Arithmetic Expressions Class 7 Maths Worksheet with Answers Chapter 2

Ganita Prakash Part-I, Grade 7, NCERT Textbook of Mathematics – Chapter 2 is titled “Arithmetic Expressions”. An arithmetic expression is a maths phrase such as 13 + 2, 20 − 4, 12 × 5, or 18 ÷ 3. Each expression stands for one value – the single number it equals. Through this Class 7 Maths chapter, you will learn to read these expressions, compare them, and work out their value. You will also see how brackets, terms, and a few easy properties guide you to the correct answer, and to a faster one.

The worksheet below draws questions from every part of the chapter. Its main topics are:

• Writing and reading arithmetic expressions
• Comparing two expressions by reasoning (greater than, less than, or equal)
• Using brackets to set the order of steps
• Terms in an expression (the parts joined by + signs)
• Swapping and grouping the terms
• Commutative and associative properties of addition
• Removing brackets and the sign change after a minus sign
• The distributive property
• Faster multiplication using brackets

Before you begin, keep these easy rules in hand:

• Always solve the bracket part first. Example: 30 + (5 × 4) = 30 + 20 = 50
• Terms are the parts of an expression joined by + signs. Work out each term, then add them. So 30 + 5 × 4 = 30 + 20 = 50
• Taking away a number is the same as adding its opposite. So 83 − 14 = 83 + (−14)
• In addition, order does not matter: a + b = b + a (commutative property)
• In addition, grouping does not matter: (a + b) + c = a + (b + c) (associative property)
• Bracket after a + sign: the signs inside do not change. Bracket after a − sign: every sign inside flips. Example: 100 − (15 + 56) = 100 − 15 − 56
• Distributive property: a × (b + c) = a × b + a × c, and a × (b − c) = a × b − a × c
• Handy trick: to multiply a number close to 100, use brackets. Example: 97 × 25 = (100 − 3) × 25 = 100 × 25 − 3 × 25

This worksheet is set in 4 levels – Basic, Standard, Advanced, and HOTS. You will find the full answer key placed right after the 28 questions.

Class 7 Maths Worksheet – Chapter 2: Arithmetic Expressions

Basic

1. Find the value of each expression:
   • 18 + 29
   • 64 − 17
   • 9 × 7
   • 96 ÷ 8
2. Fill in the blanks to make the expressions equal:
   • 27 + 14 = ____ + 19
   • 9 × ____ = 72 ÷ 2
   • 56 − ____ = 7 × 7
3. Compare using <, > or =:
   • 245 + 289 ______ 246 + 285
   • 273 − 145 ______ 272 − 144
   • 364 + 587 ______ 363 + 589
4. Write an arithmetic expression and find its value:
   • A notebook costs ₹28. What is the cost of 6 notebooks?
   • Riya has ₹100 and spends ₹37. How much money is left?
5. Identify the terms in each expression:
   • 8 × 6 + 7
   • 45 − 12 + 9
   • 36 − 4 × 5 + 12
6. Evaluate the following expressions:
   • 30 + 5 × 4
   • 90 − (35 + 18)
   • (12 + 8) × 5
7. Write two different arithmetic expressions for each value:
   • 24
   • 36

Standard

1. Write the expressions as sums of terms and then find their values:
   • 48 − 6 × 5 + 20 ÷ 4
   • −15 + 8 × 3 − 12
   • 72 − 18 + 4 × 6
2. Remove the brackets and write an equivalent expression. Then find its value:
   • 125 − (36 − 14)
   • 50 + (18 − 27)
   • 80 − (25 + 16)
3. Insert brackets in the following expressions so that they get the indicated value:
   • 24 − 7 + 4 = 13
   • 56 − 14 − 8 = 50
   • 18 + 6 × 4 = 96
4. Use the distributive property to find:
   • 7 × (13 + 4)
   • (25 − 9) × 6
   • 98 × 12
5. A cinema ticket costs ₹150 for an adult and ₹80 for a child. Find the total cost for 3 adults and 2 children.
   Write an expression before calculating.
6. A fruit seller sells 12 kg of mangoes and 5 kg of oranges every day for 8 days.
   Write an expression for the total quantity of fruit sold and find its value.
7. Compare the following without doing lengthy calculations:
   • 75 × 36 + 25 × 36 ______ 100 × 36
   • 49 × 18 ______ 50 × 18 − 18
   • 25 × (42 + 16) ______ 25 × (43 + 15)

Advance

1. Find the values by grouping suitable terms:
   • 25 + 37 − 25 + 63
   • 48 − 19 + 52 − 31
   • 125 + 76 + 24 − 25
2. A snail climbs 4 cm up a pole during the day and slips 1 cm down at night.
   The pole is 16 cm high. In how many days will the snail reach the top?
3. A family buys 4 identical meal combos. Each combo contains a sandwich costing ₹65 and a juice costing ₹35.
   Write two different expressions for the total bill and find the amount.
4. Find the following using a smart method:
   • 98 × 35
   • 104 × 25
   • 49 × 50
5. Given that 48 × 19 = 912, find:
   • 52 × 19
   • 48 × 21
   • 47 × 19
6. A shopkeeper has ₹500. He buys 3 pens at ₹28 each and 4 notebooks at ₹35 each.
   Write an expression for the money left with him and find the answer.
7. Find which pairs have the same value:
   • 75 − (18 + 7) and 75 − 18 − 7
   • 63 − (24 − 9) and 63 − 24 − 9
   • 42 + (17 − 8) and 42 + 17 − 8

HOTS

1. Use the numbers 2, 3 and 5 exactly once, along with the signs + and −, to form expressions with values:
   • 10
   • 6
   • 4
   • 0
2. Use exactly three 3s and any arithmetic operations to make:
   • 2
   • 3
   • 6
   • 9
   • 12
3. Without multiplying fully, find the value of:
   • 99 × 67 + 1 × 67
   • 48 × 125 + 2 × 125
   • 76 × 43 − 6 × 43
4. Which expression is greater? Explain using reasoning.
   • 76 × 49 or 75 × 50
   • 102 × 38 or 100 × 40
   • 47 × 25 or 50 × 23
5. A school has 18 classrooms. Each classroom has 32 students. On one day, 47 students are absent.
   Write an expression for the number of students present and find the answer.
6. A shop offers two billing methods for 5 shirts costing ₹480 each:
   • Method A: 5 × 480 − 250
   • Method B: 5 × (480 − 250)

   Which expression correctly represents a total discount of ₹250 on the bill? Find the final bill.

7. Find the error in this calculation and correct it:
   • 8 × (15 − 6) = 8 × 15 − 6 = 114

Answer Key

Basic – Answers

1. • 18 + 29 = 47
   • 64 − 17 = 47
   • 9 × 7 = 63
   • 96 ÷ 8 = 12
2. • 22, because 27 + 14 = 41 and 41 − 19 = 22.
   • 4, because 72 ÷ 2 = 36 and 9 × 4 = 36.
   • 7, because 7 × 7 = 49 and 56 − 7 = 49.
3. • 245 + 289 > 246 + 285
   • 273 − 145 = 272 − 144
   • 364 + 587 < 363 + 589
4. • 6 × 28 = ₹168
   • 100 − 37 = ₹63
5. • 8 × 6 + 7: Terms are 8 × 6 and 7.
   • 45 − 12 + 9: Terms are 45, −12 and 9.
   • 36 − 4 × 5 + 12: Terms are 36, −(4 × 5) and 12.
6. • 30 + 5 × 4 = 50
   • 90 − (35 + 18) = 37
   • (12 + 8) × 5 = 100

   Hint: Solve expressions inside brackets first. Multiplication is completed before addition when there are no brackets.

7. • 24: 12 + 12, 6 × 4
   • 36: 40 − 4, 9 × 4

Standard – Answers

1. • 48 − 6 × 5 + 20 ÷ 4 = 48 − 30 + 5 = 23
   • −15 + 8 × 3 − 12 = −15 + 24 − 12 = −3
   • 72 − 18 + 4 × 6 = 72 − 18 + 24 = 78
2. • 125 − (36 − 14) = 125 − 36 + 14 = 103
   • 50 + (18 − 27) = 50 + 18 − 27 = 41
   • 80 − (25 + 16) = 80 − 25 − 16 = 39
3. • 24 − (7 + 4) = 13
   • 56 − (14 − 8) = 50
   • (18 + 6) × 4 = 96
4. • 7 × (13 + 4) = 7 × 13 + 7 × 4 = 91 + 28 = 119
   • (25 − 9) × 6 = 25 × 6 − 9 × 6 = 150 − 54 = 96
   • 98 × 12 = (100 − 2) × 12 = 1,200 − 24 = 1,176
5. 3 × 150 + 2 × 80 = ₹610
6. (12 + 5) × 8 = 136 kg
7. • 75 × 36 + 25 × 36 = 100 × 36
   • 49 × 18 = 50 × 18 − 18
   • 25 × (42 + 16) = 25 × (43 + 15)

Advance – Answers

1. • 25 + 37 − 25 + 63 = 100
   • 48 − 19 + 52 − 31 = 50
   • 125 + 76 + 24 − 25 = 200

   Hint: Group convenient pairs, such as 25 and −25.

2. 5 days
   • Hint: After four nights, the snail reaches 12 cm. On Day 5, it climbs 4 cm and reaches the top.
3. 4 × (65 + 35) = ₹400
   4 × 65 + 4 × 35 = ₹400
4. • 98 × 35 = (100 − 2) × 35 = 3,430
   • 104 × 25 = (100 + 4) × 25 = 2,600
   • 49 × 50 = (50 − 1) × 50 = 2,450
5. • 52 × 19 = 988
   • 48 × 21 = 1,008
   • 47 × 19 = 893
6. 500 − (3 × 28 + 4 × 35) = ₹276
   • Hint: Total spent = ₹84 + ₹140 = ₹224.
7. • 75 − (18 + 7) and 75 − 18 − 7 have the same value.
   • 63 − (24 − 9) and 63 − 24 − 9 do not have the same value.
   • 42 + (17 − 8) and 42 + 17 − 8 have the same value.

HOTS – Answers

1. • 10: 2 + 3 + 5
   • 6: 5 − 2 + 3
   • 4: 5 + 2 − 3
   • 0: 2 + 3 − 5
2. • 2: (3 + 3) ÷ 3
   • 3: 3 + 3 − 3
   • 6: 3 × 3 − 3
   • 9: 3 + 3 + 3
   • 12: 3 × 3 + 3
3. • 99 × 67 + 1 × 67 = (99 + 1) × 67 = 6,700
   • 48 × 125 + 2 × 125 = (48 + 2) × 125 = 6,250
   • 76 × 43 − 6 × 43 = (76 − 6) × 43 = 3,010
4. • 76 × 49 = 3,724 and 75 × 50 = 3,750. Therefore, 75 × 50 is greater.
   • 102 × 38 = 3,876 and 100 × 40 = 4,000. Therefore, 100 × 40 is greater.
   • 47 × 25 = 1,175 and 50 × 23 = 1,150. Therefore, 47 × 25 is greater.
5. 18 × 32 − 47 = 529 students
   • Hint: Total students = 576. Subtract 47 absentees.
6. Method A is correct.
   Final bill = 5 × 480 − 250 = ₹2,150
   • Hint: Method B incorrectly gives a ₹250 discount on every shirt. That discount has gone to the gym and multiplied itself.
7. Correct calculation:
   8 × (15 − 6) = 8 × 15 − 8 × 6 = 120 − 48 = 72
   • Error: The number 8 must multiply both 15 and 6.

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