CBSE Class 7 Mathematics Arithmetic Expressions Worksheet Set 01

Long Answer Questions

Question 1. Answer the following about simple expressions.
(i) Explain what an arithmetic expression is and what is meant by its value. Give one example with its value.
(ii) Write five different expressions, each using two numbers, whose value is 36. Use all four operations +, −, × and ÷ at least once among them.
(iii) Meera saves ₹45 every day for 7 days. Write an expression for her total saving, read the expression in words and find its value.
Answer:
(i) An arithmetic expression is a mathematical phrase made of numbers joined by the operations +, −, × and ÷, such as 18 ÷ 3. Its value is the single number it works out to; the value of 18 ÷ 3 is 6, and we write 18 ÷ 3 = 6.
(ii) 30 + 6 = 36; 40 − 4 = 36; 4 × 9 = 36; 72 ÷ 2 = 36; 20 + 16 = 36. Different expressions can have the same value, so many more can be written.
(iii) Total saving = 7 × 45. It is read as “7 times 45” or “the product of 7 and 45”. Its value is 315, so Meera saves ₹315.
In simple words: An expression gives one value, and many expressions can give the same value.

Teacher's Note:
1. Use every operation at least once in (ii).
2. Read an expression in words in two ways.

Question 2. Study the idea of terms in an expression and answer.
(i) What are the terms of an expression? Explain how a subtraction in an expression is handled while writing the terms.
(ii) Write each of the following as a sum of its terms and list the terms: (a) 25 − 9 + 4, (b) 8 × 3 − 15, (c) 50 − 6 × 4 + 12.
(iii) Find the value of each of the three expressions in part (ii).
Answer:
(i) The terms of an expression are the parts separated by a + sign. A subtraction is first changed into an addition, because subtracting a number is the same as adding its inverse. So 83 − 14 = 83 + (−14), and its terms are 83 and −14. The sign always travels with the term.
(ii) (a) 25 − 9 + 4 = 25 + (−9) + 4; terms: 25, −9, 4.
(b) 8 × 3 − 15 = (8 × 3) + (−15); terms: 8 × 3, −15.
(c) 50 − 6 × 4 + 12 = 50 + (−6 × 4) + 12; terms: 50, −6 × 4, 12.
(iii) (a) 25 − 9 + 4 = 20; (b) 24 − 15 = 9; (c) 50 − 24 + 12 = 38.
Each term is evaluated first, and then all the terms are added.
In simple words: Write subtractions as adding negatives; then each term is worked out and added.

Teacher's Note:
1. Products stay as single terms.
2. Keep the sign with each term.

Question 3. Brackets tell us what to do first.
(i) State the rule that is followed when an expression contains brackets.
(ii) Find the values of 12 + (8 × 5), (12 + 8) × 5, 100 − (36 + 24) and (100 − 36) + 24.
(iii) Irfan buys a pencil box for ₹28 and a geometry set for ₹47, and pays the shopkeeper with a ₹100 note. Write an expression with brackets for the change he gets, find it, and explain why writing 100 − 28 + 47 would be wrong.
Answer:
(i) When an expression has brackets, the expression inside the brackets is worked out first, and only then are the other operations carried out.
(ii) 12 + (8 × 5) = 12 + 40 = 52; (12 + 8) × 5 = 20 × 5 = 100; 100 − (36 + 24) = 100 − 60 = 40; (100 − 36) + 24 = 64 + 24 = 88.
(iii) Total bill = 28 + 47, so change = 100 − (28 + 47) = 100 − 75 = ₹25.
100 − 28 + 47 = 72 + 47 = 119, which is more than the money he gave. That is absurd: the cost of the geometry set must also be taken away, so the bracket is necessary.
In simple words: Brackets are done first, and they decide which numbers are taken away.

Teacher's Note:
1. Same numbers, different brackets, different values.
2. A change can never be more than the money paid.

Question 4. Answer the following about swapping and grouping the terms of an expression.
(i) State the commutative property of addition and the associative property of addition in your own words.
(ii) Add the terms of the expression 15 − 8 + 6 in three different orders and show that the value is the same each time.
(iii) A shopkeeper added a long list of bills and got ₹4,382. He then found that he had left out one bill of ₹1,250. Must he add the whole list again? Give a reason and write the correct total.
Answer:
(i) Commutative property: if two terms are swapped, the sum does not change. Associative property: if the terms are grouped in different ways, the sum again does not change. Together they mean the terms may be added in any order.
(ii) 15 − 8 + 6 = 15 + (−8) + 6.
15 + (−8) + 6 = 7 + 6 = 13
(−8) + 6 + 15 = (−2) + 15 = 13
6 + 15 + (−8) = 21 − 8 = 13
The value is 13 every time.
(iii) No. Since terms can be added in any order and grouping, he can simply add the left-out bill to the total he already has: 4382 + 1250 = 5632. The correct total is ₹5,632.
In simple words: Order and grouping of terms do not change a sum.

Teacher's Note:
1. Keep −8 together as one term.
2. Add the missing bill to the old total.

Question 5. In a school assembly display the children stand in 6 equal rows. In each row there are 9 girls followed by 7 boys, as shown.
(i) Write one expression for the number of girls and one for the number of boys, and find each value.
(ii) Write two different expressions for the total number of children, one using the number of rows and the other using the two separate groups. Show that both expressions have the same value.
(iii) Name the property you have used and apply the same idea to find 6 × 48 quickly, writing every step.
Answer:
(i) Girls = 6 × 9 = 54; boys = 6 × 7 = 42.
(ii) Counting the two groups separately: 6 × 9 + 6 × 7 = 54 + 42 = 96.
Counting each row as a whole: 6 × (9 + 7) = 6 × 16 = 96.
Both give 96 children, so 6 × (9 + 7) = 6 × 9 + 6 × 7.
(iii) This is the distributive property: a multiple of a sum is the sum of the multiples. It also works for a difference. Using 48 = 50 − 2:
6 × 48 = 6 × (50 − 2) = 6 × 50 − 6 × 2 = 300 − 12 = 288.
This is quicker because 6 × 50 and 6 × 2 can be done mentally.
In simple words: Counting by rows or by groups gives the same total; this is the distributive property.

Teacher's Note:
1. Read the picture as rows and as groups.
2. Choose a round number near 48.

Question 6. Brackets with a sign in front of them.
(i) Remove the brackets and find the value of each: (a) 85 − (32 + 17), (b) 85 − (32 − 17), (c) 85 + (32 − 17).
(ii) State clearly the rule about the signs of the terms inside a bracket when the bracket is preceded by a minus sign, and when it is not.
(iii) Explain, using a simple money situation, why 500 − (250 − 100) is equal to 500 − 250 + 100 and not to 500 − 250 − 100.
Answer:
(i) (a) 85 − (32 + 17) = 85 − 32 − 17 = 53 − 17 = 36.
(b) 85 − (32 − 17) = 85 − 32 + 17 = 53 + 17 = 70.
(c) 85 + (32 − 17) = 85 + 32 − 17 = 117 − 17 = 100.
(ii) When a bracket is preceded by a minus sign, every term inside changes its sign on removing the bracket: a + term becomes a − term and a − term becomes a + term. When the bracket is not preceded by a minus sign, the terms keep their signs.
(iii) Suppose Sita has ₹500 and gets a bill of ₹250, on which a discount of ₹100 is given. She pays 250 − 100, so the money left is 500 − (250 − 100) = 500 − 150 = 350.
If she took away the whole ₹250, she would have taken ₹100 too much, so ₹100 must be added back: 500 − 250 + 100 = 350. The form 500 − 250 − 100 = 150 takes the discount away twice, so it is wrong.
In simple words: A minus before a bracket flips every sign inside it.

Teacher's Note:
1. Check each answer by working out the bracket first.
2. A discount reduces the bill, so it is added back.

Question 7. Tinkering with the terms of an expression.
(i) It is given that 72 − 25 + 38 = 85. Doing as little calculation as possible, find the values of 73 − 25 + 38, 72 − 26 + 38 and 72 − 25 + 40. Give a reason for each.
(ii) Write in your own words the rule you used in part (i).
(iii) It is given that 54 × 16 = 864. Using the idea of multiples of a sum or a difference, find 64 × 16 and 53 × 16 without doing the full multiplication.
Answer:
(i) 73 − 25 + 38 = 86, because the first term is 1 more than before.
72 − 26 + 38 = 84, because the term −26 is 1 less than −25.
72 − 25 + 40 = 87, because the last term is 2 more than before.
(ii) If one term of an expression is increased by some number, the value of the whole expression increases by that same number; if a term is decreased, the value decreases by that amount. Nothing else needs to be calculated again.
(iii) 64 × 16 = (54 + 10) × 16 = 54 × 16 + 10 × 16 = 864 + 160 = 1024.
53 × 16 = (54 − 1) × 16 = 54 × 16 − 1 × 16 = 864 − 16 = 848.
In simple words: Change one term and the value changes by the same amount.

Teacher's Note:
1. Watch the sign of the changed term.
2. Build new products from a known product.

Question 8. At a museum the entry ticket costs ₹60 for an adult and ₹25 for a child.
(i) Write an expression for the cost of tickets for 5 adults and 4 children, identify its terms and find the value.
(ii) Write an expression using brackets for the cost of tickets for 3 groups, each group having 2 adults, and find the value.
(iii) A family of 6 adults and 3 children pays with a ₹1000 note. Write an expression with brackets for the change they get back and find it.
Answer:
(i) Expression: 5 × 60 + 4 × 25. Its terms are 5 × 60 and 4 × 25. Value = 300 + 100 = ₹400.
(ii) Each group pays 2 × 60, and there are 3 groups: 3 × (2 × 60) = 3 × 120 = ₹360.
(iii) Cost of tickets = 6 × 60 + 3 × 25, so the change is
1000 − (6 × 60 + 3 × 25) = 1000 − (360 + 75) = 1000 − 435 = ₹565.
The bracket is needed so that both parts of the bill are subtracted.
In simple words: Write each kind of ticket as a term; subtract the whole bill from the note.

Teacher's Note:
1. Products are single terms.
2. Put the full bill inside a bracket after the minus.

Question 9. Expressions with a bracket inside another bracket.
(i) Evaluate 200 − [50 + (36 − 18) − 10] step by step, starting with the innermost bracket. Then write the expression without any brackets and check that the value is the same.
(ii) Evaluate 3 × [12 − (7 − 4)] in two ways: first by simplifying inside the brackets, and then by using the distributive idea.
(iii) Put brackets in the expression 48 − 12 − 6 + 2 so that its value becomes 44, and again so that its value becomes 28.
Answer:
(i) Innermost bracket: 36 − 18 = 18. Square bracket: 50 + 18 − 10 = 58. Whole expression: 200 − 58 = 142.
Without brackets, the minus before the square bracket changes every sign inside it: 200 − 50 − 36 + 18 + 10 = 150 − 36 + 18 + 10 = 142. Both ways give 142.
(ii) Inside first: 7 − 4 = 3, then 12 − 3 = 9, so the value is 3 × 9 = 27.
Distributing: 3 × 12 − 3 × (7 − 4) = 36 − 3 × 3 = 36 − 9 = 27.
(iii) For 44: 48 − (12 − 6) + 2 = 48 − 6 + 2 = 44.
For 28: 48 − 12 − (6 + 2) = 48 − 12 − 8 = 28.
Without any brackets the expression is 48 − 12 − 6 + 2 = 32, so the brackets really change the value.
In simple words: Work from the innermost bracket outwards, and brackets can change the value.

Teacher's Note:
1. The inner bracket keeps its own signs until the outer one is removed.
2. Check each answer after placing brackets.

Question 10. Reason your way through the following.
(i) Fill in <, > or = without evaluating, and justify each: (a) (24 − 9) × 15 and 24 × 15 − 9 × 15, (b) 36 × (20 + 5) and 36 × 20 + 5, (c) 77 − 18 × 4 and 77 − 18 × 3.
(ii) Explain the short method of subtracting 98 from a number and use it to find 643 − 98.
(iii) Be an expression engineer: using the digit 5 exactly three times each time, along with the operations +, −, ×, ÷ and brackets, write one expression with value 2, one with value 15 and one with value 30.
Answer:
(i) (a) (24 − 9) × 15 = 24 × 15 − 9 × 15; a multiple of a difference is the difference of the multiples.
(b) 36 × (20 + 5) > 36 × 20 + 5; on the left the whole 25 is taken 36 times, while on the right 5 is added only once (900 against 725).
(c) 77 − 18 × 4 < 77 − 18 × 3; the term −18 × 4 takes away more than −18 × 3, so less is left (5 against 23).
(ii) Since 98 = 100 − 2, subtracting 98 is the same as subtracting 100 and adding 2 back, because the minus before the bracket changes the sign of −2:
643 − 98 = 643 − (100 − 2) = 643 − 100 + 2 = 543 + 2 = 545.
(iii) Value 2: (5 + 5) ÷ 5 = 10 ÷ 5 = 2.
Value 15: 5 + 5 + 5 = 15.
Value 30: 5 × 5 + 5 = 25 + 5 = 30.
In simple words: Reason with terms and the distributive property instead of long calculations.

Teacher's Note:
1. Check each comparison with the actual values.
2. Other correct expressions in (iii) are fine too.

Case Study Based Questions

Question 11. A bill at the stationery shop. Nisha goes to a stationery shop before the new school term begins. She picks up 4 notebooks, and each notebook costs ₹35. She also picks up 3 gel pens, and each pen costs ₹12. At the counter she hands over a ₹500 note. The shopkeeper writes the whole bill as a single arithmetic expression so that he can check it quickly, and then works out the change he must return to Nisha. Nisha’s younger brother looks at the bill and says the change should be worked out as 500 − 140 + 36.
(i) Write an expression for the cost of the notebooks and find its value.
(ii) Write an expression for the total cost of all the items, list its terms and find the total cost.
(iii) Write an expression with brackets for the change Nisha gets back, and find it.
(iv) Is the brother’s expression 500 − 140 + 36 correct? Give the reason.
Answer:
(i) Cost of notebooks = 4 × 35 = ₹140.
(ii) Total cost = 4 × 35 + 3 × 12; its terms are 4 × 35 and 3 × 12. Value = 140 + 36 = ₹176.
(iii) Change = 500 − (4 × 35 + 3 × 12) = 500 − 176 = ₹324.
(iv) No. 500 − 140 + 36 = 396, because it adds the cost of the pens instead of subtracting it. The minus before the bracket changes both signs, giving 500 − 140 − 36 = 324.
In simple words: The whole bill must be taken away from ₹500.

Teacher's Note:
1. Each item type gives one term.
2. A minus before a bracket flips every sign.

Question 12. A school trip to the science centre. The students of Class 7 are going to a science centre. There are 32 students and 4 teachers in the group. The entry ticket costs ₹30 for a student and ₹50 for a teacher. The school has hired a bus for the whole trip for ₹2,400. Before the trip, the class teacher collects ₹4,000 from the class fund and plans to return whatever is left after all the payments are made. She writes every step of her calculation as an arithmetic expression on the blackboard so that the whole class can follow it.
(i) Write an expression for the cost of the students’ tickets and find its value.
(ii) Write an expression for the cost of all the tickets together and find its value.
(iii) Write a single expression with brackets for the total cost of the trip, including the bus, and find it.
(iv) How much money will be left out of ₹4,000? Write the expression and its value.
Answer:
(i) Students’ tickets = 32 × 30 = ₹960.
(ii) All tickets = 32 × 30 + 4 × 50 = 960 + 200 = ₹1,160.
(iii) Total cost = (32 × 30 + 4 × 50) + 2400 = 1160 + 2400 = ₹3,560.
(iv) Money left = 4000 − (32 × 30 + 4 × 50 + 2400) = 4000 − 3560 = ₹440.
In simple words: Add all the costs, then subtract the total from ₹4,000.

Teacher's Note:
1. Build the expression step by step.
2. Keep all costs inside one bracket.

Question 13. Two stamp collections. Ayan and Bina are cousins and both collect postage stamps. On Sunday morning Ayan had 1,245 stamps in his album and Bina had 1,243 stamps in hers. In the afternoon their uncle came home from a trip and gave both of them some stamps: Ayan received 130 new stamps and Bina received 134 new stamps. In the evening they wanted to know who has the bigger collection now, but they did not want to do a long addition. Their teacher told them that they could compare the two expressions just by looking at the numbers carefully.
(i) Write an expression for the number of stamps each cousin has now.
(ii) Who had more stamps in the morning, and by how many?
(iii) Who received more stamps in the afternoon, and by how many?
(iv) Without adding, say who has more stamps now and by how many. Write the comparison using the correct sign.
Answer:
(i) Ayan: 1245 + 130; Bina: 1243 + 134.
(ii) Ayan had more in the morning, by 1245 − 1243 = 2 stamps.
(iii) Bina received more in the afternoon, by 134 − 130 = 4 stamps.
(iv) Bina starts 2 behind but gains 4 more, so she is ahead by 4 − 2 = 2 stamps. Hence 1245 + 130 < 1243 + 134 (1375 and 1377).
In simple words: Compare the differences instead of adding the big numbers.

Teacher's Note:
1. −2 and +4 give a net +2 for Bina.
2. Check by adding if you wish.

Question 14. A record kept in a nursery. Rani looks after a small plant nursery. On Monday morning she counted 48 saplings on her shelves. During the day she sold saplings to a customer who bought 5 trays, with 3 saplings in each tray. In the evening a van from the forest office delivered 20 fresh saplings to her nursery. Rani wrote the whole day’s record as one arithmetic expression in her notebook. Her helper looked at the same expression and worked it out from left to right without thinking about terms, and got a very large answer.
(i) Write the arithmetic expression for the number of saplings Rani has at the end of the day.
(ii) Write this expression as a sum of its terms and list the terms.
(iii) Find the value of the expression.
(iv) The helper’s answer was 149. What did he do, and why is it wrong?
Answer:
(i) 48 − 5 × 3 + 20.
(ii) 48 + (−5 × 3) + 20; the terms are 48, −5 × 3 and 20.
(iii) Value = 48 − 15 + 20 = 53 saplings.
(iv) The helper worked left to right as (48 − 5) × 3 + 20 = 43 × 3 + 20 = 149. This is wrong because 5 × 3 is a single term; with no brackets, each term must be evaluated first and only then are the terms added.
In simple words: Work out each term first, then add the terms.

Teacher's Note:
1. Sold saplings give a negative term.
2. Left-to-right working breaks the term 5 × 3.

Question 15. Tiling the floor of a hall. A new activity hall is being given a tiled floor. The tiles are laid in 9 equal rows. In each row the mason first lays 8 square white tiles and then 6 square blue tiles, as shown in the picture. Each tile, white or blue, costs ₹12. The mason wants to order exactly the right number of tiles, so he writes the count as an arithmetic expression. His assistant counts the tiles in a different way and gets a different-looking expression, yet both of them get the same number of tiles.
(i) Write an expression for the number of white tiles and find its value.
(ii) Write an expression for the number of blue tiles and find its value.
(iii) Write two different expressions for the total number of tiles and show that they are equal.
(iv) Name the property used in part (iii) and find the total cost of the tiles.
Answer:
(i) White tiles = 9 × 8 = 72.
(ii) Blue tiles = 9 × 6 = 54.
(iii) Counting the two colours separately: 9 × 8 + 9 × 6 = 72 + 54 = 126. Counting each row as a whole: 9 × (8 + 6) = 9 × 14 = 126. Both give 126 tiles, so 9 × (8 + 6) = 9 × 8 + 9 × 6.
(iv) The property is the distributive property. Total cost = 12 × 126 = ₹1,512.
In simple words: Count by colour or by whole rows; both give 126 tiles.

Teacher's Note:
1. Each row has 8 + 6 = 14 tiles.
2. Every tile costs the same, so multiply the total by 12.

Question 16. A family budget. Kamal works in a printing press and earns ₹24,000 every month. His spending each month is almost the same: ₹7,500 goes on house rent, ₹6,200 on food and groceries, and ₹3,300 on travel and other needs. Whatever is left he puts into a savings account on the last day of the month. Kamal wants to know how much he will have in that account at the end of one full year if his earning and spending stay the same. He decides to write his saving first as an expression with brackets and then without brackets.
(i) Write an expression for Kamal’s total spending in one month and find its value.
(ii) Write an expression with brackets for his saving in one month and find it.
(iii) Remove the brackets in part (ii) and write the saving as a sum of terms. Check that the value is unchanged.
(iv) Write an expression for his saving in one year and find its value.
Answer:
(i) Monthly spending = 7500 + 6200 + 3300 = ₹17,000.
(ii) Monthly saving = 24000 − (7500 + 6200 + 3300) = 24000 − 17000 = ₹7,000.
(iii) Removing the bracket changes the sign of each term inside: 24000 − 7500 − 6200 − 3300. The terms are 24000, −7500, −6200 and −3300, and the value is 16500 − 6200 − 3300 = 7000, the same as before.
(iv) Yearly saving = 12 × (24000 − 17000) = 12 × 7000 = ₹84,000.
In simple words: Saving = earning minus all spending, then times 12 for a year.

Teacher's Note:
1. All spending goes inside one bracket.
2. A year has 12 months.

Question 17. Quick billing at a grain shop. Ratan runs a grain shop and has to make bills quickly for his customers. He has noticed that numbers such as 48, 98 and 49 are close to the round numbers 50, 100 and 50. So, instead of doing long multiplication, he writes 48 as 50 − 2, 98 as 100 − 2 and so on, and then multiplies. In this way he finishes a bill in his head while the customer is still putting the grain into a bag. He also keeps a small table of products he has already worked out, so that he can build new products from them.
(i) Rice costs ₹48 per kg. Using Ratan’s idea, write and evaluate an expression for the cost of 25 kg of rice.
(ii) Wheat costs ₹30 per kg. Find the cost of 98 kg of wheat using the same idea.
(iii) Ratan’s table shows 46 × 35 = 1610. Using this, find 56 × 35 without long multiplication.
(iv) Name the property that makes all these short methods work.
Answer:
(i) 25 × 48 = 25 × (50 − 2) = 25 × 50 − 25 × 2 = 1250 − 50 = 1200, so 25 kg of rice costs ₹1,200.
(ii) 98 × 30 = (100 − 2) × 30 = 100 × 30 − 2 × 30 = 3000 − 60 = 2940, so 98 kg of wheat costs ₹2,940.
(iii) 56 × 35 = (46 + 10) × 35 = 46 × 35 + 10 × 35 = 1610 + 350 = 1960.
(iv) The distributive property: the multiple of a sum or a difference is the sum or the difference of the multiples.
In simple words: Break a number into a round number plus or minus a little, then multiply each part.

Teacher's Note:
1. Pick the nearest round number.
2. Known products save time.

Question 18. A music practice routine. Arun has joined a tabla class. He practises for 2 hours every day of the week except on Tuesdays and Sundays, when the class is closed and he rests. He keeps to this routine for 6 weeks before his first stage performance. His teacher asks the class to write the number of practice days and the number of practice hours as arithmetic expressions, and warns them that some expressions that look different may still describe the same situation.
(i) On how many days in a week does Arun practise? Write it as an expression.
(ii) Write an expression with brackets for the number of practice days in 6 weeks and find its value.
(iii) Which of these expressions also describe the number of practice days in 6 weeks: 7 × 6 − 2 × 6, (7 + 2) × 6, 7 × 6, 5 × 6? Give reasons.
(iv) Write an expression for the total number of practice hours in the 6 weeks and find its value.
Answer:
(i) He rests on 2 days, so he practises on 7 − 2 = 5 days in a week.
(ii) Practice days in 6 weeks = (7 − 2) × 6 = 5 × 6 = 30 days.
(iii) 7 × 6 − 2 × 6 = 42 − 12 = 30 is correct, as it is all the days minus the rest days. 5 × 6 = 30 is correct, as it is 5 practice days in each of 6 weeks.
(7 + 2) × 6 = 54 and 7 × 6 = 42 are both wrong: the first adds the rest days and the second does not remove them.
(iv) Total hours = 2 × [(7 − 2) × 6] = 2 × 30 = 60 hours.
In simple words: 5 practice days a week for 6 weeks is 30 days, at 2 hours each is 60 hours.

Teacher's Note:
1. (7 − 2) × 6 = 7 × 6 − 2 × 6 by the distributive property.
2. Check each choice against the real count.

Question 19. Science kits for a school. A school orders science kits for its laboratory. Each kit is packed with 3 identical boxes, and every box contains 12 test tubes and 8 glass slides. The school orders 5 such kits. When the kits reach the school, the laboratory assistant opens them and finds that 4 glass items have been broken in each kit while being carried. The assistant has to write a report, and the science teacher asks her to show every count as an arithmetic expression, using brackets inside brackets where needed, so that anyone reading the report can follow the counting.
(i) How many glass items are there in one box? Write it as an expression.
(ii) Write an expression with brackets for the number of glass items in one kit and find its value.
(iii) Write an expression using a bracket inside a bracket for the number of glass items in all 5 kits, and find its value.
(iv) Write two different expressions for the number of unbroken items in the 5 kits and show that they give the same value.
Answer:
(i) Glass items in one box = 12 + 8 = 20.
(ii) Glass items in one kit = 3 × (12 + 8) = 3 × 20 = 60.
(iii) Glass items in 5 kits = 5 × [3 × (12 + 8)] = 5 × 60 = 300.
(iv) Taking all the breakages together: 5 × [3 × (12 + 8)] − 5 × 4 = 300 − 20 = 280.
Taking the breakage kit by kit: 5 × [3 × (12 + 8) − 4] = 5 × (60 − 4) = 5 × 56 = 280.
Both give 280 unbroken items; this is the distributive property at work.
In simple words: Count one box, then one kit, then all kits, and take away the broken ones.

Teacher's Note:
1. Build the expression from the inside out.
2. 4 broken in each kit means 5 × 4 in all.

Question 20. Three answers, one expression. In a Class 7 mathematics period the teacher writes the expression 90 − (25 − 8) + 10 on the board and asks everyone to find its value. When the notebooks are checked, three friends have written three different answers. Dev has written 83, Esha has written 67 and Farid has written 63. The teacher does not say at once who is right. Instead, she asks the class to work the expression out carefully, one bracket at a time, and then to look at the two wrong answers and work out exactly which step went wrong in each case.
(i) Find the correct value of the expression, showing each step.
(ii) Which of the three friends is right?
(iii) Esha removed the bracket but kept the signs inside unchanged. Show the expression she actually evaluated and explain her mistake.
(iv) Show the expression Farid actually evaluated, explain his mistake, and write the correct expression without any brackets.
Answer:
(i) Bracket: 25 − 8 = 17; then 90 − 17 = 73; then 73 + 10 = 83.
(ii) Dev is right, as his answer is 83.
(iii) Esha worked out 90 − 25 − 8 + 10 = 67. She removed the bracket but left −8 unchanged. A bracket after a minus sign changes the sign of every term inside it, so −8 should have become +8.
(iv) Farid worked out 90 − (25 − 8 + 10) = 90 − 27 = 63. He pulled the term +10 into the bracket, although it is outside the bracket. The correct bracket-free form is 90 − 25 + 8 + 10 = 83.
In simple words: Work out the bracket first and flip only the signs inside it.

Teacher's Note:
1. Check each wrong answer by rebuilding it.
2. Only terms inside the bracket change sign.