Subtracting Three or More Fractions - Step-by-step

Step 1: The denominators of the three fractions are equal to 5, so the fractions are like.

Step 2: Using a single denominator to combine the fractions, we have:

$$\frac{4}{5}-\frac{2}{5}-\frac{1}{5}$$

$$=\frac{4-2-1}{5}$$

Step 3: Solving the subtraction in the numerators, we have:

$$=\frac{4-2-1}{5}$$

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

Step 4: The fraction is now simplified.

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

$$\frac{9}{5}-\frac{6}{10}-\frac{4}{5}$$

$$=\frac{9}{5}-\frac{3}{5}-\frac{4}{5}$$

Step 2: Combining the denominators into one, we have:

$$\frac{9}{5}-\frac{3}{5}-\frac{4}{5}$$

$$=\frac{9-3-4}{5}$$

Step 3: Solving the subtraction of numerators, we have:

$$=\frac{9-3-4}{5}$$

$$=\frac{2}{5}$$

Step 4: The fraction is now simplified.

We have a subtraction of unlike fractions, so we solve like this:

Step 1: The denominators are 3, 4, and 2. The least common denominator 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: We multiply the numerators and denominators of each fraction by the numbers obtained in step 2; 4 for the first fraction, 3 for the second, and 6 for the third:

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

$$=\frac{16}{12}-\frac{3}{12}-\frac{6}{12}$$

Step 4: Solving the subtraction of like fractions, we have:

$$\frac{16}{12}-\frac{3}{12}-\frac{6}{12}$$

$$=\frac{16-3-6}{12}$$

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

Step 5: The fraction is now simplified.

Step 1: We have the denominators 5, 4, and 2. Therefore, 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: We multiply both the numerator and the denominator of each fraction by the numbers obtained in step 2; 4 for the first fraction, 5 for the second, and 10 for the third:

$$\frac{7\times 4}{5 \times 4}-\frac{3 \times 5}{4 \times 5}-\frac{1 \times 10}{2 \times 10}$$

$$=\frac{28}{20}-\frac{15}{20}-\frac{10}{20}$$

Step 4: Solving the subtraction, we have:

$$\frac{28}{20}-\frac{15}{20}-\frac{10}{20}$$

$$=\frac{28-15-10}{20}$$

$$=\frac{3}{20}$$

Step 5: The fraction is now simplified.

Step 1: The first two denominators equal 3 and the last two denominators equal 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: We multiply both the numerators and the denominators of each fraction by the numbers obtained in step 2:

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

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

Step 4: Solving the addition and subtraction of like fractions, we have:

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

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

$$=\frac{4}{21}$$

Step 5: The fraction is now simplified.

Step 1: The least common denominator of 4, 3, 5, and 2 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 have 30.

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

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

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

Step 4: Solving the additions and subtractions of like fractions, we have:

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

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

$$=\frac{23}{60}$$

Step 5: The fraction is now simplified.