Arithmetic Expressions — Questions and Answers
Welcome to HSLC Guru. This page gives complete, step-by-step solutions for ASSEB (Assam State School Education Board) Class 7 New Mathematics Chapter 2, Arithmetic Expressions (পাটীগণিতীয় ৰাশি) — a summary, every textbook “Work it Out” box and worked example solved, the activities and project, and the full Exercise 2.
Summary
An arithmetic expression connects numbers using the operations of addition (+), subtraction (−), multiplication (×) and division (÷). An expression with only one operation (such as 12 + 5 or 8 × 4) is a simple arithmetic expression, while one with more than one operation (such as 100 + 20 × 4) is a complex arithmetic expression. Every expression has a definite value.
Using the symbols ‘>’, ‘<’ and ‘=’ we can compare two expressions without even finding their values. To evaluate a complex expression correctly we use brackets and the idea of terms. Each part of an expression separated by a ‘+’ sign is a term; since subtracting a number is the same as adding its additive inverse, every expression can be split into terms joined by ‘+’ signs.
In addition, changing the order of the terms does not change the value (commutative law of addition), and changing how three terms are grouped does not change the value (associative law of addition). When a bracket is preceded by ‘+’ the signs inside stay the same on removal; when preceded by ‘−’ the signs inside change. Finally, the product of a sum (or difference) of two numbers equals the sum (or difference) of the products — the distributive property, which makes multiplying large numbers easy.
Summary: This page gives complete ASSEB Class 7 New Mathematics Chapter 2 Arithmetic Expressions question answers for English-medium students. It covers simple and complex arithmetic expressions, comparing expressions without calculation, brackets, terms, the commutative and associative laws of addition, removal of brackets and the distributive property, with every “Work it Out” box, all worked examples, the activities, the project and Exercise 2 solved in full.
Textbook Questions and Answers
Simple Arithmetic Expressions — Examples
Example 1: Raktim has 13 red marbles and 7 green marbles. Express the total number of marbles as an arithmetic expression.
Answer: Red marbles = 13, green marbles = 7. So the total is 13 + 7.
Example 2: A packet contains 20 chocolates. Express the number of chocolates in 5 packets as an arithmetic expression.
Answer: 1 packet = 20 chocolates, so 5 packets = 20 + 20 + 20 + 20 + 20 = 5 × 20.
Work it Out 2.1
1. Dibija bought one book for ₹25 and another for ₹10. Express the money spent as an arithmetic expression.
Answer: Money spent = 25 + 10 = ₹35.
2. Runjun gave ₹7 to his brother out of the ₹20 he had. Write the money Runjun has as an arithmetic expression.
Answer: Money left = 20 − 7 = ₹13.
3. Every student of class 7 has 3 pencils. Express the total number of pencils with 15 students as an arithmetic expression.
Answer: Total pencils = 15 × 3 = 45.
4. Amir divided 60 chocolates equally among 30 friends. How many does each get? Write as an arithmetic expression.
Answer: Each gets = 60 ÷ 30 = 2.
Let us Think (complete the table — value 20)
Using different numbers, complete the table so that each operation gives the value 20.
Answer: (a) addition: 10 + 10 = 20 · (b) subtraction: 30 − 10 = 20 · (c) multiplication: 4 × 5 = 20 · (d) division: 40 ÷ 2 = 20. (Many answers are possible, e.g. (a) 16 + 4 = 20.)
Work it Out 2.2
1. Fill in the blanks:
Answer: (a) 6 + 5 = 11 × 1 (since 6 + 5 = 11) · (b) 6 × 7 > 12 ÷ 2 (42 > 6; any non-zero divisor works) · (c) 15 − 10 < 42 ÷ 6 (5 < 7; any number less than 17 works) · (d) 10 ÷ 2 = 2 + 3 (since 2 + 3 = 5 and 10 ÷ 2 = 5).
2. Write whether the comparison is true or false:
Answer: (a) 10 + 5 = 8 + 7 → 15 = 15 → True · (b) 7 × 2 < 18 ÷ 3 → 14 < 6 is not true → False · (c) 36 ÷ 6 < 9 + 5 → 6 < 14 → True · (d) 25 − 5 = 10 + 10 → 20 = 20 → True · (e) 7 + 13 < 4 + 8 → 20 < 12 is not true → False · (f) 12 × 3 > 9 × 4 → 36 > 36 is not true (equal) → False.
3. Put the appropriate sign (>, <, =):
Answer: (a) 6 + 9 > 15 ÷ 3 (15 > 5) · (b) 6 + 9 = 8 + 7 (15 = 15) · (c) 15 ÷ 3 < 9 × 5 (5 < 45) · (d) 22 − 7 < 8 + 17 (15 < 25) · (e) 28 + 7 < 9 × 5 (35 < 45).
Work it Out 2.3
1. Compare the following without calculation and give a reason in each case:
Answer: (a) 213 + 145 = 214 + 144; because 214 is 1 more than 213 while 144 is 1 less than 145, so the sums are equal.
(b) 310 + 227 < 308 + 230; because 308 is 2 less than 310 but 230 is 3 more than 227, so the second sum is 1 greater.
(c) 336 − 102 < 338 − 101; the second has a larger number (338) and subtracts a smaller number (101), so its difference is larger (234 < 237).
(d) 124 − 115 < 129 − 112; the second has a larger minuend and a smaller subtrahend, so its difference is larger (9 < 17).
Complex Expressions and Brackets — Example 3
Example 3: From ₹200, Deepti bought 1 kg atta for ₹80 and 1 kg dal for ₹90. How much money is left? Express as an arithmetic expression.
Answer: Total spent = 80 + 90. Writing 200 − 80 + 90 wrongly gives 210, so a bracket is needed. Money left = 200 − (80 + 90) = 200 − 170 = ₹30.
Work it Out 2.4
Express as arithmetic expressions and find the value.
1. In an essay competition the word limit was 600. A contestant wrote a 4-page essay of 110 words per page. How many more or fewer words did the contestant write than allowed?
Answer: Words written = 4 × 110 = 440. Difference = 600 − (4 × 110) = 600 − 440 = 160 words fewer.
2. Anup bought 3 boxes of oranges with 6 in each box. He gave 5 to his sister and ate 2. How many were left?
Answer: Oranges left = (3 × 6) − (5 + 2) = 18 − 7 = 11.
3. A packet of rice costs ₹70, a bottle of mustard oil ₹160 and a packet of salt ₹20. How much is needed for 4 packets of rice, 3 bottles of oil and 2 packets of salt?
Answer: Total = (4 × 70) + (3 × 160) + (2 × 20) = 280 + 480 + 40 = ₹800.
4. A bookshelf had 120 books. 35 were taken out and 20 were put back. Find the total number of books as an arithmetic expression.
Answer: Total = (120 − 35) + 20 = 85 + 20 = 105 books.
Activity 1 (Loopy cards)
Each loopy card has a number in the pink part on the left and an expression in the green part on the right. Arrange the cards in a circle so that the value of the green expression on one card equals the number in the pink part of the next card.
Answer: First simplify each expression —
| Number (pink) | Expression (green) | Value |
|---|---|---|
| 13 | 17 − 9 | 8 |
| 0 | −3 − 4 + 6 | −1 |
| 8 | 2 × 5 − 3 | 7 |
| 10 | −1 − 1 − 1 − 1 | −4 |
| −4 | 5 + 13 − 2 | 16 |
| 16 | −3 + 7 × 2 | 11 |
| 32 | 9 × 3 − 7 × 2 | 13 |
| 11 | 12 × 2 − 24 | 0 |
| 7 | 17 − 8 + 23 | 32 |
| −1 | 8 − 3 + 5 | 10 |
Matching each green value to the pink number of the next card gives the chains: (13 → 8) → (8 → 7) → (7 → 32) → (32 → 13) and (0 → −1) → (−1 → 10) → (10 → −4) → (−4 → 16) → (16 → 11) → (11 → 0). When the chain closes, the arrangement is correct.
Terms of an Arithmetic Expression — Work it Out 2.5
Remember: each part separated by a ‘+’ sign is a term. Subtraction can be written as adding the additive inverse, e.g. 55 − 18 = 55 + (−18), so its two terms are 55 and −18.
1. Find the terms of the following expressions:
Answer: (a) −18 + 10 × 2 → −18, 10 × 2 · (b) 19 + 5 × 4 → 19, 5 × 4 · (c) −11 × 6 − 7 → −11 × 6, −7 · (d) 9 + 3 − 5 → 9, 3, −5 · (e) 4 − 6 − 7 → 4, −6, −7 · (f) 2 × 5 + 5 × 7 → 2 × 5, 5 × 7 · (g) −5 × 6 + 2 × 3 → −5 × 6, 2 × 3 · (h) 4 × 3 − 16 ÷ 4 → 4 × 3, −16 ÷ 4 · (i) 15 + 21 ÷ 7 → 15, 21 ÷ 7.
2. The figure shows the students present in a classroom. Express the attendance as an arithmetic expression using a bracket.
Answer: The students are seated in rows — three rows of 4 and one row of 3. So attendance = (4 + 4 + 4) + 3 = (3 × 4) + 3 = 12 + 3 = 15 students. (The numbers change with your own classroom picture.)
3. From the figure, express the number of balls as a simple and a complex arithmetic expression.
Answer: The abacus has 7 rods — three blue rods with 5 beads each and four coloured rods with 6 beads each. Simple expression (only addition) = 5 + 6 + 6 + 5 + 6 + 6 + 5 = 39. Complex expression (with multiplication and brackets) = (3 × 5) + (4 × 6) = 15 + 24 = 39 balls.
Activity 2 (Your own classroom)
Like question 2 above, express the attendance of your own classroom as an arithmetic expression.
Answer: (Model) Suppose your class has 5 rows of 8 students and today 3 are absent. Then attendance = (5 × 8) − 3 = 40 − 3 = 37 students. Use the real numbers from your class to build such an expression with a bracket.
Order of Terms — Commutative and Associative Laws
Biju and Riju found the sum of 8 and −5: 8 + (−5) = 3 and (−5) + 8 = 3. Both give the same value, so changing the order of terms in addition does not change the value — the commutative law of addition (Term 1 + Term 2 = Term 2 + Term 1).
Grouping the three terms of (−4) + (−3) + (−2) in two ways: [(−4) + (−3)] + (−2) = (−7) + (−2) = −9 and (−4) + [(−3) + (−2)] = (−4) + (−5) = −9. Both give −9, so changing the grouping does not change the value — the associative law of addition.
Removal of Brackets — Examples 4, 5, 6
Example 4: Aminul had ₹50. He bought a notebook for ₹25 from one shop and a chocolate for ₹10 from another. How much money is left?
Answer: Total spent = 25 + 10 = 35. Left = 50 − (25 + 10) = 50 − 35 = ₹15. Subtracting each separately, 50 − 25 − 10 = 15, so 50 − (25 + 10) = 50 − 25 − 10.
Example 5: Neev had ₹30. His father gave him ₹25 more; from that Neev gave ₹10 to his sister. How much is left with Neev?
Answer: Money left = 30 + (25 − 10) = 30 + 15 = ₹45. That is, 30 + (25 − 10) = 30 + 25 − 10 (a ‘+’ before the bracket keeps the inside signs unchanged).
Example 6: Find the value of 15 − (10 − 2).
Answer: First (10 − 2) = 8, so 15 − 8 = 7. On removing the bracket, 15 − 10 + 2 = 7 (the sign of 2 changes from − to +). So 15 − (10 − 2) = 15 − 10 + 2 = 7.
Rule: if a bracket is preceded by ‘+’, the signs inside stay the same on removal; if preceded by ‘−’, the signs inside change (positive ↔ negative).
Work it Out 2.6
1. Remove the brackets from the following expressions:
Answer: (a) 12 + (4 − 3) = 12 + 4 − 3 = 13 · (b) 30 − (5 − 2) = 30 − 5 + 2 = 27 · (c) 45 − (10 + 5) = 45 − 10 − 5 = 30 · (d) 16 + (6 + 2) = 16 + 6 + 2 = 24 · (e) 5 − (−4 + 9) = 5 + 4 − 9 = 0 · (f) 7 − (−12 − 10) = 7 + 12 + 10 = 29.
2. Write whether the following are true or false:
Answer: (a) 3 − (4 − 1) = 3 − 4 − 1 → 0 ≠ −2 → False · (b) 3 − (4 + 1) = 3 − 4 − 1 → both −2 → True · (c) 3 + (4 − 1) = 3 + 4 − 1 → both 6 → True · (d) 3 + (4 + 1) = 3 − 4 + 1 → 8 ≠ 0 → False.
3. Put ‘+’ or ‘−’ and the appropriate number in the boxes:
Answer: (a) 12 − (3 − 1) = 12 − 3 + 1 · (b) 7 − (3 + 2) = 7 − 3 − 2 · (c) 10 + 6 − 1 = 10 + (6 − 1) · (d) 30 − (12 − 4) = 30 − 12 + 4 · (e) 25 − (10 + 3) = 25 − 10 − 3 · (f) 5 − (3 + 2) = 5 − 3 − 2.
4. Find the values and put ‘=’ if equal and ‘≠’ if not equal:
Answer: (a) 5 − (3 − 1) ≠ 5 − 3 − 1 (3 ≠ 1) · (b) 7 + (8 − 3) = (7 + 8) − 3 (12 = 12) · (c) 1 − (−1 − 1) ≠ 1 + 1 − 1 (3 ≠ 1) · (d) 13 − 10 + 3 = 13 − (10 − 3) (6 = 6) · (e) 8 + (7 − 1) ≠ 8 − 7 − 1 (14 ≠ 0) · (f) 3 − (7 − 5) = 3 − 7 + 5 (1 = 1).
5. Match Column 1 with Column 2. Column 1: (A) 20 + (7 + 4), (B) 20 − (7 + 4), (C) 20 − (7 − 4). Column 2: (P) 20 − 7 + 4, (Q) 20 + 7 + 4, (R) 20 − 7 − 4.
Answer: (A) 20 + (7 + 4) = 20 + 7 + 4 → (Q) · (B) 20 − (7 + 4) = 20 − 7 − 4 → (R) · (C) 20 − (7 − 4) = 20 − 7 + 4 → (P). So the correct option is (b) A–Q, B–R, C–P.
6. Each expression has four options in its corners; choose the correct value:
Answer: (a) 6 − (4 − 1) = 6 − 3 = 3 · (b) 10 + (3 − 1) = 10 + 2 = 12 · (c) 8 − (5 + 3) = 8 − 8 = 0 · (d) 5 + (4 − 1) = 5 + 3 = 8.
7. Use brackets in the appropriate place:
Answer: (a) 40 − (2 + 8) = 30 · (b) 15 + (8 − 3) = 20 · (c) 27 − (12 − 10) = 25 · (d) −2 + (2 − 5) = −5.
Distributive Property — Examples 7 to 12
Example 7: Nitumoni and Ajay each bought a notebook for ₹50 and a pen for ₹15. Express the total money they pay the shopkeeper.
Answer: Total = 2 × (50 + 15) = 2 × 65 = 130. Also 2 × 50 + 2 × 15 = 100 + 30 = 130. So 2 × (50 + 15) = 2 × 50 + 2 × 15.
Example 8: In a school garden, 6 yellow rose saplings were planted in each of the first 4 rows and 6 red rose saplings in each of the next 5 rows. Find the total number of saplings.
Answer: Total rows = 4 + 5 = 9, with 6 saplings per row. Riyaz: (4 + 5) × 6 = 9 × 6 = 54; Namita: 4 × 6 + 5 × 6 = 24 + 30 = 54. So (4 + 5) × 6 = 4 × 6 + 5 × 6 = 54.
Example 9: Nirvan bought 12 pens at ₹20 each, but 3 were defective. Express the money he pays for the good pens.
Answer: Good pens = 12 − 3 = 9. Amount = 20 × 12 − 20 × 3 = 240 − 60 = 180, or 20 × (12 − 3) = 20 × 9 = 180. So 20 × (12 − 3) = 20 × 12 − 20 × 3 = ₹180.
Example 10: Simplify 98 × 22.
Answer: 98 × 22 = (100 − 2) × 22 = 100 × 22 − 2 × 22 = 2200 − 44 = 2156. Alternatively, 98 × (20 + 2) = 1960 + 196 = 2156.
Example 11: Find the value using brackets: 105 × 23.
Answer: 105 × 23 = (100 + 5) × 23 = 100 × 23 + 5 × 23 = 2300 + 115 = 2415.
Example 12: Find the value: 97 × 15.
Answer: 97 × 15 = (100 − 3) × 15 = 100 × 15 − 3 × 15 = 1500 − 45 = 1455.
Project
Briefly describe any five events of your daily life, collect the data and express it as arithmetic expressions.
Answer: (Model) If rice is ₹60/kg, dal ₹90/kg, oil ₹120/litre and sugar ₹50/kg, then buying 2 kg rice, 3 kg dal, 5 litres oil and 4 kg sugar costs (2 × 60) + (3 × 90) + (5 × 120) + (4 × 50) = 120 + 270 + 600 + 200 = ₹1190. Similarly: (i) 4 friends get sweets at ₹8 each = 4 × 8 = ₹32; (ii) daily reading + play over a week = (3 + 2) × 7 = 35 hours; (iii) bus fare ₹15 for 5 days = 5 × 15 = ₹75; (iv) 6 books at ₹45 each = 6 × 45 = ₹270. Write five such events of your own.
Mathematical Game
Starting with 10 points, apply the operation on each path to reach the end point, and find (and colour) the path that gives the maximum points.
Answer: Apply the operations of a path in order to the starting value 10. For example, 10 → ×6 → 60 → −20 → 40 → ×2 → 80 gives 80 points, while 10 → ×3 → 30 → +10 → 40 → ×5 → 200 gives 200 points. Compare the final values of all possible open paths and colour the one giving the largest value. (The path marked “Your path is closed” cannot be used.)
Exercise 2
1. Fill in the blanks with the appropriate numbers:
Answer: (a) 2 × (5 + 7) = 2 × 5 + 2 × 7 · (b) (6 + 8) × 3 = 6 × 3 + 8 × 3 · (c) 2 × (10 − 3) = 2 × 10 − 2 × 3 · (d) (15 − 3) × 4 = 15 × 4 − 3 × 4.
2. Determine the value (using brackets):
Answer: (a) 9 × 125 = 9 × (100 + 25) = 900 + 225 = 1125 · (b) 99 × 7 = (100 − 1) × 7 = 700 − 7 = 693 · (c) 115 × 4 = (100 + 15) × 4 = 400 + 60 = 460 · (d) 93 × 5 = (90 + 3) × 5 = 450 + 15 = 465 · (e) 151 × 6 = (150 + 1) × 6 = 900 + 6 = 906.
3. Write true or false:
Answer: (a) 5 × (3 + 4) = 5 × 3 + 4 → 35 ≠ 19 → False · (b) 9 × (7 − 5) = 9 × 7 − 9 × 5 → 18 = 18 → True · (c) (12 + 6) × 8 = (12 × 8) + (6 × 8) → 144 = 144 → True · (d) 4 × 3 + 4 × 5 = 4 × (3 + 5) → 32 = 32 → True · (e) 9 × 5 − 5 × 6 = 5 × (9 − 6) → 15 = 15 → True.
4. Compare with the sign (>, < or =):
Answer: (a) 7 × (5 + 1) = 7 × 5 + 7 (42 = 42) · (b) (3 − 4) × 8 < 3 × 8 − 4 (−8 < 20) · (c) −1 × (5 + 3) < −5 × 1 + 3 × 1 (−8 < −2) · (d) 107 × 3 = 100 × 3 + 7 × 3 (321 = 321) · (e) 29 × 4 < 30 × 4 (116 < 120) · (f) (12 − 5) × 8 < 12 × 8 − 5 (56 < 91).
5. Express the numbers in the given patterns using brackets and find the sum.
Answer: (a) The triangular pattern has six circles marked 7 and six circles marked 2. Sum = (6 × 7) + (6 × 2) = 42 + 12 = 54. (b) The hexagonal pattern has four circles marked 5 and eight circles marked 3. Sum = (4 × 5) + (8 × 3) = 20 + 24 = 44. (Grouping equal numbers and multiplying makes the addition easier.)
6. Express these situations correctly and find the values:
Answer: (a) Sahil reads 4 hours and plays 2 hours a day. In a week (7 days), time spent reading and playing = (4 + 2) × 7 = 6 × 7 = 42 hours.
(b) There are 4 sections with 45 students each; 4 from each section join the quiz. Non-participants = 4 × (45 − 4) = 4 × 41 = 164 students (or (4 × 45) − (4 × 4) = 180 − 16 = 164).
7. The steps to evaluate 8 × (5 − 4) are: (a) 40 − 32, (b) 8 × 5 − 8 × 4, (c) 8. Which order is correct?
Answer: The correct order is (b) → (a) → (c) [8 × 5 − 8 × 4 = 40 − 32 = 8], i.e. option (C).
8. Choose the correct answer:
Answer: (A) (7 − 2) × 8 = 5 × 8 = 40 → (c) 40 · (B) 6 × (−5 + 3) = 6 × (−2) = −12 → (d) −12 · (C) −9 × (3 + 4) = −9 × 7 = −63 → (b) −63.
9. Priya does yoga for 1 hour each evening except Tuesday and Saturday. Which expression gives the total hours in 10 weeks?
Answer: Yoga days per week = 7 − 2 = 5. Total hours = (7 − 2) × 1 × 10 = 50. So the correct option is (A) (7 − 2) × 1 × 10.
10. Using only the number 5 (repeated as needed) with basic operations, form expressions that give 1, 2, 3, 4 and 5.
Answer: 1 = 5 ÷ 5 · 2 = (5 + 5) ÷ 5 · 3 = (5 + 5 + 5) ÷ 5 · 4 = (5 × 5 − 5) ÷ 5 · 5 = 5 × 5 ÷ 5 (or 5 + 5 − 5).
11. Put suitable numbers in the shapes (green, red and blue markers) and find the sum.
Answer: This is a shape-addition puzzle: markers of the same colour stand for the same number, arranged as a column addition. Choosing suitable numbers (for example green = 1, red = 2, blue = 3) and adding column by column gives the total sum. It is an open exploratory activity for you to try.
12. Using the numbers 1, 2, 3, 4 only once each, make 10.
Answer: 1 + 2 + 3 + 4 = 10.
Additional Questions and Answers
Multiple Choice Questions (MCQ)
1. An arithmetic expression with only one operation is called — (a) complex expression (b) simple expression (c) a term (d) a bracket
Answer: (b) simple expression.
2. 12 + 5 is a — (a) simple expression (b) complex expression (c) equation (d) term
Answer: (a) simple expression.
3. The correct value of 100 + 20 × 4 is — (a) 480 (b) 180 (c) 124 (d) 80
Answer: (b) 180 [100 + (20 × 4) = 100 + 80].
4. The value of 200 − (80 + 90) is — (a) 30 (b) 210 (c) 10 (d) 170
Answer: (a) 30.
5. The number of terms in 9 + 3 − 5 is — (a) 1 (b) 2 (c) 3 (d) 4
Answer: (c) 3 [terms: 9, 3, −5].
6. Changing the order of terms in addition without changing the value is called — (a) associative law (b) commutative law (c) distributive property (d) bracket rule
Answer: (b) commutative law.
7. When a ‘−’ sign precedes a bracket, on removal the signs inside — (a) stay the same (b) change (c) become zero (d) double
Answer: (b) change.
8. The value of (4 + 5) × 6 is — (a) 54 (b) 34 (c) 24 (d) 30
Answer: (a) 54.
9. 98 × 22 = (100 − 2) × 22 uses which property? (a) commutative (b) associative (c) distributive (d) none
Answer: (c) distributive property.
10. The value of 60 ÷ 30 is — (a) 3 (b) 30 (c) 2 (d) 90
Answer: (c) 2.
Fill in the Blanks
1. Each part of an expression separated by a ‘+’ sign is called a ______. Answer: term.
2. To evaluate a complex expression, first find the value inside the ______. Answer: bracket.
3. Changing the order of terms in addition without changing the value is the ______ law. Answer: commutative.
4. Changing the grouping of three terms without changing the value is the ______ law. Answer: associative.
5. 2 × (50 + 15) = 2 × 50 + 2 × ______. Answer: 15.
True or False
1. 12 + 5 is a complex arithmetic expression. Answer: False (it is a simple expression).
2. 100 + 20 × 4 = 480. Answer: False (correct value is 180).
3. Changing the order of terms in addition changes the value. Answer: False.
4. When ‘+’ precedes a bracket, the signs inside stay the same on removal. Answer: True.
5. (12 + 6) × 8 = 12 × 8 + 6 × 8. Answer: True.
Short Answer Questions
1. What is the difference between a simple and a complex arithmetic expression?
Answer: A simple expression has only one operation (e.g. 12 + 5); a complex expression has more than one different operation together (e.g. 100 + 20 × 4).
2. What is a term? Explain with an example.
Answer: Each part of an expression separated by a ‘+’ sign is a term. In 24 + 9, the terms are 24 and 9. Since subtraction is adding the additive inverse, 55 − 18 = 55 + (−18), so its terms are 55 and −18.
3. State the commutative and associative laws of addition.
Answer: Commutative law: changing the order of two terms does not change the sum (a + b = b + a). Associative law: changing the grouping of three terms does not change the sum [(a + b) + c = a + (b + c)].
4. Using brackets, find the value of 105 × 23.
Answer: 105 × 23 = (100 + 5) × 23 = 100 × 23 + 5 × 23 = 2300 + 115 = 2415.
Key Terms
| Term | Meaning |
|---|---|
| Arithmetic expression | An expression formed by joining numbers with +, −, × and ÷ |
| Simple expression | An expression with only one operation |
| Complex expression | An expression with more than one operation |
| Term | Each part of an expression separated by a ‘+’ sign |
| Bracket | The ( ) symbol that fixes the order of operations |
| Evaluation | Finding the value of an expression |
| Commutative law | Order of terms does not change the sum |
| Associative law | Grouping of terms does not change the sum |
| Distributive property | a × (b + c) = a × b + a × c |
| Removal of brackets | Rewriting an expression without brackets, adjusting signs |