--- title: "Fractions, decimals and percentages" subtitle: "Number Foundations · Fractions and decimals · Lesson 10" --- # Fractions, decimals and percentages **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A 25% discount, a quarter off, 0.25 of the price: the same saving, written three ways. Which is easiest depends on the job. :::teacher-note **In one sentence:** Students use a fraction bar and a hundred grid to see one amount as a fraction, a decimal and a percentage, convert in every direction, and meet a recurring decimal (AC9M7N04, node 2). **Students should be able to say:** I can convert between fractions, decimals and percentages. I can explain why 0.5 = 50%, not 5%. I can compare amounts written in different forms. **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 How many of 100 squares is three quarters? :::keep-together **Which is the same amount as $\tfrac{3}{4}$?** ☐ $3.4\%$ ☐ $34\%$ ☐ $75\%$ ☐ $0.34$ My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 75%. 3/4 = 75/100 (× 25 on the top and the bottom), and out of 100 is a percentage: 75%. As a decimal, 0.75. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Converting :::keep-together ### Three ways Here is how to move between the three. 1. $\tfrac{3}{4} = \tfrac{75}{100} = 75\%$ — Fraction to percentage: make it out of 100 (× 25 on the top and the bottom). 2. $\tfrac{3}{8} = 3 \div 8 = 0.375$ — Fraction to decimal: divide the top by the bottom. 3. $0.375 \times 100 = 37.5\%$ — Decimal to percentage: multiply by 100. 4. $16\% = \tfrac{16}{100} = \tfrac{4}{25}$ — Percentage to fraction: put it over 100, then simplify. 5. $45\% = 0.45$ — Percentage to decimal: divide by 100. Try one: write $\tfrac{3}{8}$ as a decimal. **Write $\tfrac{3}{8}$ as a decimal.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 0.375 3 ÷ 8 = 0.375. As a percentage: 37.5%. ::: :::keep-together ### Find the mistake **Max writes $0.5$ as a percentage. Click the line where his working goes wrong.** ``` 1 Write 0.5 as a percentage. 2 Percent means out of 100. 3 0.5 has a 5 after the point. 4 So 0.5 = 5%. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 4 Line 4: 0.5 is 5 tenths, which is 50 hundredths. Out of 100: 50%. Multiply a decimal by 100 for the percentage. ::: :::keep-together ### Percentage to fraction **Write $16\%$ as a fraction in its simplest form.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 4/25 16% = 16/100 = 4/25 (÷ 4). ::: :::typical ## One change at a time **Fifths.** Each task changes one thing. **Decimal to percentage.** **Percentage to decimal.** **Fraction to percentage.** **A decimal that never ends.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## All three :::keep-together ### Decimal to fraction **Write $0.45$ as a fraction in its simplest form.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 9/20 0.45 = 45/100 = 9/20. ::: :::keep-together ### Fraction to percentage **Write $\tfrac{3}{5}$ as a percentage.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 60 3/5 = 60/100 = 60%. ::: :::keep-together ### Order them **Which is smallest: $0.6$, $\tfrac{2}{3}$ or $65\%$?** ☐ 0.6 ☐ 2/3 ☐ 65% ::: :::teacher-note **Answer:** 0.6 Write each as a decimal: 0.6, 0.666… and 0.65. The smallest is 0.6. ::: :::keep-together ### Review: simplest form **Review: write $\tfrac{9}{12}$ in its simplest form.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3/4 ÷ 3: 3/4. ::: ## Make: eighths that are whole percentages Which eighths cannot be shaded exactly on the grid? Why? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Write 3/5 as a decimal and as a percentage, and 0.08 as a percentage.** {{lines-3}} ::: :::teacher-note **Answer:** 0.6 and 60%; 0.08 = 8%. :::