EDEXCEL GCSE HIGHER MATHS - What are Adding, Multiplying, and Dividing Fractions

Adding, Multiplying, and Dividing Fractions

Adding and Subtracting Fractions

1. Find a Common Denominator:

• If the denominators are the same, you can simply add or subtract the numerators.
• If the denominators are different, you need to find a common denominator. This is the smallest number that both denominators divide into.
• To do this, find the least common multiple (LCM) of the denominators.

2. Adjust the Fractions:

• Multiply the numerator and denominator of each fraction by the factor that will make the denominator equal to the common denominator.

3. Add or Subtract the Numerators:

• Once you have the same denominator, simply add or subtract the numerators.

4. Simplify the Result:

• If possible, simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCD).

Example:

1/2 + 3/4 

• The LCM of 2 and 4 is 4.
• Multiply the first fraction by 2/2: (1/2) * (2/2) = 2/4
• The second fraction already has a denominator of 4.
• Add the numerators: 2/4 + 3/4 = 5/4
• Simplify: 5/4 can be written as 1 1/4

Multiplying Fractions

1. Multiply the Numerators:

• Multiply the numerators of the fractions together.

2. Multiply the Denominators:

• Multiply the denominators of the fractions together.

3. Simplify the Result:

• If possible, simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCD).

Example:

2/3 * 1/4

• Multiply the numerators: 2 * 1 = 2
• Multiply the denominators: 3 * 4 = 12
• The result is 2/12
• Simplify: 2/12 = 1/6

Dividing Fractions

1. Flip the Second Fraction:

• Find the reciprocal of the second fraction by flipping the numerator and denominator.

2. Multiply the Fractions:

• Multiply the first fraction by the reciprocal of the second fraction.

3. Simplify the Result:

• If possible, simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCD).

Example:

2/3 / 1/2 

• Flip the second fraction: 1/2 becomes 2/1
• Multiply the fractions: (2/3) * (2/1) = 4/3

Note: When dividing fractions, you can think of it as "keep, change, flip". Keep the first fraction, change the division sign to multiplication, and flip the second fraction.