1 } { 2 }$$

Verify

Solution Steps

Reduce the fraction \frac{12}{20} to lowest terms by extracting and canceling out 4.

$$\frac{1}{4}=\frac{3}{5}+\frac{5}{20}\text{ and }\frac{12}{20}+\frac{5}{20}=\frac{17}{20}+\frac{1}{2}$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$\frac{1}{4}=\frac{3}{5}+\frac{1}{4}\text{ and }\frac{12}{20}+\frac{5}{20}=\frac{17}{20}+\frac{1}{2}$$

Least common multiple of 5 and 4 is 20. Convert \frac{3}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{1}{4}=\frac{12}{20}+\frac{5}{20}\text{ and }\frac{12}{20}+\frac{5}{20}=\frac{17}{20}+\frac{1}{2}$$

Since \frac{12}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}=\frac{12+5}{20}\text{ and }\frac{12}{20}+\frac{5}{20}=\frac{17}{20}+\frac{1}{2}$$

Add 12 and 5 to get 17.

$$\frac{1}{4}=\frac{17}{20}\text{ and }\frac{12}{20}+\frac{5}{20}=\frac{17}{20}+\frac{1}{2}$$

Least common multiple of 4 and 20 is 20. Convert \frac{1}{4} and \frac{17}{20} to fractions with denominator 20.

$$\frac{5}{20}=\frac{17}{20}\text{ and }\frac{12}{20}+\frac{5}{20}=\frac{17}{20}+\frac{1}{2}$$

Compare \frac{5}{20} and \frac{17}{20}.

$$\text{false}\text{ and }\frac{12}{20}+\frac{5}{20}=\frac{17}{20}+\frac{1}{2}$$

Since \frac{12}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\text{false}\text{ and }\frac{12+5}{20}=\frac{17}{20}+\frac{1}{2}$$

Add 12 and 5 to get 17.

$$\text{false}\text{ and }\frac{17}{20}=\frac{17}{20}+\frac{1}{2}$$

Least common multiple of 20 and 2 is 20. Convert \frac{17}{20} and \frac{1}{2} to fractions with denominator 20.

$$\text{false}\text{ and }\frac{17}{20}=\frac{17}{20}+\frac{10}{20}$$

Since \frac{17}{20} and \frac{10}{20} have the same denominator, add them by adding their numerators.

$$\text{false}\text{ and }\frac{17}{20}=\frac{17+10}{20}$$

Add 17 and 10 to get 27.

$$\text{false}\text{ and }\frac{17}{20}=\frac{27}{20}$$

Compare \frac{17}{20} and \frac{27}{20}.

$$\text{false}\text{ and }\text{false}$$

The conjunction of \text{false} and \text{false} is \text{false}.

$$\text{false}$$