Multi-Step Word Problems

Multi-step word problems are one of the most challenging parts of the CEM 11+ maths paper. They require you to read carefully, plan your approach, and carry out several calculations in sequence. CEM deliberately uses word problems to test whether you truly understand maths, not just whether you can follow a procedure.

---

Why Word Problems Are Important in CEM

CEM papers are known for their emphasis on problem-solving. Unlike papers that give you a straightforward calculation, CEM questions wrap maths inside real-life stories. You need to:

1. Understand what the question is really asking
2. Identify the mathematical operations required
3. Carry out the steps in the right order
4. Check your answer makes sense

CEM Exam Insight: CEM word problems often mix topics — for example, a single question might involve fractions, money, and division. You must be flexible and ready to use any skill from your toolkit.

---

A Step-by-Step Approach

Use this method for every word problem:

Step 1: Read the Question Twice

Read it once to get the gist. Read it again to identify the key information and the question being asked. Underline or circle important numbers and words.

Step 2: Decide What Operations to Use

Look for clue words:

Clue Words	Operation
total, altogether, sum, combined	Addition
difference, how many more, left	Subtraction
each, per, every, times	Multiplication
share, divide, split, each gets	Division
of (as in "1/3 of")	Multiplication
how many groups, how many fit	Division

Step 3: Work Through Each Step

Write down each calculation clearly. Keep intermediate answers neat.

Step 4: Check Your Answer

• Does it make sense in context?
• Have you answered the actual question asked?
• Can you estimate to verify?

---

Worked Examples

Example 1: Fractions and Money

A baker makes 180 cakes. He sells 2/3 in the morning and 1/4 of the remainder in the afternoon. How many cakes are left?

• Morning sales: 2/3 of 180 = 120 cakes sold
• Remaining after morning: 180 - 120 = 60 cakes
• Afternoon sales: 1/4 of 60 = 15 cakes sold
• Cakes left: 60 - 15 = 45 cakes

Example 2: Division with Remainders

48 children need to travel by minibus. Each minibus holds 15 children. How many minibuses are needed?

• 48 ÷ 15 = 3 remainder 3
• 3 minibuses carry 45 children, leaving 3 behind
• You need one more minibus for the remaining children
• Answer: 4 minibuses

Important: When the question asks "how many are needed", you must always round up, because you cannot have part of a minibus!

Example 3: Ratio and Spending