# Adding and Subtracting Fractions with Unlike Denominators *30 minutes, 3 stages* When you add or subtract fractions, they need to speak the same language. Fractions with different denominators are like trying to combine metres and centimetres without converting first. You'll learn to find common denominators so you can combine fractions accurately ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30281)). ## Stage 1: Find the Common Denominator (10 min) Two fractions can only be added or subtracted when they have the same denominator. Your job is to rewrite each pair of fractions so they match. **Task 1:** For each pair, identify which denominator is a multiple of the other. Write the factor that relates them. Example: 1/4 and 1/8. Since 8 = 4 × 2, the factor is 2. - 2/3 and 5/6 - 3/5 and 7/10 - 1/4 and 3/16 - 4/9 and 2/3 **Task 2:** Rewrite each pair with a common denominator. - 1/2 and 3/8 - 2/5 and 1/3 - 3/4 and 5/12 ## Stage 2: Add and Subtract (15 min) Now that you can find common denominators, add or subtract the fractions. Remember: you only add or subtract the numerators. The denominator stays the same. **Task 1:** Add these fractions. Show your working. - 1/4 + 1/8 = - 2/5 + 3/10 = - 1/3 + 1/6 = **Task 2:** Subtract these fractions. Show your working. - 5/6 − 1/3 = - 7/8 − 1/4 = - 3/5 − 2/10 = **Task 3:** Solve this problem. You have 3/4 of a pizza. Your friend eats 1/6 of the whole pizza from your slice. How much pizza do you have left? ## Stage 3: Check Your Understanding (5 min) Answer these questions to see what you've learned. **Self-check:** 1. Why do fractions need a common denominator before you add or subtract them? Give an example with two fractions that have different denominators. 2. When you add 2/3 + 1/4, what is the common denominator you would use, and what does each fraction become? 3. Look at your answer to the pizza problem. Does your answer make sense? Explain why or why not. --- *AILI student homework · language en · model claude-haiku-4-5-20251001 · generated 2026-09-17 · id a40c9eac-02e5-48b7-8495-ee8825f28ecd* ### Sources - node:n1: Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29915) - node:n2: How can fractions contribute to a sense of number? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29942) - node:n3: Students interpret fractions in relation to one whole. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29943) - node:n4: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29945) - node:n5: Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30025) - node:n6: How can fractions be characterized in different ways? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30050) - node:n7: Students apply equivalence to the interpretation of fractions. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30051) - node:n8: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30053) - node:n9: Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30135) - node:n10: In what ways can fractions communicate numbers greater than one? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30160) - node:n11: Students interpret improper fractions. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30161) - node:n12: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30163) - node:n13: How can the composition of fractions facilitate operating with fractions? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30166) - node:n14: Students add and subtract fractions with common denominators. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30167) - node:n15: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30169) - node:n16: Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30237) - node:n17: How can the infinite nature of the number line broaden the perception of number? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30238) - node:n18: Students investigate magnitude with positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30239) - node:n19: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30241) - node:n20: How can the addition and subtraction of fractions be generalized? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30280) - node:n21: Students add and subtract fractions with denominators within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30281) - node:n22: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/30283) - node:n23: Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculations (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20863) - node:n24: How can multiplication and division be generalized? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20890) - node:n25: Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20891) - node:n26: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893) - node:n27: Number (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34135) - node:n28: Develop number sense. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34136) - node:n29: Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denomi (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34141) - node:n30: Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculations (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20979) - node:n31: How can the density of the number line contribute to a sense of number? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20980) - node:n32: Students interpret rational and irrational numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20981) - node:n33: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20983) - node:n34: Number (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34211) - node:n35: Develop number sense. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34212) - node:n36: Demonstrate an understanding of rational numbers by: - comparing and ordering rational numbers - solving problems that i (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34215)