OCR GCSE Maths: Operations with Fractions

OCR GCSE Maths: Operations with Fractions

This tutorial will focus on mastering operations with fractions, including addition, subtraction, multiplication, and division. We will explore how to work with both proper and improper fractions, including mixed numbers, and apply these skills to solve multi-step problems. We will also consider scenarios involving negative values.

1. Finding a Common Denominator

Before adding or subtracting fractions, they must share a common denominator. This means finding the least common multiple (LCM) of the denominators.

Example:

To add 1/3 and 2/5, we find the LCM of 3 and 5, which is 15. We then adjust each fraction:

1/3 = 5/15 
2/5 = 6/15

Now we can add the fractions: 5/15 + 6/15 = 11/15

2. Addition and Subtraction

Adding and Subtracting Fractions:

Once fractions have a common denominator, add or subtract the numerators and keep the denominator the same.

Example:

3/4 + 1/4 = 4/4 = 1
5/7 - 2/7 = 3/7

Adding and Subtracting Mixed Numbers:

1. Convert mixed numbers to improper fractions.
2. Find a common denominator.
3. Add or subtract the numerators.
4. Simplify the result, if possible.

Example:

2 1/3 + 1 2/5 = 7/3 + 7/5 = 35/15 + 21/15 = 56/15 = 3 11/15

3. Multiplication

Multiplying Fractions:

Multiply the numerators and the denominators of the fractions. Simplify the result, if possible.

Example:

2/3 x 1/4 = (2 x 1) / (3 x 4) = 2/12 = 1/6

Multiplying Mixed Numbers:

1. Convert mixed numbers to improper fractions.
2. Multiply the fractions as described above.
3. Simplify the result, if possible.

Example:

1 1/2 x 2 1/3 = 3/2 x 7/3 = 21/6 = 3 1/2

4. Division

Dividing Fractions:

To divide by a fraction, multiply by its reciprocal. The reciprocal of a fraction is found by flipping the numerator and denominator.

Example:

2/3 ÷ 1/2 = 2/3 x 2/1 = 4/3 = 1 1/3

Dividing Mixed Numbers:

1. Convert mixed numbers to improper fractions.
2. Divide the fractions as described above.
3. Simplify the result, if possible.

Example:

2 1/2 ÷ 1 1/4 = 5/2 ÷ 5/4 = 5/2 x 4/5 = 2

5. Negative Fractions

Adding and Subtracting with Negative Fractions:

Treat negative signs like any other coefficient. Remember the rules for adding and subtracting integers.

Example:

-1/2 + 1/4 = -2/4 + 1/4 = -1/4

Multiplying and Dividing with Negative Fractions:

Follow the same rules as multiplying and dividing integers.

Example:

-2/3 x 1/2 = -2/6 = -1/3
-1/2 ÷ 2/3 = -1/2 x 3/2 = -3/4 

6. Multi-Step Problems

Fraction operations can be applied to solve multi-step problems involving various scenarios.

Example:

A recipe requires 1 1/2 cups of flour. If you want to make half the recipe, how much flour do you need?

1. Convert 1 1/2 to an improper fraction: 3/2
2. Divide 3/2 by 2: (3/2) ÷ 2 = 3/4 cup of flour

Practice

• Practice solving various problems involving fractions, mixed numbers, and negative values.
• Utilize online resources and textbooks for additional practice questions.
• Familiarize yourself with the different types of problems that may arise in OCR GCSE Maths exams.

Remember: Mastering fraction operations is essential for success in GCSE Maths. Practice diligently and seek help when needed.