EDEXCEL GCSE FOUNDATION MATHS - What are Fractions with Whole Numbers

Fractions with Whole Numbers

What are Fractions with Whole Numbers?

Fractions with whole numbers are numbers that combine a whole number with a fraction. They are also known as mixed numbers.

Example:

• 2 1/2 (read as "two and a half")
• 3 3/4 (read as "three and three quarters")

Understanding the Parts:

• Whole Number: This represents the whole units.
• Fraction: This represents a part of a whole unit.

Converting Between Mixed Numbers and Improper Fractions

Mixed Number to Improper Fraction:

1. Multiply the whole number by the denominator of the fraction: 2 x 2 = 4
2. Add the numerator to the result: 4 + 1 = 5
3. Keep the same denominator: 5/2

Improper Fraction to Mixed Number:

1. Divide the numerator by the denominator: 5 ÷ 2 = 2 remainder 1
2. The quotient (2) becomes the whole number.
3. The remainder (1) becomes the numerator of the fraction.
4. Keep the same denominator (2): 2 1/2

Example:

• Convert 3 2/5 to an improper fraction:
  • (3 x 5) + 2 = 17
  • 17/5
• Convert 11/3 to a mixed number:
  • 11 ÷ 3 = 3 remainder 2
  • 3 2/3

Adding and Subtracting Fractions with Whole Numbers

1. Convert mixed numbers to improper fractions.
2. Find a common denominator for the fractions.
3. Add or subtract the numerators.
4. Keep the denominator the same.
5. Simplify the answer if necessary (convert back to a mixed number if needed).

Example:

• 2 1/4 + 3 3/8:
  • 2 1/4 = 9/4
  • 3 3/8 = 27/8
  • (9/4) x (2/2) = 18/8
  • 18/8 + 27/8 = 45/8
  • 45/8 = 5 5/8

Multiplying and Dividing Fractions with Whole Numbers

1. Convert mixed numbers to improper fractions.
2. Multiply or divide the fractions as usual.
3. Simplify the answer if necessary (convert back to a mixed number if needed).

Example:

• 2 1/2 x 1 1/3:
  • 2 1/2 = 5/2
  • 1 1/3 = 4/3
  • (5/2) x (4/3) = 20/6
  • 20/6 = 3 1/3

Practical Applications

Fractions with whole numbers are used in everyday life, including:

• Cooking: Measuring ingredients
• Shopping: Calculating prices and discounts
• Time: Telling time
• Distance: Measuring distances

Key Takeaways

• Fractions with whole numbers (mixed numbers) combine whole units with parts of a unit.
• It's important to be able to convert between mixed numbers and improper fractions.
• Basic operations (addition, subtraction, multiplication, division) can be performed on mixed numbers using the rules of fractions.
• Mixed numbers have wide applications in various aspects of daily life.