Subtracting Fractions with Whole Numbers (Mixed numbers)

Step 1: Converting the mixed fraction to an improper fraction, we have:

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

$$=\frac{3}{2}-\frac{1}{2}$$

Step 2: We have like fractions because the denominators are the same. Therefore, we continue to step 6.

Steps 3-5: Not applicable.

Step 6: We subtract the like fractions by using a single denominator and subtracting the numerators:

$$=\frac{3}{2}-\frac{1}{2}$$

$$=\frac{3-1}{2}$$

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

Step 7: Simplifying, we have:

$$=1$$

Step 1: Converting both mixed fractions to improper fractions, we have:

$$2\frac{2}{3}-1\frac{1}{3}$$

$$=\frac{8}{3}-\frac{4}{3}$$

Step 2: The denominators are equal to 3, so the fractions are like. Thus, we continue to step 6.

Steps 3-5: Not applicable.

Step 6: We combine the denominators of the like fractions and subtract the numerators:

$$=\frac{8}{3}-\frac{4}{3}$$

$$=\frac{8-4}{3}$$

$$=\frac{4}{3}$$

Step 7: We can simplify by writing as a mixed fraction:

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

Step 1: We convert the first mixed fraction to an improper fraction:

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

$$=\frac{5}{3}-\frac{2}{5}$$

Step 2: The fractions are unlike because the denominators are different. Thus, we continue to step 3.

Step 3: The denominators are 3 and 5, so the least common denominator is 15.

Step 4: Dividing 15 by 3 (first denominator), we get 5. Dividing 15 by 5 (second denominator), we get 3.

Step 5: We multiply the numerator and the denominator by the numbers obtained in step 4:

$$=\frac{5\times 5}{3\times 5}-\frac{2\times 3}{5\times 3}$$

$$=\frac{25}{15}-\frac{6}{15}$$

Step 6: We combine the denominators of the like fractions and subtract the numerators:

$$=\frac{25}{15}-\frac{6}{15}$$

$$=\frac{25-6}{15}$$

$$=\frac{19}{15}$$

Step 7: We can simplify by writing as a mixed number:

$$=1 \frac{4}{15}$$

Step 1: We convert both mixed fractions to improper fractions:

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

$$=\frac{11}{4}-\frac{3}{2}$$

Step 2: Since we have unlike fractions, we continue to step 3.

Step 3: We have denominators 4 and 2, so the least common denominator is 4.

Step 4: Dividing 4 by 4 (first denominator), we get 1. Dividing 4 by 2 (second denominator), we get 2.

Step 5: We multiply the numerator and the denominator by the numbers obtained in step 4:

$$=\frac{11\times 1}{4\times 1}-\frac{3\times 2}{2\times 2}$$

$$=\frac{11}{4}-\frac{6}{4}$$

Step 6: Combining the denominators and subtracting the numerators, we have:

$$=\frac{11-4}{4}$$

$$=\frac{5}{4}$$

Step 7: We can simplify by writing as a mixed number:

$$=1 \frac{1}{4}$$

Step 1: We convert the two mixed fractions to improper fractions:

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

$$=\frac{17}{5}-\frac{3}{5}-\frac{6}{5}$$

Step 2: The fractions are like, so we continue to step 6.

Steps 3-5: Not applicable.

Step 6: Using a single denominator and subtracting the numerators, we have:

$$=\frac{17}{5}-\frac{3}{5}-\frac{6}{5}$$

$$=\frac{17-3-6}{5}$$

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

Step 7: Converting to a mixed fraction, we have:

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

Step 1: We convert the three mixed fractions to improper fractions, and we have:

$$3\frac{3}{4}-1\frac{2}{3}-1\frac{4}{5}$$

$$=\frac{15}{4}-\frac{5}{3}-\frac{9}{5}$$

Step 2: We have three unlike fractions, so we continue to step 3.

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

Step 4: 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.

Step 5: We multiply the numerators and denominators of the fractions by the numbers obtained in step 4:

$$=\frac{15\times 15}{4\times 15}-\frac{5\times 20}{3\times 20}-\frac{9\times 12}{5\times 12}$$

$$=\frac{225}{60}-\frac{100}{60}-\frac{108}{60}$$

Step 6: Subtracting the like fractions, we have:

$$=\frac{225-100-108}{60}$$

$$=\frac{17}{60}$$