Simple Word Problems Involving Operations

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Word problems present mathematical situations in everyday language. Your task is to translate the words into mathematical operations (addition, subtraction, multiplication, division) and then solve. The key skill is identifying which operation to use.

Keywords That Signal Operations:

Operation	Keywords to Look For
Addition (+)	sum, total, plus, add, combined, together, in all, how many altogether, increased by, more than
Subtraction (−)	difference, minus, subtract, less, decreased by, remaining, left, how many more, how many fewer, lost, spent
Multiplication (×)	product, multiply, times, groups of, each, repeated addition, at the same rate
Division (÷)	quotient, divide, share equally, split, groups of, each gets, how many groups, average

Translating Words to Operations:

Word Statement	Mathematical Operation
”The sum of 5 and 7”	$5 + 7$
“12 minus 5”	$12 - 5$
“4 multiplied by 6”	$4 \times 6$
“20 divided by 4”	$20 \div 4$
“5 more than a number”	$x + 5$
“A number decreased by 3”	$x - 3$
“Twice a number”	$2x$
“Half of a number”	$x/2$
“The product of 4 and a number”	$4x$

Basic Problem Types:

1. Combine/Add: Two or more quantities are put together “Chidi has 12 apples and buys 8 more. How many does he have?” $12 + 8 = 20$

2. Take Away/Subtract: One quantity is removed from another “Ada had 25 sweets and gave 9 to her friend. How many does she have left?” $25 - 9 = 16$

3. Repeated Groups (Multiply): Same quantity repeated “There are 7 boxes with 5 pencils in each box. How many pencils altogether?” $7 \times 5 = 35$

4. Share Equally (Divide): Splitting into equal groups “30 oranges are shared equally among 6 children. How many does each child get?” $30 \div 6 = 5$

⚡ Exam Tip (NCEE): The most common error is choosing the wrong operation. When you finish reading the problem, ask yourself: “Am I joining quantities together, taking one away from another, repeating groups of the same size, or splitting into equal parts?” If the answer is “joining” → add. “Taking away” → subtract. “Repeating” → multiply. “Splitting” → divide.

⚡ NCEE Strategy: Read the problem twice. The first time, understand what is happening. The second time, identify the numbers and what is being asked. Write down the numbers and the operation before solving.

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding of problem-solving.

Two-Step Word Problems:

These problems require two operations to solve.

Example: “A farmer has 45 chickens. He buys 3 more cages with 8 chickens in each cage. How many chickens does he have now?”

Step 1: Chickens from new cages: $3 \times 8 = 24$ Step 2: Total chickens: $45 + 24 = 69$

Example: “Tolu has 120 stickers. She gives 25 to her sister and then puts the remaining stickers into 5 equal piles. How many stickers in each pile?”

Step 1: Stickers remaining: $120 - 25 = 95$ Step 2: Stickers per pile: $95 \div 5 = 19$

Worked Examples:

Example 1 — Buying items: “Emeka buys 4 notebooks at ₦250 each and 3 pens at ₦80 each. How much change does he get from ₦2,000?”

Step 1: Cost of notebooks: $4 \times 250 = ₦1,000$ Step 2: Cost of pens: $3 \times 80 = ₦240$ Step 3: Total cost: $1,000 + 240 = ₦1,240$ Step 4: Change: $2,000 - 1,240 = ₦760$

Example 2 — Age problems: “Tunde is 12 years old. His sister is 4 years younger. Their mother is 3 times Tunde’s age. How old is their mother?”

Tunde’s age: 12 years Sister’s age: $12 - 4 = 8$ years Mother’s age: $3 \times 12 = 36$ years

Example 3 — Distance and sharing: “A rope 48 metres long is cut into 6 equal pieces. 2 pieces are used for a project. How many metres of rope are left?”

Step 1: Length of each piece: $48 \div 6 = 8$ metres Step 2: Used pieces: $2 \times 8 = 16$ metres Step 3: Remaining: $48 - 16 = 32$ metres

Units and Conversions:

Always keep track of units:

• ₦ = Naira, k = kobo (100 kobo = ₦1)
• kg = kilogram, g = gram (1000g = 1kg)
• km = kilometre, m = metre (1000m = 1km)
• litres: l, ml (1000ml = 1l)

⚡ Common NCEE Error: Not writing the unit in the answer. A question asking “How many metres…” requires “metres” as part of the answer. Without the unit, the answer is incomplete and may lose marks.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Multi-Step Word Problems:

When a problem has more than two operations:

Example: “A school orders 8 cartons of exercise books. Each carton has 20 books. Each book has 50 pages. How many pages are there in all the books?”

Step 1: Total books: $8 \times 20 = 160$ books Step 2: Total pages: $160 \times 50 = 8,000$ pages

Average Problems:

Average (Mean) = Sum of values ÷ Number of values

Example: “The marks scored by Chidi in 5 subjects are: 72, 85, 60, 90, and 78. What is his average mark?”

Average $= (72 + 85 + 60 + 90 + 78) \div 5 = 385 \div 5 = 77$

To find the sum when average is given: Sum = Average × Number of items “If a student’s average mark over 4 exams is 75, what was the total of his marks?” Total $= 75 \times 4 = 300$

Rate Problems:

Example: “A car travels 240 km in 4 hours. What is its average speed?” Speed = Distance ÷ Time = $240 \div 4 = 60$ km/h

Distance = Speed × Time — “If a cyclist rides at 15 km/h for 3 hours, how far does he travel?” Distance $= 15 \times 3 = 45$ km

Time = Distance ÷ Speed — “How long does it take to travel 180 km at 60 km/h?” Time $= 180 \div 60 = 3$ hours

Percentage Word Problems:

Example: “A jacket costs ₦4,000. It is sold at a discount of 15%. What is the sale price?”

Discount amount: $15%$ of $4,000 = (15/100) \times 4,000 = ₦600$ Sale price: $4,000 - 600 = ₦3,400$

OR: Sale price $= 4,000 \times (1 - 15/100) = 4,000 \times 0.85 = ₦3,400$

Profit and Loss:

Example: “A trader buys a basket of tomatoes for ₦5,000 and sells them for ₦6,500. What is the profit and profit percentage?”

Profit = Selling Price - Cost Price = $6,500 - 5,000 = ₦1,500$ Profit % = (Profit ÷ Cost Price) × 100 = $(1,500/5,000) \times 100 = 30%$

⚡ Extended Tip — Using Variables in Word Problems: When problems become complex, introduce variables:

“The price of 3 books and 2 pens is ₦1,400. If a book costs ₦400, what is the cost of one pen?”

Let $p$ = cost of one pen $3(400) + 2p = 1,400$ $1,200 + 2p = 1,400$ $2p = 200$ $p = ₦100$

This approach is particularly useful when the NCEE includes algebra-based word problems.

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