Understanding Fractions

Hello, Year 4! Today, we are going to learn about adding fractions. Fractions are parts of a whole. For example, if you have a pizza and you eat 1 out of 4 slices, you have eaten \frac{1}{4} of the pizza.

What is a Fraction?

A fraction has two parts:

  • The top number is called the numerator. It tells us how many parts we have.
  • The bottom number is called the denominator. It tells us how many equal parts the whole is divided into.

Adding Fractions with the Same Denominator

When adding fractions, it is easiest when they have the same denominator.

Example:

If you have \frac{1}{4} and you want to add another \frac{2}{4}, you do this:

  • Keep the denominator the same (which is 4).
  • Add the numerators: 1 + 2 = 3.

So, \frac{1}{4} + \frac{2}{4} = \frac{3}{4}.

Key Rule for Same Denominator

  1. Keep the denominator the same.
  2. Add the numerators.

Adding Fractions with Different Denominators

Sometimes, the fractions have different denominators. To add these, we first need to make the denominators the same. This is called finding a common denominator.

Example:

Let’s add \frac{1}{3} and \frac{1}{4}.

  1. The denominators are 3 and 4. The common denominator will be 12 (the smallest number that both 3 and 4 can divide into).
  2. Now, we change the fractions:
    • \frac{1}{3} = \frac{4}{12} (because 1 \times 4 = 4 and 3 \times 4 = 12)
    • \frac{1}{4} = \frac{3}{12} (because 1 \times 3 = 3 and 4 \times 3 = 12)
  3. Now we can add:
    • \frac{4}{12} + \frac{3}{12} = \frac{7}{12}.

Key Rule for Different Denominators

  1. Find a common denominator.
  2. Change both fractions so they have the same denominator.
  3. Add the numerators and keep the common denominator.

Tips and Tricks

  • Visuals Help: Drawing pictures or using fraction bars can help you see how fractions are added.
  • Practice Makes Perfect: The more you practice adding fractions, the easier it will become!
  • Check Your Work: Always double-check your fractions to make sure they are in their simplest form.

Questions

Easy Level Questions

  1. \frac{1}{4} + \frac{1}{4} = ?
  2. \frac{2}{5} + \frac{1}{5} = ?
  3. \frac{1}{8} + \frac{3}{8} = ?
  4. \frac{2}{6} + \frac{1}{6} = ?
  5. \frac{3}{10} + \frac{2}{10} = ?
  6. \frac{4}{8} + \frac{1}{8} = ?
  7. \frac{5}{12} + \frac{1}{12} = ?
  8. \frac{1}{3} + \frac{1}{3} = ?
  9. \frac{2}{7} + \frac{3}{7} = ?
  10. \frac{1}{2} + \frac{1}{2} = ?
  11. \frac{2}{8} + \frac{3}{8} = ?
  12. \frac{1}{6} + \frac{1}{6} = ?
  13. \frac{3}{5} + \frac{1}{5} = ?
  14. \frac{1}{10} + \frac{2}{10} = ?
  15. \frac{2}{3} + \frac{1}{3} = ?
  16. \frac{3}{4} + \frac{1}{4} = ?
  17. \frac{1}{9} + \frac{1}{9} = ?
  18. \frac{5}{6} + \frac{1}{6} = ?
  19. \frac{2}{12} + \frac{1}{12} = ?
  20. \frac{4}{5} + \frac{1}{5} = ?

Medium Level Questions

  1. \frac{1}{2} + \frac{1}{4} = ?
  2. \frac{2}{3} + \frac{1}{6} = ?
  3. \frac{3}{10} + \frac{2}{5} = ?
  4. \frac{1}{3} + \frac{2}{9} = ?
  5. \frac{3}{4} + \frac{1}{8} = ?
  6. \frac{5}{12} + \frac{1}{4} = ?
  7. \frac{2}{5} + \frac{1}{10} = ?
  8. \frac{1}{6} + \frac{1}{3} = ?
  9. \frac{2}{7} + \frac{3}{14} = ?
  10. \frac{1}{5} + \frac{1}{10} = ?
  11. \frac{3}{8} + \frac{1}{4} = ?
  12. \frac{2}{9} + \frac{1}{3} = ?
  13. \frac{1}{4} + \frac{1}{2} = ?
  14. \frac{1}{3} + \frac{2}{6} = ?
  15. \frac{3}{5} + \frac{2}{15} = ?
  16. \frac{4}{9} + \frac{1}{3} = ?
  17. \frac{1}{2} + \frac{1}{6} = ?
  18. \frac{2}{4} + \frac{1}{2} = ?
  19. \frac{3}{5} + \frac{1}{10} = ?
  20. \frac{1}{8} + \frac{1}{4} = ?

Hard Level Questions

  1. \frac{1}{2} + \frac{1}{3} = ?
  2. \frac{3}{5} + \frac{2}{3} = ?
  3. \frac{2}{3} + \frac{3}{4} = ?
  4. \frac{1}{6} + \frac{1}{2} = ?
  5. \frac{5}{12} + \frac{1}{3} = ?
  6. \frac{2}{7} + \frac{3}{8} = ?
  7. \frac{1}{5} + \frac{2}{7} = ?
  8. \frac{3}{10} + \frac{1}{2} = ?
  9. \frac{4}{5} + \frac{1}{10} = ?
  10. \frac{1}{4} + \frac{3}{10} = ?
  11. \frac{2}{9} + \frac{1}{6} = ?
  12. \frac{1}{3} + \frac{2}{5} = ?
  13. \frac{3}{8} + \frac{1}{3} = ?
  14. \frac{5}{6} + \frac{1}{2} = ?
  15. \frac{1}{2} + \frac{3}{10} = ?
  16. \frac{2}{5} + \frac{1}{4} = ?
  17. \frac{2}{3} + \frac{3}{5} = ?
  18. \frac{1}{7} + \frac{2}{3} = ?
  19. \frac{3}{4} + \frac{2}{5} = ?
  20. \frac{5}{8} + \frac{1}{3} = ?

Answers

Easy Level Answers

  1. \frac{2}{4}
  2. \frac{3}{5}
  3. \frac{4}{8}
  4. \frac{3}{6}
  5. \frac{5}{10}
  6. \frac{5}{8}
  7. \frac{6}{12}
  8. \frac{2}{3}
  9. \frac{5}{7}
  10. \frac{2}{2} = 1
  11. \frac{5}{8}
  12. \frac{2}{6}
  13. \frac{4}{5}
  14. \frac{3}{10}
  15. 1
  16. \frac{5}{4}
  17. \frac{2}{9}
  18. 1
  19. \frac{3}{12}
  20. 1

Medium Level Answers

  1. \frac{3}{4}
  2. \frac{5}{6}
  3. \frac{5}{10} = \frac{1}{2}
  4. \frac{5}{9}
  5. \frac{7}{8}
  6. \frac{8}{12} = \frac{2}{3}
  7. \frac{5}{10} = \frac{1}{2}
  8. \frac{1}{2}
  9. \frac{5}{14}
  10. \frac{3}{10}
  11. \frac{5}{8}
  12. \frac{5}{27}
  13. \frac{3}{4}
  14. \frac{5}{9}
  15. \frac{11}{15}
  16. \frac{5}{9}
  17. \frac{2}{3}
  18. \frac{3}{4}
  19. \frac{7}{10}
  20. \frac{5}{8}

Hard Level Answers

  1. \frac{5}{6}
  2. \frac{19}{15}
  3. \frac{17}{12}
  4. \frac{2}{3}
  5. \frac{9}{12} = \frac{3}{4}
  6. \frac{38}{56} = \frac{19}{28}
  7. \frac{19}{35}
  8. \frac{11}{10} = 1 \frac{1}{10}
  9. \frac{11}{10} = 1 \frac{1}{10}
  10. \frac{29}{40}
  11. \frac{13}{54}
  12. \frac{23}{15} = 1 \frac{8}{15}
  13. \frac{43}{24} = 1 \frac{19}{24}
  14. \frac{4}{3}
  15. \frac{8}{15}
  16. \frac{8}{20} = \frac{2}{5}
  17. \frac{29}{15} = 1 \frac{14}{15}
  18. \frac{23}{21} = 1 \frac{2}{21}
  19. \frac{31}{20} = 1 \frac{11}{20}
  20. \frac{23}{24}

Happy learning, and remember, practice makes perfect!