Chapter 4: Expressions using Letters–Numbers
(Class 7 • Ganita Prakash New Mathematics • CBSE)
Part A — 20 Most-Important 1-Mark Questions (with Solutions)
Q1 If \(a=23\) and \(s=a+3\), find \(s\).
\(s=23+3=26\).
Q2 Perimeter of a square of side \(q\).
\(4q\).
Q3 Write “5 more than a number \(x\)” as an expression.
\(x+5\).
Q4 Simplify \(p+p+p+p\).
\(4p\).
Q5 Evaluate \(7k\) for \(k=4\).
\(28\).
Q6 Is \(5u\) equal to \(5+u\)?
No; \(5u\) is \(5\times u\), \(5+u\) is “5 more than \(u\)”.
Q7 Simplify \(10y-3-\,10(y-3)\).
\(10y-3-10y+30=27\).
Q8 Combine like terms: \(8x-3x+7\).
\(5x+7\).
Q9 If a rectangle has length \(l\) and breadth \(b\), write its perimeter.
\(2l+2b\).
Q10 Value of \(3(2m-1)\) when \(m=5\).
\(3(10-1)=27\).
Q11 Write “13 less than twice a number \(t\)”.
\(2t-13\).
Q12 Simplify \(4(x+y)-y\).
\(4x+3y\).
Q13 Evaluate \(23-10\times2\).
\(23-20=3\).
Q14 Evaluate \(7\times4+9\times6\).
\(28+54=82\).
Q15 Translate “product of 35 and \(c\) plus product of 60 and \(j\)”.
\(35c+60j\).
Q16 For L-shapes using 2 sticks each, write sticks needed for \(n\) L’s.
\(2n\).
Q17 Simplify \((4x+3y)-(3x+4y)\).
\(x-y\).
Q18 Combine: \(5c+3c+10c\).
\(18c\).
Q19 Expand \(6(p+2)\).
\(6p+12\).
Q20 If side of an equilateral triangle is \(s\), perimeter = ?
\(3s\).
Part B — 20 Most-Important 2-Mark Questions (with Solutions)
Q1 If \(s=a+3\) and \(a=18\), find \(s\). Then express \(a\) in terms of \(s\).
\(s=21\). Also \(a=s-3\).
Q2 Write and simplify the perimeter of a rectangle as a sum of sides.
\(p=l+b+l+b=2l+2b\).
Q3 A shop rents \(x\) chairs, \(y\) tables. Pay at start: ₹40 /chair, ₹75 /table; refund on return: ₹6 /chair, ₹10 /table. Net paid?
\((40x+75y)-(6x+10y)=34x+65y\).
Q4 Evaluate \(5m+3\) for \(m=2\) and \(m=-2\).
\(m=2\Rightarrow 13\); \(m=-2\Rightarrow -7\).
Q5 Expand and simplify \(3(2x-5)+7\).
\(6x-15+7=6x-8\).
Q6 Combine like terms: \(9p-4p+6q-11+3p-2q+5\).
\((9-4+3)p+(6-2)q+(-11+5)=8p+4q-6\).
Q7 Show \(3+2(y-1)=2y+1\).
\(3+2y-2=2y+1\).
Q8 Evaluate \(10y-3\) and \(10(y-3)\) at \(y=5\). Are they equal?
\(47\) and \(20\). Not equal.
Q9 For matchstick pattern with \(y\) triangles in a row, prove count \(=2y+1\).
Start \(=3\). Each new triangle adds 2 sticks: \(3+2(y-1)=2y+1\).
Q10 Express “cost of \(c\) coconuts at ₹35 and \(j\) kg jaggery at ₹60”.
₹\((35c+60j)\).
Q11 Simplify \(2d-d-(d-c)\) and \(2d-(d-d)-c\).
First: \(c\). Second: \(2d-c\).
Q12 Put \(p=4,\,q=1\) in \(7p-3q\), \(8p-4q\), \(6p-2q\) and sum.
\(25,\,28,\,22\) → total \(75\).
Q13 Find the \(n\)th term of \(4,8,12,16,\dots\).
\(4n\) (often written without “×” as \(4n\)).
Q14 Translate to algebra: “2 less than 13 times a number \(x\)”.
\(13x-2\).
Q15 Simplify \((5c)+(3c)+(10c)-(2c)\).
\(16c\).
Q16 Evaluate \(20+8(16-6)\).
\(20+8\cdot10=100\).
Q17 If \(l=3,\,b=4\), check \(l+b+l+b=2l+2b\).
Both give \(14\). Verified.
Q18 Expand and collect: \(4(x+y)-y\).
\(4x+3y\).
Q19 Write “\(10\) more than \(8\) times \(t\)”.
\(8t+10\).
Q20 Combine: \(2p+q-(p+q)\).
\(p\).
Part C — 20 Most-Important 3-Mark Questions (with Solutions)
Q1 Derive the perimeter of a rectangle and evaluate for \(l=12\text{ cm}, b=7\text{ cm}\).
Sum of sides \(=l+b+l+b=2l+2b\Rightarrow 2(12)+2(7)=38\text{ cm}\).
Q2 Charu’s round scores: \(7p-3q,\,8p-4q,\,6p-2q\). Show final score \(=21p-9q\).
\((7+8+6)p-(3+4+2)q=21p-9q\).
Q3 For the calendar 2×2 block with top-left \(a\), show diagonal sums are equal.
Block numbers: \(a,\,a+1,\,a+7,\,a+8\). Diagonals: \(a+(a+8)=2a+8\) and \((a+1)+(a+7)=2a+8\). Equal.
Q4 A pencil-and-eraser sale over 3 days: pencils \(5,3,10\) at ₹\(c\), erasers \(4,6,1\) at ₹\(d\). Write total and simplify.
Pencils \(=5c+3c+10c=18c\); erasers \(=4d+6d+1d=11d\). Total \(=18c+11d\) (simplest).
Q5 Show \(3+2(y-1)=2y+1\) equals \(2y+1\) and hence matches \(2y+1\) rule in matchstick pattern.
Expand: \(3+2y-2=2y+1\). Same as formula \(2y+1\).
Q6 Simplify: \(4(2r+3s+5)-20-8r-12s\).
\(8r+12s+20-20-8r-12s=0\).
Q7 If \(a=5\), compare \(10a-3\) and \(10(a-3)\). Explain.
\(10a-3=47\); \(10(a-3)=20\). Different because subtraction occurs before/after multiplying by 10.
Q8 Translate & simplify: “sum of three consecutive multiples of \(x\)” as \(x,2x,3x\).
Sum \(=x+2x+3x=6x\).
Q9 If \(l=3, b=4\), verify \(l+b+l+b\) and \(2l+2b\) have same value by substitution.
Both \(=14\). Hence equivalent.
Q10 Evaluate \(3(3a-3b)-8a-4b-16\).
\(9a-9b-8a-4b-16=a-13b-16\).
Q11 For \(x=5,y=1\), compute \(4(x+y)-y\) two ways: expand first vs substitute first.
Expand: \(4x+3y=20+3=23\). Substitute first: \(4(6)-1=24-1=23\). Same.
Q12 Explain why \(3a+2b\neq5\) in general.
LHS depends on \(a,b\). RHS is constant. Only equal for specific pairs, not as an identity.
Q13 If \(n\)th term of a sequence is \(4n\), find term numbers where the value is a multiple of 8.
\(4n\) multiple of 8 \(\Rightarrow n\) even. Terms \(n=2,4,6,\dots\).
Q14 Add \((4d-7c+9)\) and \((8c-11+9d)\).
\(13d+c-2\).
Q15 Subtract \((9a-6b+14)\) from \((6a+9b-18)\).
\((6a+9b-18)-(9a-6b+14)=-3a+15b-32\).
Q16 Write & simplify: \(2d-d-c-c\).
\(d-2c\).
Q17 If \(w\) is a calendar date, fill a 2×3 block when bottom-middle is \(w\).
Bottom row: \(w-1,\,\boxed{w},\,w+1\). Top row: \(w-8,\,w-7,\,w-6\).
Q18 For a row of \(w\) adjacent unit squares made by matchsticks, show total sticks \(=3w+1\).
First square: 4 sticks; each new square shares 1 side \(\Rightarrow +3\). So \(4+3(w-1)=3w+1\).
Q19 For numbers arranged by rows of 4: row \(r\), column \(c\). Give a formula for the number.
\(\;N=4(r-1)+c\).\div>
Q20 In 10 day–night cycles, net snail displacement if climbs \(u\) cm by day, slips \(d\) cm by night.
\(10(u-d)\) cm (downward if \(d>u\)).
Part D — All Textbook Exercise Questions (Solved)
4.1 The Notion of Letter-Numbers — Figure it Out
1 Formulas for perimeters: (a) equilateral triangle (side \(s\)) (b) regular pentagon (side \(p\)) (c) regular hexagon (side \(h\)).
(a) \(3s\);\; (b) \(5p\);\; (c) \(6h\).
2 Munirathna’s pipe: existing \(=20\) m, attach \(k\) m. Combined length?
\(20+k\) meters.
3 Total money with ₹100, ₹20, ₹5 notes. Complete table rows.
For counts \((A,B,C)\): total \(=100A+20B+5C\).
• Row \((3,5,6)\): \(300+100+30=₹430\).
• Row \((8,4,z)\): \(800+80+5z=₹(880+5z)\).
• Row \((x,y,z)\): \(100x+20y+5z\).
• Row \((3,5,6)\): \(300+100+30=₹430\).
• Row \((8,4,z)\): \(800+80+5z=₹(880+5z)\).
• Row \((x,y,z)\): \(100x+20y+5z\).
4 Flour mill start-up 10 s; grinding \(y\) kg at \(8\) s/kg. Choose the correct expression.
\(\boxed{10+8y}\) seconds.
5 Write expressions: (a) 5 more than a number \(n\) (b) 4 less than a number \(t\) (c) 2 less than 13 times a number \(x\) (d) 13 less than twice a number \(x\).
(a) \(n+5\);\; (b) \(t-4\);\; (c) \(13x-2\);\; (d) \(2x-13\).
6 Describe situations: (a) \(8x+3y\) (b) \(15j-2k\).
(a) ₹8 per notebook, ₹3 per pencil; buying \(x\) notebooks and \(y\) pencils costs ₹\(8x+3y\).
(b) Quiz: \(j\) correct (+15 each), \(k\) wrong (−2 each) ⇒ score \(15j-2k\).
(b) Quiz: \(j\) correct (+15 each), \(k\) wrong (−2 each) ⇒ score \(15j-2k\).
7 Calendar 2×3 block: bottom middle date is \(w\). Fill others.
Using calendar steps: right \(+1\), down \(+7\).
Top row: \(w-8,\;w-7,\;w-6\). Bottom row: \(w-1,\;\boxed{w},\;w+1\).
Top row: \(w-8,\;w-7,\;w-6\). Bottom row: \(w-1,\;\boxed{w},\;w+1\).
4.2 Revisiting Arithmetic Expressions — Evaluate
1 \(23-10\times2\)
\(3\).
2 \(83+28-13+32\)
\(130\).
3 \(34-14+20\)
\(40\).
4 \(42+15-(8-7)\)
\(56\).
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