--- title: "Adding and subtracting fractions" subtitle: "Number Foundations · Fractions and decimals · Lesson 12" --- # Adding and subtracting fractions **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A recipe needs 1/3 of a cup of milk and 1/4 of a cup of cream. Will it all fit in a half-cup measure? You cannot tell until the parts are the same size. :::teacher-note **In one sentence:** Students cut two fraction bars into the same number of parts to add and subtract fractions with different denominators, use the LCM as the lowest common denominator, and extend the idea to mixed numerals and decimals (AC9M7N06, node 1). **Students should be able to say:** I can add and subtract fractions with different denominators using a common denominator. I can add and subtract mixed numerals and decimals. I can explain why the tops and the bottoms are not simply added. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Is the answer more or less than $\tfrac{1}{3}$ on its own? :::keep-together **What is $\tfrac{1}{3} + \tfrac{1}{4}$?** ☐ $\tfrac{2}{7}$ ☐ $\tfrac{1}{7}$ ☐ $\tfrac{7}{12}$ ☐ $\tfrac{2}{12}$ My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 7/12: 1/3 = 4/12 and 1/4 = 3/12, and 4 + 3 = 7 twelfths. 2/7 is less than 1/3 on its own, so it cannot be the sum. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Common denominators :::keep-together ### Same parts, then count Here is the method, then a mixed numeral and a decimal. 1. $\tfrac{1}{3} + \tfrac{1}{4} = \tfrac{4}{12} + \tfrac{3}{12}$ — The LCM of 3 and 4 is 12: write both in twelfths. 2. $= \tfrac{7}{12}$ — Same parts: add the tops, keep the bottom. 3. $2\tfrac{1}{2} - \tfrac{3}{4} = \tfrac{10}{4} - \tfrac{3}{4} = \tfrac{7}{4} = 1\tfrac{3}{4}$ — A mixed numeral: write it as quarters first. 4. $3.45 + 2.70 = 6.15$ — Decimals: line up the points (the same parts: tenths, hundredths). Now try one: $\tfrac{2}{5} + \tfrac{1}{3}$. **Work out $\tfrac{2}{5} + \tfrac{1}{3}$. Give your answer in simplest form.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 11/15 2/5 = 6/15 and 1/3 = 5/15, so 6/15 + 5/15 = 11/15. ::: :::keep-together ### Find the mistake **Ella adds $\tfrac{1}{2} + \tfrac{1}{3}$. Click the line where her method goes wrong.** ``` 1 Work out 1/2 + 1/3. 2 Add the tops and add the bottoms. 3 1 + 1 = 2 and 2 + 3 = 5 4 So 1/2 + 1/3 = 2/5. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: halves and thirds are different sizes, so they cannot be counted together. 1/2 = 3/6 and 1/3 = 2/6: 5/6. (2/5 is less than 1/2 on its own.) ::: :::keep-together ### Decimals **Work out $3.45 + 2.7$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6.15 Line up the points: 3.45 + 2.70 = 6.15. Tenths with tenths, like fractions with the same bottom. ::: :::typical ## One change at a time **Subtract.** Each task changes one thing. **Without the board.** **A mixed numeral.** **One already fits.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Add and subtract :::keep-together ### Add **Work out $\tfrac{3}{4} + \tfrac{1}{6}$ in simplest form.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 11/12 9/12 + 2/12 = 11/12. ::: :::keep-together ### Mixed numerals **Work out $3\tfrac{1}{3} - 1\tfrac{1}{2}$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1 5/6 3 1/3 = 20/6 and 1 1/2 = 9/6, so 11/6 = 1 5/6. ::: :::keep-together ### Decimals in context **A plank is 2.4 m long. 0.65 m is cut off. How long is the rest, in metres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1.75 2.40 − 0.65 = 1.75 m. ::: :::keep-together ### Review: LCM **Review: find the LCM of 6 and 10.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 30 6 = 2 × 3 and 10 = 2 × 5: LCM = 2 × 3 × 5 = 30. ::: ## Make: a sum of one Then find a pair where neither bottom is a multiple of the other. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Work out 2/3 + 1/5 and 1 1/4 − 2/3.** {{lines-3}} ::: :::teacher-note **Answer:** 10/15 + 3/15 = 13/15. 15/12 − 8/12 = 7/12. :::