Adding & Subtracting Fractions

National Curriculum Links

Year 7 Mathematics – Number: Fractions and Decimals

• Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.
• Solve problems involving the addition and subtraction of fractions.

This lesson supports the statutory requirements for Year 7 pupils in England as outlined in the programme of study for the National Curriculum for Mathematics (DfE, 2014).

---

Learning Objectives

By the end of this lesson, pupils will be able to:

1. Identify and find a common denominator when adding and subtracting fractions with different denominators.
2. Add and subtract proper fractions and mixed numbers accurately using equivalent fractions.
3. Simplify answers where appropriate.
4. Apply understanding of fractions to solve problems.

---

Lesson Duration

60 minutes
Class size: 25 pupils

---

Lesson Outline

1. Starter Activity (10 minutes)

• Objective: Activate prior knowledge of fractions and equivalent fractions.
• Pupils will list pairs of equivalent fractions (e.g., 1/2 = 2/4, 3/6 = 1/2) on mini-whiteboards.
• Quick revision: emphasise how to find equivalent fractions by multiplying numerator and denominator by the same number.

Teacher Notes: Ensure pupils understand what a denominator and numerator are and how equivalent fractions represent the same value.

---

2. Introduction (10 minutes)

• Briefly explain that you cannot add or subtract fractions directly when they have different denominators; you need a common denominator first.
• Use visual fraction bars or circles to demonstrate why fractions must be expressed with the same denominator before performing the operation.

Key points to cover:

• What a denominator represents (the total parts of a whole)
• Why common denominators are necessary for addition and subtraction
• How to find the least common denominator (LCD)

---

3. Teaching Examples (15 minutes)

Example 1: Adding fractions with different denominators
[ \frac{1}{4} + \frac{1}{6} ]

• Find the least common denominator (LCD): multiples of 4 are 4, 8, 12... multiples of 6 are 6, 12... LCD is 12.
• Convert each to an equivalent fraction: (\frac{1}{4} = \frac{3}{12}), (\frac{1}{6} = \frac{2}{12})
• Add: (\frac{3}{12} + \frac{2}{12} = \frac{5}{12})
• This fraction cannot be simplified further.

Example 2: Subtracting fractions with different denominators
[ \frac{5}{8} - \frac{1}{3} ]

• LCD of 8 and 3 is 24.
• Convert: (\frac{5}{8} = \frac{15}{24}), (\frac{1}{3} = \frac{8}{24})
• Subtract: (\frac{15}{24} - \frac{8}{24} = \frac{7}{24})
• Simplify if needed: (\frac{7}{24}) is already in simplest form.

Example 3: Adding mixed numbers
[ 1 \frac{1}{5} + 2 \frac{2}{3} ]

• Convert to improper fractions: (1 \frac{1}{5} = \frac{6}{5}), (2 \frac{2}{3} = \frac{8}{3})
• LCD of 5 and 3 is 15.
• Convert to equivalent fractions: (\frac{6}{5} = \frac{18}{15}), (\frac{8}{3} = \frac{40}{15})
• Add: (\frac{18}{15} + \frac{40}{15} = \frac{58}{15})
• Convert back to a mixed number: (3 \frac{13}{15})

---

4. Guided Practice (15 minutes)

• Pupils work in pairs to complete the following questions. Teacher circulates to offer support and address misconceptions.

Questions:

1. (\frac{3}{7} + \frac{2}{5})
2. (\frac{4}{9} - \frac{1}{6})
3. (2 \frac{1}{4} + 1 \frac{2}{3})
4. (3 \frac{3}{8} - 1 \frac{1}{2})

---

5. Review & Model Answers (5 minutes)

Question	Solution	Explanation
1	(\frac{3}{7} + \frac{2}{5} = \frac{15}{35} + \frac{14}{35} = \frac{29}{35})	LCD = 35, Equivalent fractions found, added numerators. Simplified if possible (not needed).
2	(\frac{4}{9} - \frac{1}{6} = \frac{8}{18} - \frac{3}{18} = \frac{5}{18})	LCD = 18, converted, then subtracted.
3	(2 \frac{1}{4} + 1 \frac{2}{3} = \frac{9}{4} + \frac{5}{3} = \frac{27}{12} + \frac{20}{12} = \frac{47}{12} = 3 \frac{11}{12})	Converted mixed numbers to improper fractions, added, converted back.
4	(3 \frac{3}{8} - 1 \frac{1}{2} = \frac{27}{8} - \frac{3}{2} = \frac{27}{8} - \frac{12}{8} = \frac{15}{8} = 1 \frac{7}{8})	Proper fraction conversion, subtraction and re-conversion to a mixed number.

---

6. Plenary (5 minutes)

• Discuss the importance of finding common denominators and equivalent fractions.
• Quick oral quiz: “What is the least common denominator of 5 and 10?”, “What should you do before adding fractions?”, “How do you convert mixed numbers to improper fractions?”

---

7. Homework (Optional)

• Worksheet with 8-10 problems mixing addition and subtraction of fractions and mixed numbers varying in difficulty. Encourage fully worked answers, simplification, and conversion back to mixed numbers when necessary.

---

Differentiation & Support

• Provide fraction wall visual aids and number line diagram for students needing extra support.
• Challenge higher ability pupils with fraction problems involving 3 or more fractions or introducing improper fractions and their simplification in more depth.

---

Assessment for Learning

• Monitor mini-whiteboard activity for starter engagement.
• Observe and support pairs during guided practice.
• Use plenary questioning to check misconceptions and understanding on the spot.
• Analyse homework for individual pupil progress.

---

This detailed 60-minute plan fully aligns with the Year 7 mathematics requirements from the National Curriculum England and ensures clear conceptual understanding of adding and subtracting fractions with different denominators.