Chapter 2: Arithmetic Expressions
Part 1 — 20 Most Important 1-Mark Questions (with Solutions)
1What is an arithmetic expression? Give one example.
A number phrase using \(+\!,-,\times,\div\). Example: \(13+2\).
2Find the value of \(13+2\). Write the equality.
Value \(=15\). So, \(13+2=15\).
3Which symbol shows equality between an expression and its value?
The equality sign \(=\).
4Mallika spends ₹25 per day from Monday–Friday. Write the expression for a week’s lunch cost.
\(5\times 25\).
5Write two different expressions whose value is \(12\).
Examples: \(10+2,\; 15-3,\; 3\times 4,\; 24\div 2\) (any two).
6Compare: \(10+2\) and \(7+1\).
\(12\gt 8\Rightarrow 10+2\gt 7+1\).
7Fill the blank: \(13+4=\_\_+6\).
\(13+4=17\Rightarrow \_\_+6=17\Rightarrow \boxed{11}\).
8Compare: \(113-25\) and \(112-24\).
Both equal \(88\). Hence \(113-25=112-24\).
9Identify the terms in \(83-14\).
Write as \(83+(-14)\). Terms: \(83\) and \(-14\).
10Identify the terms in \(6\times 5+3\).
Terms: \(6\times 5\) and \(3\).
11Evaluate \(30+(5\times 4)\).
\(30+20=50\).
12Write an expression for Irfan’s change if he pays ₹100 for items of ₹15 and ₹56.
\(100-(15+56)\).
13Write \(-18-3\) as a sum of terms.
\(-18+(-3)\).
14State the commutative property of addition using \(a,b\).
\(a+b=b+a\).
15Remove brackets: \(200-(40+3)\).
\(200-40-3=157\).
16Remove brackets: \(500-(250-100)\).
\(500-250+100=350\).
17Which property: \(2\times(43+24)=2\times 43+2\times 24\)?
Distributive property of multiplication over addition.
18Are \((4+3)\times 5\) and \(4\times 5+3\times 5\) equal?
Yes, both equal \(35\).
19Which arrangement does \(5\times 2+3\) describe?
“3 more than \(5\times 2\)”; value \(=13\).
20Raghu has four 2-kg packets and also packs \(100\) kg into 2-kg packets. Write packets expression.
\(4+\dfrac{100}{2}=4+50=54\) packets.
Chapter 2: Arithmetic Expressions
Part 2 — 20 Most Important 2-Mark Questions (with Solutions)
1Fill the blanks so that both sides are equal: \(22+\_\_ = 6\times 5\).
Right side \(=30\). So \(22+\boxed{8}=30\).
2Arrange in increasing order of values: \(67-19,\; 67-20,\; 35+25,\; 5\times 11,\; 120\div 3\).
Values: \(48,\;47,\;60,\;55,\;40\). Order: \(120\div 3\,(40)\lt 67-20\,(47)\lt 67-19\,(48)\lt 5\times 11\,(55)\lt 35+25\,(60)\).
3Compare without heavy calculation: \(245+289\) \(\square\) \(246+285\).
Shift \(+1\) from \(285\) to \(245\): left becomes \(246+288\), still \(=534\); right is \(246+285=531\). So \(245+289\gt 246+285\).
4Compare: \(273-145\) \(\square\) \(272-144\).
Both reduce by 1 on each side → difference same. \(273-145=128\), \(272-144=128\). Hence \(=\).
5Write \(23-2\times 4+16\) as a sum of terms and evaluate.
As terms: \(23+(-2\times 4)+16=23-8+16=31\).
6Identify the terms in \(4+15-9\) and compute the value using the “sum of terms”.
Terms: \(4,\;15,\;-9\). Sum \(=4+15+(-9)=10\).
7Remove brackets: \(100-(15+56)\) and compute.
\(100-15-56=29\).
8Remove brackets: \(500-(250-100)\) and compute.
\(500-250+100=350\).
9Write a story for \(30+5\times 4\) and evaluate using correct order.
“30 loose marbles plus 5 bags of 4” → \(30+(5\times4)=30+20=50\).
10State and apply the commutative property to show \(6+(-4)=(-4)+6\).
Commutative law: \(a+b=b+a\). Hence \(6+(-4)=(-4)+6=2\).
11Show by distributive property that \(2\times(43+24)=2\times 43+2\times 24\) and compute.
LHS \(=2\times 67=134\). RHS \(=86+48=134\). Equal.
12Compare without full evaluation: \(124+245\) \(\square\) \(129+245\).
Right has \(5\) more in first addend ⇒ total \(5\) more. So \(124+245\lt 129+245\).
13Write the total cost if 4 friends buy dosas at ₹23 each and leave ₹5 tip. Identify terms and find value.
Expression: \(4\times 23+5\). Terms: \(4\times 23,\;5\). Value \(=92+5=97\).
14Ruby saw \(33\) students playing; teacher called “groups of 5”. Write expression and value.
\(6\times 5+3\) (6 full groups and 3 left). Value \(=33\).
15Use distributive property to simplify \(4\times 5+3\times 5\).
\((4+3)\times 5=7\times 5=35\).
16Fill the box using distributive law: \(5\times(9-2)=5\times 9-5\times \square\).
\(\boxed{2}\).
17“Tinker the terms”: If \(53+(-16)=37\), find \(54+(-16)\) and \(53+(-15)\) without recomputing fully.
First term +1 ⇒ total \(38\). Second: second term +1 (i.e., less negative) ⇒ total \(38\).
18Compute quickly using distributive idea: \(97\times 25\).
\((100-3)\times 25=2500-75=2425\).
19Choose the expression for Irfan’s change when he pays ₹100 for ₹15 biscuit and ₹56 dal: \(100-15+56\) or \(100-(15+56)\)? Explain.
\(100-(15+56)\) because we subtract the total cost first; removing brackets gives \(100-15-56\).
20Compare by reasoning: \((34-28)\times 42\) \(\square\) \(34\times 42-28\times 42\).
By distributive property they are equal: \((34-28)\times 42=34\times 42-28\times 42\).
Chapter 2: Arithmetic Expressions
Part 3 — 20 Most Important 3-Mark Questions (with Solutions)
1Write an expression for: “200 minus the sum of 40 and 3”. Remove brackets and evaluate.
Expression: \(200-(40+3)\). Removing brackets: \(200-40-3=157\).
2Show that \(500-(250-100)=500-250+100\). Verify by evaluation.
LHS: \(500-(250-100)=500-150=350\). RHS: \(500-250+100=350\). Verified.
3Hira has 28 coins in one bag and 35 in another. She gifts away 10 coins from the second bag. Write expression and solve.
Expression: \(28+(35-10)\). = \(28+25=53\) coins left.
4Identify terms and find value: \(39-2\times 6+11\).
Write as \(39+(-2\times 6)+11=39-12+11=38\). Terms: \(39,\;-12,\;11\).
5Story problem: Binu earns ₹20000/month, spends ₹5000 rent, ₹5000 food, ₹2000 other. Find annual savings.
Monthly save \(=20000-(5000+5000+2000)=8000\). Annual \(=8000\times 12=96000\).
6A snail climbs 3 cm by day, slips 2 cm by night. Pole height 10 cm. In how many days will it reach top?
Net progress/day = 1 cm. After 7 days snail at 7 cm. On 8th day climbs 3 cm to reach 10 cm. So in 8 days.
7Melvin reads 2-page stories every day except Tue & Sat. In 8 weeks, how many stories?
Reading days/week = 5. Stories/week = \(5\times 2/2=5\). Actually each story=2 pages, so 1 story/day. In 8 weeks=5×8=40 stories.
8Evaluate quickly: \(95\times 8\) using distributive property.
\((100-5)\times 8=800-40=760\).
9Evaluate: \(49-7+8\) and compare with itself written differently.
\(49-7+8=50\). Equal on both sides. Thus \(=\).
10Check if \(83\times 42-18\) equals \(83\times 40-18\).
First: \(3486-18=3468\). Second: \(3320-18=3302\). Not equal. First is greater.
11Compare: \(145-17\times 8\) and \(145-17\times 6\).
First: \(145-136=9\). Second: \(145-102=43\). So second is greater.
12Use distributive law: \(23\times 48-35\) vs \(23\times (48-35)\).
First: \(1104-35=1069\). Second: \(23\times 13=299\). Not equal.
13Window height = grill 3 cm + gap 2 cm + border 5 cm. Write expression and total.
\(3+2+5=10\) cm.
14Show that \((4+3)\times 5=4\times 5+3\times 5\).
LHS \(=7\times 5=35\). RHS \(=20+15=35\). Verified distributive property.
15Use distributive idea to evaluate \(104\times 15\).
\((100+4)\times 15=1500+60=1560\).
16In a parade, 4 rows of 5 scouts + 3 rows of 5 guides. Write two equivalent expressions and compute.
\(4\times 5+3\times 5=20+15=35\). Or \((4+3)\times 5=35\).
17Evaluate: \(27-(18+4)\) and compare with \(27+(-18-4)\).
First: \(27-22=5\). Second: \(27-22=5\). Equal.
18Using reasoning, is \((76-53)\times 88\) equal to \(88\times(53-76)\)?
\((76-53)\times 88=23\times 88=2024\). Second: \(88\times -23=-2024\). Not equal; opposite signs.
19Write an expression for total mangoes in 1 week if Rahim supplies 9 kg/day and Shyam 11 kg/day. Compute.
Daily=9+11=20 kg. Weekly=20×7=140 kg.
20Compute quickly: \(49\times 50\) using distributive property.
\((50-1)\times 50=2500-50=2450\).
Chapter 2: Arithmetic Expressions
Part 4 — All Textbook Exercise Questions with Perfect Solutions
2.1 — Simple Expressions & Comparing
2.1–F1Fill in to balance the equality.
(a) \(13+4=\boxed{11}+6\) (since both sides \(=17\)).
(b) \(22+\boxed{8}=6\times 5\) (since \(22+8=30\)).
(c) \(8\times \boxed{8}=64\div 2\) (RHS \(=32\Rightarrow 8\times 4\), so the blank is \(4\)).
(d) \(34-\boxed{9}=25\) (since \(34-9=25\)).
2.1–F2Arrange in increasing order by value: \(67-19,\; 67-20,\; 35+25,\; 5\times 11,\; 120\div 3\).
Values: \(48,\;47,\;60,\;55,\;40\). Order: \(120\div 3\,(40)\lt 67-20\,(47)\lt 67-19\,(48)\lt 5\times 11\,(55)\lt 35+25\,(60)\).
2.1–CCompare using reasoning (no heavy calculation).
(a) \(245+289 \;\boxed{>}\; 246+285\) (shift \(+1\) from 289 to 245 ⇒ \(246+288=534\) vs \(246+285=531\)).
(b) \(273-145 \;\boxed{=}\; 272-144\) (subtracting 1 from both numbers keeps difference same: both \(=128\)).
(c) \(364+587 \;\boxed{<}\; 363+589\) (RHS has net \(+1\) overall).
(d) \(124+245 \;\boxed{<}\; 129+245\) (RHS +5 larger).
(e) \(213-77 \;\boxed{<}\; 214-76\) (RHS increases by \(+1\) and also subtracts \(1\) less ⇒ net \(+2\)).
2.2 — Reading & Evaluating Complex Expressions
2.2–E1Find values by writing as a sum of terms.
(a) \(28-7+8=28+(-7)+8=29\).
(b) \(39-2\times 6+11=39+(-12)+11=38\).
(c) \(40-10+10+10=40+(-10)+10+10=50\).
(d) \(48-10\times 2+16\div 2=48-20+8=36\).
(e) \(6\times 3-4\times 8\times 5=18-(32\times 5)=18-160=-142\).
2.2–E2Write a situation and evaluate.
(a) \(89+21-10=100\). (E.g., ₹89 in wallet, get ₹21, spend ₹10 ⇒ ₹100).
(b) \(5\times 12-6=60-6=54\). (E.g., 5 packs of 12 pens minus 6 gifted).
(c) \(4\times 9+2\times 6=36+12=48\). (E.g., 4 trays of 9 apples plus 2 trays of 6 oranges).
2.2–E3Write expression, identify terms, and value.
(a) Queen Alia: Elsa doubles \(100\Rightarrow 200\), Anna halves \(100\Rightarrow 50\). Total \(=200+50=250\). Expression \(=2\times 100+\tfrac{1}{2}\times 100\). Terms \(200,50\).
(b) Metro fare: Adult ₹40, Child ₹20. (i) \(4\times 40+3\times 20=160+60=220\). (ii) Two groups of 3 adults: \(2\times (3\times 40)=240\).
(c) Window height: \(3+2+5=10\) cm.
Removing Brackets — I
RB–1Fill to keep both sides equal.
(a) \(24+(6-4)=24+6\;\boxed{-}\;4\) ⇒ \(24+2=26\).
(b) \(38+(\boxed{9\;-\;4})=38+9-4=43\).
(c) \(24-(6+4)=24\;\boxed{-}\;6\;\boxed{-}\;4\) ⇒ \(14\).
(d) \(24-6-4=24-6\;\boxed{-}\;4\) (already balanced).
(e) \(27-(8+3)=27\;\boxed{-}\;8\;\boxed{-}\;3=16\).
(f) \(27-(\boxed{8\;+\;3})=27-8+3\) is not equal; correct removal is \(27-8-3\). (Hence the intended fill is \(8+3\) on LHS; RHS should be \(27-8-\!3\)).
RB–2Remove brackets and simplify.
(a) \(14+(12+10)=14+12+10=36\).
(b) \(14-(12+10)=14-12-10=-8\).
(c) \(14+(12-10)=14+12-10=16\).
(d) \(14-(12-10)=14-12+10=12\).
(e) \(-14+12-10=-12\).
(f) \(14-(-12-10)=14+12+10=36\).
RB–3Pairs: guess equality, then verify.
(a) \((6+10)-2\) vs \(6+(10-2)\): both \(=14\). Equal (associativity).
(b) \(16-(8-3)=16-5=11\) vs \((16-8)-3=8-3=5\). Not equal.
(c) \(27-(18+4)=27-22=5\) and \(27+(-18-4)=27-22=5\). Equal.
RB–4Identify expressions with same value (reasoning, not full computation).
(a) \(319+537\) and \(-537+319\) are not equal (the second is \(319-537\)). Equal pair is \(537-319\) with \(+218\) vs \(319-537=-218\). Hence only rearrangements that keep signs same are equal: here, none except identical form.
(b) From: \(87+46-109,\; 87+46-109,\; 87+46-109,\; 87-46+109,\; 87-(46+109),\; (87-46)+109\).
Equal sets:
• The three copies of \(87+46-109\) are of course equal (value \(=24\)).
• \((87-46)+109=41+109=150\) (not equal to 24).
• \(87-(46+109)=87-155=-68\) (not equal).
• \(87-46+109=150\) (same as previous 150).
So equality groups: {all copies of \(87+46-109\)} and { \(87-46+109,\; (87-46)+109\) }.
RB–5Add brackets to get indicated values.
(a) \(34-9+12=13\Rightarrow 34-(9+12)=34-21=13\).
(b) \(56-14-8=34\Rightarrow 56-(14-8)=56-6=50\) (not 34). Correct: \((56-14)-8=42-8=34\).
(c) \(-22-12+10+22=-22\Rightarrow -22-(12-10)+22=-22-2+22=-2\) (not \(-22\)). Correct: \(-22-(12+10)+22=-22-22+22=-22\).
RB–6Fill so both sides equal.
(a) \(423+\boxed{-4}=419+\boxed{0}\) (both become \(419\)). Many answers possible; one valid pair shown.
(b) \(207-68=139\Rightarrow 210-\boxed{71}=139\).
RB–7Using \(2,3,5\) and \(+,-\) (with brackets), generate different values (sample).
Examples: \(2-3+5=4,\; 3-(5-2)=0,\; 5-(3-2)=4,\; (5+3)-2=6,\; 2-(3-5)=4,\; (2+3)-5=0.\)
RB–8Jasoda’s trick: to do “\(-9\)” as “\(-10)+1\)”.
(a) Always correct because \(-9=(-10)+1\Rightarrow n-9=(n-10)+1\).
(b) Similar: subtract 19 as \(-20)+1\); add 29 as \(+30-1\); etc. Example: \(63-19=(63-20)+1=44\).
RB–9Match equal forms.
For \(73-14+1\): equals \(73+(-14)+1=73-(14-1)=73-(13)=60\Rightarrow\) equal to \(73-(14-1)\) i.e. option (b). Also equals \(73+(-14+1)\) i.e. option (c).
For \(73-14-1\): equals \(73-(14+1)=73-15=58\Rightarrow\) equal to \(73-(14+1)\) i.e. option (a). Also equals \(73+(-14-1)\) i.e. option (d).
Removing Brackets — II (Distributive Property)
DP–1Complete using distributive law.
(a) \(3(6+7)=3\cdot 6+3\cdot 7\).
(b) \((8+3)4=8\cdot 4+3\cdot 4\).
(c) \(3(5+8)=3\cdot 5+3\cdot \boxed{8}\).
(d) \((9+2)4=9\cdot 4+\boxed{2\cdot 4}\).
(e) \(3(\boxed{9}+4)=\boxed{3\cdot 9}+3\cdot 4\).
(f) \((\boxed{7}+6)4=13\cdot 4+\boxed{0}\) (one correct fill: left \(= (7+6)4=52\); right \(=52+0\)).
(g) \(3(\boxed{5}+\boxed{2})=3\cdot 5+3\cdot 2\).
(h) \((\boxed{2}+\boxed{3})\boxed{4}=2\cdot 4+3\cdot 4\).
(i) \(5(9-2)=5\cdot 9-5\cdot \boxed{2}\).
(j) \((5-2)7=5\cdot 7-2\cdot \boxed{7}\).
(k) \(5(8-3)=5\cdot 8-\boxed{5\cdot 3}\).
(l) \((8-3)7=8\cdot 7-\boxed{3\cdot 7}\).
(m) \(5(12-\boxed{2})=\boxed{5\cdot 12}-5\cdot \boxed{2}\).
(n) \((15-\boxed{9})7=\boxed{15\cdot 7}-\boxed{9\cdot 7}\).
(o) \(5(\boxed{9}-\boxed{4})=5\cdot 9-5\cdot 4\).
(p) \((\boxed{17}-\boxed{9})\boxed{7}=17\cdot 7-9\cdot 7\).
DP–2Insert \(<,>,=\) by reasoning.
(a) \((8-3)29 \;\boxed{>}\; (3-8)29\) (left positive, right negative).
(b) \(15+9\cdot 18 \;\boxed{<}\; (15+9)\cdot 18\) (RHS multiplies 15 too).
(c) \(23(17-9) \;\boxed{\neq}\; 23\cdot 17+23\cdot 9\) (should be \(23\cdot 17-23\cdot 9\)); hence \(<\).
(d) \((34-28)42 \;\boxed{=}\; 34\cdot 42-28\cdot 42\) (distributive equality).
DP–3Make 14 in different ways: \(\_\times(\_+\_)=14\).
Examples: \(1\times(7+7),\; 2\times(4+3),\; 7\times(1+1),\; 14\times(1+0)\) (using 0 allowed), \( \; \) also \( \; \) \( \boxed{ \; } \) many valid variants exist.
DP–4Find sums in two different ways (using grouping/distributive). (Teacher may draw arrays; sample method.)
E.g., sum of \(8+8+8+8+8 = 5\times 8 = 40\). Or group \( (8+8)+(8+8)+8=16+16+8=40\). Students can present two valid expressions yielding same result.
Mixed Word Problems & Reasoning
MW–1Mango supply per week: Rahim \(9\) kg/day, Shyam \(11\) kg/day, 7 days.
Daily \(=9+11=20\) kg ⇒ Weekly \(=20\times 7=140\) kg.
MW–2Binu monthly: ₹20,000 income; spends ₹5,000 (rent) + ₹5,000 (food) + ₹2,000 (other). Find yearly savings.
Monthly save \(=20000-(5000+5000+2000)=8000\). Yearly \(=8000\times 12=96,000\).
MW–3Snail climbs 3 cm/day, slips 2 cm/night; pole 10 cm. Days to reach top?
Net \(=1\) cm/day until last day. After 7 days at 7 cm; day 8 climb reaches \(10\) cm. Answer: \(\boxed{8\text{ days}}\).
MW–4Melvin reads a 2-page story daily except Tue & Sat. In 8 weeks, how many stories?
Reading days/week \(=7-2=5\). Each reading day → 1 story. In 8 weeks: \(5\times 8=40\) stories. Matching expressions: \((7-2)\times 8\) or \(7\times 8-2\times 8\).
MW–5Evaluate in different ways.
(a) \(1-2+3-4+5-6+7-8+9-10\)
Pair as \((1-2)+(3-4)+\cdots+(9-10)=(-1)+(-1)+(-1)+(-1)+(-1)=-5\).
(b) \(1-1+1-1+1-1+1-1+1-1=0\) (five pairs of \(1-1=0\)).
MW–6Compare by reasoning.
(a) \(49-7+8\) vs itself → \(=\).
(b) \(83\cdot 42-18\) vs \(83\cdot 40-18\): left larger (since \(83\cdot 42>83\cdot 40\)).
(c) \(145-17\cdot 8\) vs \(145-17\cdot 6\): second larger (subtracts smaller amount).
(d) \(23\cdot 48-35\) vs \(23\cdot (48-35)\): not equal; RHS \(=23\cdot 13\), LHS \(=1104-35\).
(e) \((16-11)12\) vs \(-11\cdot 12+16\cdot 12\): equal by distributive: \(5\cdot 12= (16-11)12\).
(f) \((76-53)88\) vs \(88(53-76)\): values are opposites: \(+2024\) vs \(-2024\) ⇒ \(>\).
(g) \(25(42+16)\) vs \(25(43+15)\): both sums \(=58\) ⇒ equal.
(h) \(36(28-16)=36\cdot 12=432\) vs \(35(27-15)=35\cdot 12=420\) ⇒ first \(>\).
MW–7Which expressions are equal to the given one (without computation)?
(a) Given \(83-37-12 = 83+(-37)+(-12)=83-(37+12)\).
Equals: (ii) \(84-(37+12)\) is \(\neq\) (different first term); (iii) \(83-38-13\neq\) (subtracts 1 more and 1 more again);
(iv) \(-37+83-12\) \(=83-37-12\) (commutative for addition of terms) ⇒ **Equal**.
Hence equal forms: original and (iv).
(b) Given \(93+37\cdot 44+76\) means terms \(93,\;37\cdot 44,\;76\).
(i) \(37+93\cdot 44+76\) swaps 93 and 37 (changes structure) ⇒ not equal.
(ii) \(93+37\cdot 76+44\) changes the product term ⇒ not equal.
(iii) \((93+37)(44+76)\) multiplies sums ⇒ not equal.
(iv) \(37\cdot 44+93+76\) reorders terms only ⇒ **Equal**.
MW–8Choose a number and create ten different expressions with that value. (Open-ended practice.)
Example target \(=50\): \(25+25,\; 60-10,\; 2\times 25,\; 100\div 2,\; 75-25,\; 5\times 10,\; 40+10,\; 55-5,\; (30+20),\; 200\div 4\).
Extra — “Terms Table” Completion (from Try This)
TTComplete the “Expression as sum of terms” and list the terms.
1) \(13-2+6 = 13+(-2)+6\). Terms: \(13,\,-2,\,6\).
2) \(5+6\times 3 = 5+(6\times 3)\). Terms: \(5,\;6\times 3\).
3) \(4+15-9 = 4+15+(-9)\). Terms: \(4,\,15,\,-9\).
4) \(23-2\times 4+16 = 23+(-2\times 4)+16\). Terms: \(23,\,-2\times 4,\,16\).
5) \(28+19-8 = 28+19+(-8)\). Terms: \(28,\,19,\,-8\).