a. [tex]\frac{11}{12}[/tex]
b. [tex]\frac{39}{20}[/tex]
c. [tex]\frac{20}{21}[/tex]
Step-by-step explanation:
Step 1; First, we convert the given fractions into improper ones. To do this, we multiply the whole number with the denominator of the fraction and add with it the same fraction's numerator whereas the denominator remains unchanged. To convert the fraction
3[tex]\frac{1}{4}[/tex] = (3 × 4) + 1 / 4 = [tex]\frac{13}{4}[/tex],
2[tex]\frac{1}{3}[/tex] = (2 × 3) + 1 / 3 = [tex]\frac{7}{3}[/tex],
6[tex]\frac{1}{5}[/tex] = (6 × 5) + 1 / 5 = [tex]\frac{31}{5}[/tex],
4[tex]\frac{1}{4}[/tex] = (4 × 4) + 1 / 4 = [tex]\frac{17}{4}[/tex],
5[tex]\frac{2}{7}[/tex] = (5 × 7) + 2 / 7 = [tex]\frac{37}{7}[/tex],
4[tex]\frac{1}{3}[/tex] = (4 × 3) + 1 / 3 = [tex]\frac{13}{3}[/tex].
Step 2; Now we subtract, using LCM to arrive at the answer
3[tex]\frac{1}{4}[/tex] - 2[tex]\frac{1}{3}[/tex] = [tex]\frac{13}{4}[/tex] - [tex]\frac{7}{3}[/tex] = [tex]\frac{39-28}{12}[/tex] = [tex]\frac{11}{12}[/tex],
6[tex]\frac{1}{5}[/tex] - 4[tex]\frac{1}{4}[/tex] = [tex]\frac{31}{5}[/tex] - [tex]\frac{17}{4}[/tex] = [tex]\frac{124-85}{20}[/tex] = [tex]\frac{39}{20}[/tex],
5[tex]\frac{2}{7}[/tex] - 4[tex]\frac{1}{3}[/tex] = [tex]\frac{37}{7}[/tex] - [tex]\frac{13}{3}[/tex] = [tex]\frac{111-91}{21}[/tex] = [tex]\frac{20}{21}[/tex].
