A word problem is a mathematics question written in the form of a story or real-life situation, instead of just numbers and symbols.

It describes a scenario you might face in everyday life—like sharing food, measuring ingredients, or keeping track of money—and asks you to solve it using math.

• It is written in sentences instead of only equations.


• You must understand the story, pick out the important numbers, and decide which operation (addition, subtraction, multiplication, or division) to use.

1. They connect math to real life.


2. Students learn to translate language into mathematical steps.


3. Many exam and class questions are word problems.

1. Read carefully — understand what the problem is asking.


2. Underline / identify fractional parts — write them as fractions.


3. Decide whether you’re doing addition or subtraction (or both).


4. Find a common denominator (if needed) — usually the LCM.


5. Convert fractions to equivalent fractions with that denominator.


6. Add or subtract the numerators.


7. Simplify the resulting fraction if possible.


8. Answer in context — write the answer with units or in fraction / mixed number form.


9. Check if your answer makes sense in the context (e.g. you don’t get more than the whole when adding parts that shouldn’t exceed).

Cake Sharing

A cake was cut into 8 equal slices. Mary ate 3/8 and John ate 2/8. How much of the cake was eaten in total?

Workings: 3/8 + 2/8 = 5/8

Answer: 5/8 of the cake.

Milk in Jugs

A jug had 5/6 litre of milk. Then 1/4 litre was poured in. What is the new quantity?

Workings: LCM(6,4)=12 → 5/6 = 10/12, 1/4 = 3/12. 10/12 + 3/12 = 13/12 = 1 1/12 litres.

Answer: 1 1/12 litres.

Walking Distance

Tina walked 7/10 km and then 3/5 km more. How much did she walk in total?

Workings: 3/5 = 6/10. 7/10 + 6/10 = 13/10 = 1 3/10 km.

Answer: 1 3/10 km.

Filling Tanks

Tank A is 2/3 full, and Tank B is 3/4 full. Together, how many full tanks do they make?

Workings: LCM(3,4)=12 → 2/3 = 8/12, 3/4 = 9/12. 8/12 + 9/12 = 17/12 = 1 5/12 tanks.

Answer: 1 5/12 tanks.

Recipe Ingredients

Recipe calls for 3/5 cup of flour and 2/7 cup of sugar, plus 1/10 cup more flour. What is the total flour + sugar?

Workings: First total flour: 3/5 + 1/10. LCM(5,10)=10 → 3/5 = 6/10. 6/10 + 1/10 = 7/10. Then add sugar: 7/10 + 2/7. LCM(10,7)=70 → 7/10 = 49/70, 2/7 = 20/70. 49/70 + 20/70 = 69/70.

Answer: 69/70 cups.

Bead Making

Jane uses 4/9 of bead string on one design and 1/6 on another. How much string used in total?

Workings: LCM(9,6)=18 → 4/9 = 8/18, 1/6 = 3/18. 8/18 + 3/18 = 11/18.

Answer: 11/18 of string.

Garden Plots

One plot is 5/12 hectare, another is 7/18. Combined area?

Workings: LCM(12,18)=36 → 5/12 = 15/36, 7/18 = 14/36. 15/36 + 14/36 = 29/36 hectare.

Answer: 29/36 hectare.

Juice Serving

A jug contains 11/15 litre of juice. Another jug has 2/5 litre. How much together?

Workings: LCM(15,5)=15 → 2/5 = 6/15. 11/15 + 6/15 = 17/15 = 1 2/15 litres.

Answer: 1 2/15 litres.

Paper Use

A printer used 3/8 ream and then 5/16 ream more. How much used in total?

Workings: LCM(8,16)=16 → 3/8 = 6/16. 6/16 + 5/16 = 11/16 ream.

Answer: 11/16 ream.

Time Spent

A student studied 5/6 hour and then 1/4 hour more. Total study time?

Workings: LCM(6,4)=12 → 5/6 = 10/12, 1/4 = 3/12. 10/12 + 3/12 = 13/12 = 1 1/12 hour.

Answer: 1 1/12 hour.

Cookies Eaten

John ate 2/7 of cookies; Mary ate 3/14. What fraction was eaten in total?

Workings: LCM(7,14)=14 → 2/7 = 4/14. 4/14 + 3/14 = 7/14 = 1/2.

Answer: 1/2 of the cookies.

Land Sharing

Plots of land: 3/10 and 2/15. Combined?

Workings: LCM(10,15)=30 → 3/10 = 9/30, 2/15 = 4/30. 9/30 + 4/30 = 13/30.

Answer: 13/30 of land.

Cake Leftover

A cake was cut into 8 slices. Mary ate 3/8. How much remains?

Workings: 8/8 − 3/8 = 5/8.

Answer: 5/8 of the cake remains.

Milk Left

A jug had 7/10 litre. 2/5 litre was used. How much left?

Workings: 2/5 = 4/10. 7/10 − 4/10 = 3/10.

Answer: 3/10 litre left.

Distance Remaining

A runner must run 2 km. He ran 5/6 km. How many km remain?

Workings: 2 km = 12/6. 12/6 − 5/6 = 7/6 = 1 1/6 km.

Answer: 1 1/6 km left.

Fuel Left

A tank holds 1 litre. Already used 3/4. What remains?

Workings: 1 = 4/4. 4/4 − 3/4 = 1/4 litre.

Answer: 1/4 litre remains.

Paper Remaining

Printer used 2/5 ream from 1 ream. How much left?

Workings: 1 = 5/5. 5/5 − 2/5 = 3/5 ream.

Answer: 3/5 ream remains.

Land Left

Farm had 7/12 hectare; sold 1/4. How much remains?

Workings: 1/4 = 3/12. 7/12 − 3/12 = 4/12 = 1/3 hectare.

Answer: 1/3 hectare remains.

Time Left

Hour = 60/60. Used 3/4 hour. How much time remains?

Workings: 3/4 = 45/60. 60/60 − 45/60 = 15/60 = 1/4 hour (15 minutes).

Answer: 1/4 hour = 15 minutes left.

Chocolate Bar

You had 1 bar. You ate 3/10. How much remains?

Workings: 1 = 10/10. 10/10 − 3/10 = 7/10.

Answer: 7/10 of the bar remains.

Book Pages Left

Book has 200 pages. You read 3/5 of it. How many pages left?

Workings: 3/5 × 200 = 120. 200 − 120 = 80 pages. 80/200 = 4/10 = 2/5.

Answer: 2/5 of the book remains (80 pages).

Juice Remaining

You had 5/6 litre. Drank 1/8. How much remains?

Workings: LCM(6,8)=24 → 5/6 = 20/24, 1/8 = 3/24. 20/24 − 3/24 = 17/24.

Answer: 17/24 litre remains.

Beads Left

You used 4/9 of beads from full string. How much is left?

Workings: 1 = 9/9. 9/9 − 4/9 = 5/9.

Answer: 5/9 of the beads remain.

Water Remaining

Tank had 1 litre. Used 3/7 litre. What remains?

Workings: 1 = 7/7. 7/7 − 3/7 = 4/7 litre.

Answer: 4/7 litre remains.

1. Label your fractions (e.g. “ate”, “left”, “used”).


2. Write what is the “whole” when needed (1 = whole = fraction with that denominator).


3. Always convert to same denominator before adding/subtracting.


4. After answer, interpret: “5/8 of the cake remains” etc.


5. Check your final answer in the context: you cannot have more than whole when subtracting parts, etc.