Question

adding & subtracting fractions- pixel art posted in google classroom. if correct then the answer box will turn green. circle your answer.

1. -3/4 + 2/4 =
2. -2/7 + 4/7 =
3. -2/8 + -5/8 =
4. -2/5 - 2/5 =
5. -2/3 - (-1/3) =
6. -2/7 + -4/7
7. -2/3 + 7/8 =
8. 1/4 - (-2/9) =
9. 2/8 - (-3/5) =

Explanation:

Step1: Add or subtract numerators for same - denominator fractions

For \(-\frac{3}{4}+\frac{2}{4}\), since the denominators are the same, we add the numerators: \(-3 + 2=-1\), so \(-\frac{3}{4}+\frac{2}{4}=-\frac{1}{4}\).
For \(-\frac{2}{7}+\frac{4}{7}\), with the same denominator, we add the numerators: \(-2 + 4 = 2\), so \(-\frac{2}{7}+\frac{4}{7}=\frac{2}{7}\).
For \(-\frac{2}{8}+(-\frac{5}{8})\), we add the numerators: \(-2+( - 5)=-7\), so \(-\frac{2}{8}+(-\frac{5}{8})=-\frac{7}{8}\).
For \(-\frac{2}{5}-\frac{2}{5}\), we subtract the numerators: \(-2-2=-4\), so \(-\frac{2}{5}-\frac{2}{5}=-\frac{4}{5}\).
For \(-\frac{2}{3}-(-\frac{1}{3})\), this is equivalent to \(-\frac{2}{3}+\frac{1}{3}\), and we add the numerators: \(-2 + 1=-1\), so \(-\frac{2}{3}-(-\frac{1}{3})=-\frac{1}{3}\).
For \(-\frac{2}{7}+(-\frac{4}{7})\), we add the numerators: \(-2+( - 4)=-6\), so \(-\frac{2}{7}+(-\frac{4}{7})=-\frac{6}{7}\).

Step2: Find a common denominator for different - denominator fractions

For \(-\frac{2}{3}+\frac{7}{8}\), the common denominator of 3 and 8 is 24. We rewrite the fractions: \(-\frac{2}{3}=-\frac{2\times8}{3\times8}=-\frac{16}{24}\) and \(\frac{7}{8}=\frac{7\times3}{8\times3}=\frac{21}{24}\). Then \(-\frac{16}{24}+\frac{21}{24}=\frac{-16 + 21}{24}=\frac{5}{24}\).
For \(\frac{1}{4}-(-\frac{2}{9})\), which is \(\frac{1}{4}+\frac{2}{9}\), the common denominator of 4 and 9 is 36. We rewrite the fractions: \(\frac{1}{4}=\frac{1\times9}{4\times9}=\frac{9}{36}\) and \(\frac{2}{9}=\frac{2\times4}{9\times4}=\frac{8}{36}\). Then \(\frac{9}{36}+\frac{8}{36}=\frac{9 + 8}{36}=\frac{17}{36}\).
For \(\frac{2}{8}-(-\frac{3}{5})\), which is \(\frac{2}{8}+\frac{3}{5}\), the common denominator of 8 and 5 is 40. We rewrite the fractions: \(\frac{2}{8}=\frac{2\times5}{8\times5}=\frac{10}{40}\) and \(\frac{3}{5}=\frac{3\times8}{5\times8}=\frac{24}{40}\). Then \(\frac{10}{40}+\frac{24}{40}=\frac{10 + 24}{40}=\frac{34}{40}=\frac{17}{20}\).

Answer:

1. \(-\frac{1}{4}\)
2. \(\frac{2}{7}\)
3. \(-\frac{7}{8}\)
4. \(-\frac{4}{5}\)
5. \(-\frac{1}{3}\)
6. \(-\frac{6}{7}\)
7. \(\frac{5}{24}\)
8. \(\frac{17}{36}\)
9. \(\frac{17}{20}\)