# WORKSHEET ## Title: Adding and Subtracting Fractions with Unlike Denominators **Name:** __________________________ **Date:** __________________________ **Class:** __________________________ ### Learning Objectives By the end of this worksheet, learners should be able to: 1. Find a common denominator for fractions with unlike denominators. 2. Add fractions with unlike denominators accurately. 3. Subtract fractions with unlike denominators accurately. 4. Solve real-life problems involving addition and subtraction of fractions. --- ## Concept Review ### What are Unlike Denominators? The **denominator** is the bottom number of a fraction. For example: $$ \frac{2}{3}+\frac{1}{4} $$ The denominators are **3 and 4**. Since they are different, they are called **unlike denominators**. ### Rule for Adding or Subtracting Fractions You **cannot directly add or subtract the numerators** when the denominators are different. Follow these steps: 1. Find a **common denominator**. 2. Convert each fraction into an **equivalent fraction** with the common denominator. 3. Add or subtract the numerators. 4. Keep the common denominator. 5. Simplify the answer if possible. ### Remember **The denominator tells us the size of the parts.** Before adding or subtracting, the parts must be the same size. --- ## Worked Examples ### Example 1: Addition Find: $$ \frac{1}{2}+\frac{1}{3} $$ **Step 1: Find a common denominator.** The lowest common multiple of 2 and 3 is 6. $$ \frac{1}{2}=\frac{3}{6} $$ $$ \frac{1}{3}=\frac{2}{6} $$ **Step 2: Add the numerators.** $$ \frac{3}{6}+\frac{2}{6}=\frac{5}{6} $$ **Answer:** $$ \boxed{\frac{5}{6}} $$ --- ### Example 2: Subtraction Find: $$ \frac{3}{4}-\frac{1}{6} $$ **Step 1: Find a common denominator.** The lowest common multiple of 4 and 6 is 12. $$ \frac{3}{4}=\frac{9}{12} $$ $$ \frac{1}{6}=\frac{2}{12} $$ **Step 2: Subtract the numerators.** $$ \frac{9}{12}-\frac{2}{12}=\frac{7}{12} $$ **Answer:** $$ \boxed{\frac{7}{12}} $$ --- ### Example 3: Addition and Simplification Find: $$ \frac{2}{5}+\frac{1}{10} $$ The common denominator is 10. $$ \frac{2}{5}=\frac{4}{10} $$ Therefore: $$ \frac{4}{10}+\frac{1}{10}=\frac{5}{10} $$ Simplify: $$ \frac{5}{10}=\frac{1}{2} $$ **Answer:** $$ \boxed{\frac{1}{2}} $$ --- # Practice Activities ## A. Multiple Choice Choose the correct answer. ### 1. What is: $$ \frac{1}{3}+\frac{1}{6} $$ A. \(\frac{2}{9}\) B. \(\frac{1}{2}\) C. \(\frac{2}{6}\) D. \(\frac{1}{9}\) ### 2. What is: $$ \frac{3}{4}-\frac{1}{8} $$ A. \(\frac{2}{6}\) B. \(\frac{5}{8}\) C. \(\frac{2}{8}\) D. \(\frac{1}{2}\) ### 3. What is the lowest common denominator of 3 and 5? A. 8 B. 10 C. 15 D. 20 ### 4. What is: $$ \frac{2}{3}+\frac{1}{4} $$ A. \(\frac{3}{7}\) B. \(\frac{8}{12}\) C. \(\frac{11}{12}\) D. \(\frac{7}{12}\) --- ## B. Fill in the Blanks ### 5. $$ \frac{1}{2}=\frac{?}{8} $$ ### 6. $$ \frac{2}{3}=\frac{?}{12} $$ ### 7. $$ \frac{5}{6}-\frac{1}{3}=\frac{?}{6} $$ ### 8. $$ \frac{1}{4}+\frac{1}{2}=\frac{?}{4} $$ --- ## C. Calculate Show your working. ### 9. $$ \frac{1}{2}+\frac{1}{5} $$ ### 10. $$ \frac{3}{5}-\frac{1}{2} $$ ### 11. $$ \frac{2}{3}+\frac{3}{4} $$ ### 12. $$ \frac{5}{6}-\frac{1}{4} $$ ### 13. $$ \frac{3}{8}+\frac{1}{6} $$ ### 14. $$ \frac{7}{10}-\frac{1}{4} $$ --- ## D. True or False Write **True** or **False**. ### 15. To add fractions with unlike denominators, we should first find a common denominator. --- ### 16. $$ \frac{1}{2}+\frac{1}{3}=\frac{2}{5} $$ --- ### 17. $$ \frac{3}{4}-\frac{1}{4}=\frac{2}{4} $$ --- ### 18. Equivalent fractions have the same value even though they may look different. --- --- ## E. Problem Solving ### 19. Sharing Pizza Ada ate \(\frac{1}{4}\) of a pizza, while Tunde ate \(\frac{1}{3}\) of the same pizza. What fraction of the pizza did they eat altogether? **Working:** --- --- **Answer:** __________________ --- ### 20. Reading a Book David read \(\frac{3}{5}\) of a book on Monday. On Tuesday, he read another \(\frac{1}{4}\) of the book. What fraction of the book did he read altogether? **Working:** --- --- **Answer:** __________________ --- ### 21. Water in a Container A container was \(\frac{7}{8}\) full. A person used \(\frac{1}{3}\) of the container's capacity. What fraction of the container's capacity remained? **Working:** --- --- **Answer:** __________________ --- ## F. Critical Thinking ### 22. Amaka says: > “To add \(\frac{1}{2}+\frac{1}{3}\), I add the top numbers and bottom numbers, so the answer is \(\frac{2}{5}\).” Is Amaka correct? Explain your answer. --- --- --- --- ### 23. Which is greater? $$ \frac{2}{3}+\frac{1}{6} $$ or $$ \frac{1}{2}+\frac{1}{4} $$ Show your working. --- --- **Answer:** __________________ --- # Application Challenge ### 24. Planning a School Garden A school plans to use part of its garden for vegetables. They use: * \(\frac{2}{5}\) of the garden for tomatoes. * \(\frac{1}{4}\) of the garden for carrots. **a.** What fraction of the garden is used for tomatoes and carrots altogether? **b.** What fraction of the garden is left for other plants? Show all your working. --- --- --- --- **Answer:** a. __________________ b. __________________ --- # ANSWER KEY ### Multiple Choice 1. **B — \(\frac{1}{2}\)** $$ \frac{1}{3}=\frac{2}{6} $$ $$ \frac{2}{6}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2} $$ 2. **B — \(\frac{5}{8}\)** $$ \frac{3}{4}=\frac{6}{8} $$ $$ \frac{6}{8}-\frac{1}{8}=\frac{5}{8} $$ 3. **C — 15** 4. **C — \(\frac{11}{12}\)** $$ \frac{2}{3}=\frac{8}{12} $$ $$ \frac{1}{4}=\frac{3}{12} $$ $$ \frac{8}{12}+\frac{3}{12}=\frac{11}{12} $$ --- ### Fill in the Blanks 5. **4** $$ \frac{1}{2}=\frac{4}{8} $$ 6. **8** $$ \frac{2}{3}=\frac{8}{12} $$ 7. **3** $$ \frac{5}{6}-\frac{2}{6}=\frac{3}{6} $$ 8. **3** $$ \frac{1}{4}+\frac{2}{4}=\frac{3}{4} $$ --- ### Calculate 9. $$ \frac{1}{2}+\frac{1}{5} =\frac{5}{10}+\frac{2}{10} =\boxed{\frac{7}{10}} $$ 10. $$ \frac{3}{5}-\frac{1}{2} =\frac{6}{10}-\frac{5}{10} =\boxed{\frac{1}{10}} $$ 11. $$ \frac{2}{3}+\frac{3}{4} =\frac{8}{12}+\frac{9}{12} =\boxed{\frac{17}{12}} $$ or $$ \boxed{1\frac{5}{12}} $$ 12. $$ \frac{5}{6}-\frac{1}{4} =\frac{10}{12}-\frac{3}{12} =\boxed{\frac{7}{12}} $$ 13. $$ \frac{3}{8}+\frac{1}{6} =\frac{9}{24}+\frac{4}{24} =\boxed{\frac{13}{24}} $$ 14. $$ \frac{7}{10}-\frac{1}{4} =\frac{14}{20}-\frac{5}{20} =\boxed{\frac{9}{20}} $$ --- ### True or False 15. **True** 16. **False** $$ \frac{1}{2}+\frac{1}{3} =\frac{3}{6}+\frac{2}{6} =\frac{5}{6} $$ 17. **False** $$ \frac{3}{4}-\frac{1}{4}=\frac{2}{4}=\frac{1}{2} $$ The statement is not in simplest form, so as written it is **not completely correct** if the expected answer is simplified. 18. **True** --- ### Problem Solving 19. $$ \frac{1}{4}+\frac{1}{3} =\frac{3}{12}+\frac{4}{12} =\boxed{\frac{7}{12}} $$ They ate **\(\frac{7}{12}\)** of the pizza. 20. $$ \frac{3}{5}+\frac{1}{4} =\frac{12}{20}+\frac{5}{20} =\boxed{\frac{17}{20}} $$ David read **\(\frac{17}{20}\)** of the book. 21. $$ \frac{7}{8}-\frac{1}{3} =\frac{21}{24}-\frac{8}{24} =\boxed{\frac{13}{24}} $$ **\(\frac{13}{24}\)** of the container's capacity remained. --- ### Critical Thinking 22. **No, Amaka is not correct.** Fractions with unlike denominators cannot be added by simply adding the numerators and denominators. A common denominator is needed. $$ \frac{1}{2}+\frac{1}{3} =\frac{3}{6}+\frac{2}{6} =\boxed{\frac{5}{6}} $$ 23. First expression: $$ \frac{2}{3}+\frac{1}{6} =\frac{4}{6}+\frac{1}{6} =\frac{5}{6} $$ Second expression: $$ \frac{1}{2}+\frac{1}{4} =\frac{2}{4}+\frac{1}{4} =\frac{3}{4} $$ Since: $$ \frac{5}{6}>\frac{3}{4} $$ **Answer: \(\frac{2}{3}+\frac{1}{6}\) is greater.** --- ### Application Challenge 24. **a.** $$ \frac{2}{5}+\frac{1}{4} =\frac{8}{20}+\frac{5}{20} =\boxed{\frac{13}{20}} $$ **b.** The whole garden is: $$ 1=\frac{20}{20} $$ Therefore: $$ \frac{20}{20}-\frac{13}{20} =\boxed{\frac{7}{20}} $$ **Answers:** a. **\(\frac{13}{20}\)** used for tomatoes and carrots. b. **\(\frac{7}{20}\)** left for other plants. --- # TEACHER NOTES ### Teaching Suggestions * Begin by reviewing equivalent fractions and multiplication facts. * Use fraction strips, paper circles, or drawings to demonstrate why unlike denominators must be changed before adding or subtracting. * Encourage learners to **show every step**, especially when finding common denominators. * Allow learners to work in pairs for Questions 19–24 before completing the final answers independently. * For assessment, Questions 1–18 can be used for individual practice, while Questions 19–24 can be used for deeper assessment. ### Common Misconceptions 1. **Adding denominators:** Learners may incorrectly do \(\frac{1}{2}+\frac{1}{3}=\frac{2}{5}\). 2. **Finding the wrong common denominator:** Learners may choose a number that is not a multiple of both denominators. 3. **Changing only the denominator:** Learners may forget that the numerator must also be multiplied by the same number. 4. **Forgetting to simplify:** Learners may leave answers such as \(\frac{5}{10}\) instead of \(\frac{1}{2}\). 5. **Subtraction errors:** Learners may subtract the denominators instead of keeping the common denominator unchanged. ### Follow-Up Activity Give learners pairs of fraction cards. Ask them to: 1. Pick two fractions with unlike denominators. 2. Find their common denominator. 3. Add or subtract them. 4. Explain their method to a partner. 5. Create one fraction problem for another learner to solve. **Teacher discussion question:** “Why must fractions have the same denominator before we can add or subtract them?”