Maths shelf · Class 7
Tara's market receipt
Three kites and bags: one receipt says ₹29, another says ₹39. Both are right. How?
What you will learn: Write an arithmetic expression for a real bill, use brackets for the part that repeats, and turn it into a rule with a letter-number like 8n + 5.
What should I know first?
If this feels new, try this first. It is fine to go back.
- Which pack is the better buy? Class 5
Small test at the end: scroll down to the end of this page for five short questions that check what you have learnt. Tap an answer, then press Check answer. Go to the questions ↓
Jump to: Check yourself · For grown-ups · For teachers
Safety first
Fly kites only in open spaces, far from wires and roads, with a grown-up.
Keep it safe:
- Fly kites only in open spaces, far from electric wires, roofs without walls and roads, and never with glass-coated (manja) string.
- If you use coins or counters to act out the bill, keep them away from babies: nothing goes in the mouth.
You will need
- Paper and a pencilFor receipts and expressions.
- Counters or slips of paperTo stand for kites and bags.
- A real shop bill, if you have oneTo find what repeats and what is paid once.
Time: About 40 minutes.
What do you think?
Tara paid ₹29 and Tanmay paid ₹39 for three kites each. Has the shop made a mistake?
Make a prediction and write one reason for it. Then tap the guess closest to yours to see how to test it. It is fine to change your mind after checking.
Yes, one of them was cheated
Let's check. Act it out with counters: three kites, and the bags each of them took. Add up both bills.
No, they bought different things
What was different? Write each bill as a sum, kite by kite and bag by bag.
I need more information
What would you ask the shopkeeper? Find what was paid once and what was paid three times.
Not sure
That is fine. Write each bill as a sum, item by item, and compare the two.
Need a hint?
Count the bags. Did each of them buy one bag or three?
The story
Tara and Tanmay buy kites at the market for Sankranti. Each kite costs ₹8 and a paper bag costs ₹5. Tara's receipt says ₹29. Tanmay's says ₹39. "We both bought three kites!" says Tanmay. "The shop has cheated one of us." Dhruv looks at the two receipts. "Wait. Tara, how many bags did you take?" "One. I put all three kites in it." Tanmay looks at his three bags.
The idea
An expression is a way of writing a calculation, like 3 × 8 + 5.
The rule: do multiplication and division before addition and subtraction, unless there are brackets. So 3 × 8 + 5 = 24 + 5 = 29.
Brackets are worked out first. 3 × (8 + 5) means "three lots of (a kite and a bag)": 3 × 13 = 39.
When the number of kites can change, call it n. One shared bag: 8n + 5. A bag each: 13n, which is the same as 8n + 5n.
Worked example
Writing both receipts
Write an expression for each receipt and work it out.
- Tara: three kites and one bag. 3 × 8 + 5.
- Multiply first: 24 + 5 = 29.
- Tanmay: three lots of (kite and bag). 3 × (8 + 5).
- Brackets first: 3 × 13 = 39.
Tara's bill is ₹29 and Tanmay's is ₹39. The extra ₹10 is two more bags.
Try it
Act it out.
Use counters for kites and slips for bags. Lay out Tara's shopping and Tanmay's.
Write the long sum.
Write each bill item by item: 8 + 8 + 8 + 5, and 8 + 5 + 8 + 5 + 8 + 5.
Shorten it.
Turn repeated adding into multiplication. Put brackets around the part that repeats.
Check the order.
Work out 3 × 8 + 5 and 3 × (8 + 5). Which one needs brackets, and why?
Make a rule.
Fill in the table for 1, 2, 3, 4 and 5 kites with one bag. Write the rule with n for the number of kites.
Work backwards.
A receipt says ₹61 for some kites and one bag. How many kites? Use the rule.
What you make (paper or offline)
Your receipt card
Make a receipt card for a shop you know: a price for each thing, plus one charge paid once.
Write the expression for 5 and 6 things, then the rule with n.
Give it to someone and ask them to find the cost of 10.
Make it on paper. Keep it with you. Nothing to upload.
What did we find out?
Read this after you have tried it. Look back at your guess and your reason first.
Tara paid for 3 kites and 1 bag: 3 × 8 + 5 = 29.
Tanmay paid for 3 kites and 3 bags: 3 × (8 + 5) = 39.
Brackets show what repeats. Without brackets, multiply before you add.
For any number of kites n with one shared bag, the cost is 8n + 5.
Check yourself
Five questions about what this page teaches. Choose an answer and press Check answer, or open "See the answer and why". Nothing is saved or sent: your choices stay on this screen and disappear when you leave or reload the page.
How do you want to answer? You choose, and you can change at any time.
Stuck? Open one hint at a time.
Help me understand the question
There are two operations here, × and +. Which one comes first when there are no brackets?
Show me a picture
Think of a bill: 3 kites at ₹8 each, and then one ₹5 bag.
Help me choose the first step
Do the multiplication first: 3 × 8. Then add.
Show me a worked example
A different one: 2 × 5 + 4. Multiply first: 2 × 5 = 10. Then add 4: 14.
Now try the question again on your own.
See the answer and why
- A. 39 Not this one. That adds 8 + 5 first. Without brackets, multiply before adding.Common mix-up: Added before multiplying. Without brackets, multiply or divide before you add or subtract. On a bill, 3 × 8 + 5 means three kites at ₹8, then one bag. Read "The idea" again
- B. 120 Not this one. That multiplies all three numbers. The 5 is added, not multiplied.Common mix-up: One sign for every number. Each sign belongs to the numbers on either side of it. Read it like a bill: what is multiplied, and what is added once? Read "The idea" again
- C. 16 Not this one. That adds all three numbers. The 3 multiplies the 8.Common mix-up: One sign for every number. Each sign belongs to the numbers on either side of it. Read it like a bill: what is multiplied, and what is added once? Read "The idea" again
- D. 29 Correct. Multiply first: 3 × 8 = 24, then add 5.
Stuck? Open one hint at a time.
Help me understand the question
Each kite has its own bag. What repeats three times: the kite, the bag, or both together?
Show me a picture
Draw three boxes. Put one kite and one bag in each box.
Help me choose the first step
Write the cost of one box first: 8 + 5. Then ask how many boxes there are.
Show me a worked example
A different order: 4 plates, each with a ₹10 samosa and ₹2 chutney, cost 4 × (10 + 2).
Now try the question again on your own.
See the answer and why
- A. 3 × 8 + 5 Not this one. This has only one bag, like Tara's receipt.Common mix-up: What do the brackets hold? Brackets hold the part that repeats, as one group. 3 × (8 + 5) is three kite-and-bag sets; 3 × 8 + 5 is three kites and only one bag. Read "The idea" again
- B. 3 × (8 + 5) Correct. Each kite comes with a bag, so "kite and bag" repeats three times.
- C. 8 + 5 × 3 Not this one. This is one kite and three bags.Common mix-up: What do the brackets hold? Brackets hold the part that repeats, as one group. 3 × (8 + 5) is three kite-and-bag sets; 3 × 8 + 5 is three kites and only one bag. Read "The idea" again
- D. 3 + 8 + 5 Not this one. This adds the number of kites to the prices.Common mix-up: One sign for every number. Each sign belongs to the numbers on either side of it. Read it like a bill: what is multiplied, and what is added once? Read "The idea" again
Stuck? Open one hint at a time.
Help me understand the question
n is the number of kites. The bag is shared, so how many times is the bag paid for?
Show me a picture
Try it with n = 2: two kites and one bag. Write down what that costs.
Help me choose the first step
The part that repeats is multiplied by n. The part paid once is added once.
Show me a worked example
A different rule: an auto charges ₹30 to start and ₹12 for each km. For k km the fare is 12k + 30.
Now try the question again on your own.
See the answer and why
- A. 13n Not this one. This is a bag with every kite.Common mix-up: Paid once, or for every item? Ask which cost comes with every kite (multiply it by n) and which is paid only once (add it once). Read "The idea" again
- B. 8 + 5n Not this one. This is one kite and n bags.Common mix-up: Paid once, or for every item? Ask which cost comes with every kite (multiply it by n) and which is paid only once (add it once). Read "The idea" again
- C. 8n + 5 Correct. n kites at 8 each is 8n, and the bag is paid once: + 5.
- D. 8(n + 5) Not this one. This would be the cost of n + 5 kites.Common mix-up: What do the brackets hold? Brackets hold the part that repeats, as one group. 3 × (8 + 5) is three kite-and-bag sets; 3 × 8 + 5 is three kites and only one bag. Read "The idea" again
Stuck? Open one hint at a time.
Help me understand the question
Put n = 4 into the rule 8n + 5.
Show me a picture
8n means 8 × n: four kites at ₹8 each, and then the bag.
Help me choose the first step
Work out 8 × 4 first, then add the bag.
Show me a worked example
A different number: with 8n + 5 and n = 2, the cost is 8 × 2 + 5 = 16 + 5 = ₹21.
Now try the question again on your own.
See the answer and why
- A. ₹52 Not this one. That is 13 × 4, a bag with every kite.Common mix-up: Paid once, or for every item? Ask which cost comes with every kite (multiply it by n) and which is paid only once (add it once). Read "The idea" again
- B. ₹72 Not this one. That is 8 × (4 + 5). The 5 is not inside the brackets.Common mix-up: What do the brackets hold? Brackets hold the part that repeats, as one group. 3 × (8 + 5) is three kite-and-bag sets; 3 × 8 + 5 is three kites and only one bag. Read "The idea" again
- C. ₹37 Correct. 8 × 4 + 5 = 32 + 5 = 37.
- D. ₹17 Not this one. That is 8 + 4 + 5. 8n means 8 × n.Common mix-up: 8n means 8 × n. A number written next to a letter means multiply: 8n is 8 × n, not 8 + n. Read "The idea" again
Stuck? Open one hint at a time.
Help me understand the question
You know the total, ₹61. You want to find n, the number of kites.
Show me a picture
Write it as a bill: 8 × (number of kites) + 5 = 61. The bag is already inside the 61.
Help me choose the first step
Take off the part paid once first: 61 − 5. Then share what is left between ₹8 kites.
Show me a worked example
A different receipt: ₹45 for some ₹8 kites and one ₹5 bag. 45 − 5 = 40, and 40 ÷ 8 = 5 kites.
Now try the question again on your own.
See the answer and why
- A. 8 Not this one. 61 ÷ 8 is about 7.6. Taking off the ₹5 bag first gives exactly 7.Common mix-up: Undo in reverse order. To work backwards from a total, undo the last step first: take off the + 5, then divide by 8. Read "The idea" again
- B. 7 Correct. Take off the bag: 61 − 5 = 56. Then 56 ÷ 8 = 7 kites.
- C. 6 Not this one. 6 kites and a bag cost 8 × 6 + 5 = ₹53, not ₹61.
- D. 4 Not this one. 61 ÷ 13 assumes a bag with every kite, and it does not divide exactly.Common mix-up: Paid once, or for every item? Ask which cost comes with every kite (multiply it by n) and which is paid only once (add it once). Read "The idea" again
Think back
How do brackets change what an expression means?
Why does the 5 appear once in 8n + 5, but the 8 is multiplied by n?
Investigate further
- An auto-rickshaw charges ₹30 to start and ₹12 for each km. Write the rule for k km.
- Write two different expressions that both equal 39, one with brackets and one without.
Can you use it here?
Look at an electricity, phone or tuition bill at home. What part is paid once, and what part repeats?
Ask someone at home
Ask someone at home to buy (or pretend to buy) a few things with one bag, then with a bag each. Write both expressions.
No one free to join in? That's fine. You can do it by yourself with drawings, and ask a grown-up to help with the materials.
For grown-upsTap a heading to open it. The safety notes are at the top of the page.
Before you start
- Paper, a pencil, and counters or slips. Keep coins and counters away from babies; nothing in the mouth.
- A real bill helps: tuition, phone or electricity.
Questions that help
- "What is paid once? What repeats?"
- "Where do the brackets go, and why?"
- "Can you work backwards from the total?"
What's really going on
Children often work left to right (3 × 8 + 5 as 3 × 13) or add first. The real bill shows why the order rule makes sense.
Brackets are not decoration: they change which part repeats.
Replacing "how many" with a letter n is the first step into algebra: the rule works for any number.
Other ways to do it
- No counters? Use spoons for kites and cups for bags.
- Try samosas at ₹12 each and a ₹4 plate charge.
For teachersLearning aims, classroom ideas and what to look for.
Learning aims
- Write and evaluate arithmetic expressions with and without brackets.
- Explain the order of operations in a real context.
- Write a simple rule with a letter-number and use it forwards and backwards.
Subject links
- NCERT Class 7 Ganita Prakash: Arithmetic Expressions; Expressions using Letter-Numbers.
- Class 7 activity "Growing patterns" (rules from patterns).
- Money and best buys (Class 5).
These links are general. They have not been checked against a specific board syllabus.
In the classroom
- A pretend shop: groups write receipts for each other's orders and swap them to check.
- Give totals and ask for every possible shopping list that fits.
What to look for
- Places brackets around what repeats.
- Explains why 3 × 8 + 5 is not 39.
- Uses the rule backwards to find n.