Adding Three or More Fractions - Step-by-step

Step 1: All three fractions have denominators equal to 5, so we have like fractions.

Step 2: Combining the fractions into a single denominator, we have:

$$\frac{3}{5}+\frac{2}{5}+\frac{1}{5}$$

$$=\frac{3+2+1}{5}$$

Step 3: Adding the numerators, we have:

$$=\frac{3+2+1}{5}$$

$$=\frac{6}{5}$$

Step 4: Writing in mixed numbers, we have:

$$=1\frac{1}{5}$$

Step 1: The fractions have denominators 5, 10, and 5. These fractions do not appear to be like fractions at first glance. However, we can simplify the second fraction as follows:

$$\frac{1}{5}+\frac{6}{10}+\frac{4}{5}$$

$$=\frac{1}{5}+\frac{3}{5}+\frac{4}{5}$$

Step 2: Now, we can write as follows:

$$\frac{1}{5}+\frac{3}{5}+\frac{4}{5}$$

$$=\frac{1+3+4}{5}$$

Step 3: Adding the numerators, we have:

$$=\frac{1+3+4}{5}$$

$$=\frac{8}{5}$$

Step 4: We can write the fraction as a mixed number:

$$=1\frac{3}{5}$$

In this case, we have unlike denominators, so we solve as follows:

Step 1: The least common denominator of 3, 4, and 2 is 12.

Step 2: Dividing 12 by 3 (first denominator), we get 4. Dividing 12 by 4 (second denominator), we get 3. Dividing 12 by 2 (third denominator), we get 6.

Step 3: By multiplying the numerators and denominators of each fraction by the numbers obtained in step 2, we have:

$$\frac{2\times 4}{3 \times 4}+\frac{1 \times 3}{4 \times 3}+\frac{1 \times 6}{2 \times 6}$$

$$=\frac{8}{12}+\frac{3}{12}+\frac{6}{12}$$

Step 4: We solve the addition of like fractions from step 3:

$$\frac{8}{12}+\frac{3}{12}+\frac{6}{12}$$

$$=\frac{8+3+6}{12}$$

$$=\frac{17}{12}$$

Step 5: We can write as a mixed number:

$$=1\frac{5}{12}$$

Step 1: We have the denominators 5, 4, and 2. The least common denominator is 20.

Step 2: Dividing 20 by 5 (first denominator), we get 4. Dividing 20 by 4 (second denominator), we get 5. Dividing 20 by 2 (third denominator), we get 10.

Step 3: If we multiply both the numerator and the denominator of each fraction by the numbers obtained in step 2, we have:

$$\frac{2\times 4}{5 \times 4}+\frac{3 \times 5}{4 \times 5}+\frac{1 \times 10}{2 \times 10}$$

$$=\frac{8}{20}+\frac{15}{20}+\frac{10}{20}$$

Step 4: Now, we solve the addition of like fractions from step 3, and we have:

$$\frac{8}{20}+\frac{15}{20}+\frac{10}{20}$$

$$=\frac{8+15+10}{20}$$

$$=\frac{33}{20}$$

Step 5: Writing as a mixed number, we have:

$$=1\frac{13}{20}$$

Step 1: The first two fractions have a denominator equal to 3 and the last two fractions have a denominator equal to 7. Therefore, the least common denominator is 21.

Step 2: Dividing 21 by 3 (first and second denominators), we get 7. Dividing 21 by 7 (third and fourth denominators), we get 3.

Step 3: By multiplying both the numerators and the denominators of each fraction by the numbers obtained in step 2, we have:

$$\frac{2\times 7}{3 \times 7}+\frac{1 \times 7}{3 \times 7}+\frac{2 \times 3}{7 \times 3}+\frac{3 \times 3}{7 \times 3}$$

$$=\frac{14}{21}+\frac{7}{21}+\frac{6}{21}+\frac{9}{21}$$

Step 4: Solving the addition from step 3, we have:

$$\frac{14}{21}+\frac{7}{21}+\frac{6}{21}+\frac{9}{21}$$

$$=\frac{14+7+6+9}{21}$$

$$=\frac{36}{21}$$

Step 5: Simplifying and writing as a mixed number, we have:

$$=\frac{12}{7}$$

$$=1\frac{5}{7}$$

Step 1: We have the denominators 4, 3, 5 and 2. Their least common denominator is 60.

Step 2: Dividing 60 by 4 (first denominator), we get 15. Dividing 60 by 3 (second denominator), we get 20. Dividing 60 by 5 (third denominator), we get 12. Dividing 60 by 2, we get 30.

Step 3: We multiply the numerators and denominators of each fraction by the numbers obtained in step 2:

$$\frac{3\times 15}{4 \times 15}+\frac{2 \times 20}{3 \times 20}+\frac{4 \times 12}{5 \times 12}+\frac{1 \times 30}{2 \times 30}$$

$$=\frac{45}{60}+\frac{40}{60}+\frac{48}{60}+\frac{30}{60}$$

Step 4: Solving the addition of like fractions from step 3, we have:

$$\frac{45}{60}+\frac{40}{60}+\frac{48}{60}+\frac{30}{60}$$

$$=\frac{45+40+48+30}{60}$$

$$=\frac{163}{60}$$

Step 5: Writing as a mixed number, we have:

$$=2\frac{43}{60}$$