Fractions, Decimals, and Percentages

Fractions, decimals, and percentages are three different ways of showing parts of a whole. In the CEM 11+ exam, you must be able to convert between them, compare them, and use them in calculations — often under time pressure. This lesson will give you the tools and techniques you need.

---

Understanding Fractions

A fraction has a numerator (top number) and a denominator (bottom number):

• The numerator tells you how many parts you have.
• The denominator tells you how many equal parts the whole is divided into.

For example, 3/4 means 3 parts out of 4 equal parts.

Equivalent Fractions

Equivalent fractions have the same value but different numerators and denominators. You create them by multiplying or dividing the top and bottom by the same number:

Fraction	× 2	× 3	× 4
1/2	2/4	3/6	4/8
2/3	4/6	6/9	8/12
3/5	6/10	9/15	12/20

Simplifying Fractions

Divide the numerator and denominator by their Highest Common Factor (HCF):

Simplify 18/24:

• HCF of 18 and 24 is 6
• 18 ÷ 6 = 3, 24 ÷ 6 = 4
• Answer: 3/4

---

Adding and Subtracting Fractions

To add or subtract fractions, they must have the same denominator.

Worked Example: 2/3 + 1/4

1. Find a common denominator: LCM of 3 and 4 = 12
2. Convert: 2/3 = 8/12, 1/4 = 3/12
3. Add: 8/12 + 3/12 = 11/12

Answer: 11/12

Worked Example: 5/6 - 1/4

1. Common denominator: LCM of 6 and 4 = 12
2. Convert: 5/6 = 10/12, 1/4 = 3/12
3. Subtract: 10/12 - 3/12 = 7/12

Answer: 7/12

---

Multiplying and Dividing Fractions

Multiplying

Multiply the numerators together and the denominators together:

2/3 × 4/5 = (2 × 4) / (3 × 5) = 8/15

Dividing (Keep, Flip, Multiply)

To divide by a fraction, flip the second fraction and multiply:

3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8

---

Finding a Fraction of an Amount

Divide by the denominator, then multiply by the numerator:

Find 3/8 of 240:

• 240 ÷ 8 = 30
• 30 × 3 = 90

Answer: 90

CEM Tip: In the CEM exam, fraction-of-an-amount questions often appear in word problems. Read carefully to identify what fraction and what amount you are working with.

---

Decimals

Place Value in Decimals