Expressions using Letter Numbers Class 7 Solutions Ganita Prakash Maths Chapter 4✦ Step-by-step
HBSE 7th Class Maths Solutions Chapter 4 Expressions using Letter-Numbers (NCERT Ganita Prakash) — every question worked out step by step, including the calendar, rope, matchstick and pattern figures. Tap Solve step by step.
Class 7 Maths Chapter 4 Expressions using Letter Numbers Solutions
Key ideas used in this chapter
Letter-numbera letter stands for an unknown number
No × symbol\(8\times x = 8x\)
Like termsonly same-letter terms can be added
Minus a bracket\(a-(b-c)=a-b+c\)
4.1 The Notion of Letter-Numbers — Figure It Out (Pages 84–85)
Q1, Q2, Q4Build expressions
(Q1) Perimeter of an equilateral triangle, regular pentagon, regular hexagon. (Q2) A 20 m pipe joined to one of length k m. (Q4) A mill starts in 10 s and grinds 8 s per kg for y kg.
Q1
perimeter = number of sides × side: 3s, 5t, 6r
Q2
20 + k ⇒ (20 + k) m
Q4
start 10 + grind 8 per kg ⇒ 10 + 8y ⇒ option (d)
Q3, Q5, Q6Write & describe
(Q3) Total money from a ×₹100, b ×₹20, c ×₹5 notes. (Q5) (a) 5 more than a number (b) 4 less (c) 2 less than 13× (d) 13 less than 2×. (Q6) A situation for 8x + 3y.
Q3
Total = 100a + 20b + 5c rupees
Q5
x + 5; y − 4; 13m − 2; 2s − 13
Q6
e.g. 8 tables at ₹x + 3 chairs at ₹y = ₹(8x + 3y)
Q7Calendar grid (figure)
In a 2×3 block of dates the bottom-middle cell is w. Write the other five cells. (In the figure the block is 12 13 14 / 19 20 21, with w = 20.)
Step 1
left & right of w differ by 1: w−1 and w+1
Step 2
the row above is 7 days earlier (one week): subtract 7
Top row
w−8, w−7, w−6
Bottom row
w−1, w, w+1 (check: 12,13,14 / 19,20,21 ✓)
4.4 Simplification — Figure It Out (Pages 93–94)
Q1Add the pictures
Add the numbers in each picture and simplify (try two ways — by rows and by like terms).
(a)
two rows (5y−6+x) + (x+2+5y): collect x's, y's, numbers ⇒ 2x + 10y − 4
(b)
four groups of (2p+3q) with (−2)×2 + 3×2 ⇒ 8p + 12q + 2
(c)
12 k-terms and 4 g-terms ⇒ 60k − 20g
Q2Simplify
(a) p+p+p+p ; p+p+p+q ; p+q+p−q (b) p−q+p−q ; p+q−p+q (c) p+q−(p+q) ; p−q−p−q (d) 2d−d−d−d ; 2d−d−d−c (e) 2d−d−(d−c) ; 2d−(d−d)−c (f) 2d−d−c−c
(a)
4p; 3p+q; (p+p)+(q−q) = 2p
(b)
2p−2q; (p−p)+(q+q) = 2q
(c)
0; p−p−q−q = −2q
(d)
2d−3d = −d; 2d−2d−c = −c
(e),(f)
2d−d−d+c = c and 2d−c; d − 2c
4.5 Patterns & Relationships — Figure It Out (Page 102)
Q1, Q2Choose the expression
(Q1) Jowar roti ₹30, pulao ₹20, x and y plates — earnings? (Q2) p only champak, q only marigold, r both; one flag each — flags given?
Q1
roti 30x + pulao 20y ⇒ 30x + 20y ⇒ option (a)
Q2
the three groups are different customers ⇒ total = p + q + r flags ⇒ option (a)
Q3, Q4, Q6Word problems
(Q3) Snail climbs u, slips d, 10 cycles. (Q4) Radha cycles 5 km/day week 1, +z each week — total in 3 weeks. (Q6) Train: 3 legs of t min, stops 2 min at 3 stations.
Q3
net per cycle u−d; 10 cycles ⇒ 10(u−d); if d>u the snail moves down
Q4
7(5) + 7(5+z) + 7(5+2z) = 35+35+7z+35+14z = 105 + 21z km
Q6
travel 4t + stops 3×2 = 4t + 6; if t = 4 ⇒ 16 + 6 = 22 min
Q7Simplify
(a) 3a+9b−6+8a−4b−7a+16 (b) 3(3a−3b)−8a−4b−16 (c) 2(2x−3)+8x+12 (d) 8x−(2x−3)+12 (e) 8h−(5+7h)+9 (f) 23+4(6m−3n)−8n−3m−18
(a)
a: 3+8−7=4; b: 9−4=5; num: −6+16=10 ⇒ 4a + 5b + 10
(b)
9a−9b−8a−4b−16 = a − 13b − 16
(c),(d)
4x−6+8x+12 = 12x+6; 8x−2x+3+12 = 6x+15
(e)
8h−5−7h+9 = h + 4
(f)
23+24m−12n−8n−3m−18 = 21m − 20n + 5
Q8Add the expressions
(a) 4d−7c+9 and 8c−11+9d (b) −6f+19−8s and −23+13f+12s (c) 8d−14c+9 and 16c−(11+9d) (e) 13m−12n and 12n−13m
(a)
d: 4+9=13; c: −7+8=1; num: 9−11=−2 ⇒ 13d + c − 2
(b)
f: −6+13=7; s: −8+12=4; num: 19−23=−4 ⇒ 7f + 4s − 4
(c)
8d−14c+9+16c−11−9d = −d + 2c − 2
(e)
(13m−13m)+(−12n+12n) = 0
Q9Subtract the expressions
(a) 9a−6b+14 from 6a+9b−18 (b) −15x+13−9y from 7y−10+3x (c) 17g+9−7h from 11−10g+3h (f) 8g+4h−10 from 7h−8g+20
(a)
(6a+9b−18) − (9a−6b+14) = 6a+9b−18−9a+6b−14 = −3a + 15b − 32
(b)
7y−10+3x+15x−13+9y = 18x + 16y − 23
(c)
11−10g+3h−17g−9+7h = −27g + 10h + 2
(f)
7h−8g+20−8g−4h+10 = −16g + 3h + 30
Q11Rope folding (figure)
A straight rope cut once gives 2 pieces; folded once then cut gives 3; folded twice gives 4. How many pieces if folded 10 times? For r folds?
Pattern
0 folds → 2, 1 fold → 3, 2 folds → 4 — each fold adds one piece.
Rule
pieces = r + 2
10 folds
10 + 2 = 12 pieces
Q12Matchstick squares (figure)
1 square uses 4 sticks, 2 squares use 7, 3 squares use 10. How many for 10 squares? For w squares?
Pattern
4, 7, 10, … — each new square adds 3 sticks (start 4, then +3).
Rule
sticks = 3w + 1
10 squares
3×10 + 1 = 31 sticks
Q13Traffic signal
Colours repeat Red, Yellow, Green, Yellow, … Find the colour at 90, 190, 343 and an expression for each colour's positions.
Positions
even positions are yellow ⇒ 90, 190 → yellow; 343 = 4×86−1 → green
Expressions
Red: 4x−3 · Yellow: 2x · Green: 4x−1
Q14Growing squares (figure)
The X-shapes have 5, 9, 13 squares in Steps 1, 2, 3. How many in Step 4, 10, 50? Give a general formula.
Pattern
5, 9, 13, … — each step adds 4 (one to each arm).
Rule
squares in Step x = 4x + 1
Steps 4, 10, 50
17, 41, 201
Q154-column grid
Numbers fill a 4-column grid row by row. (a) expression for each column (b) row/column of 124, 147, 201 (c) number in row r, column c.
(a)
Col 1: 4x−3 · Col 2: 4x−2 · Col 3: 4x−1 · Col 4: 4x
(b)
124 = 4×31 → row 31, col 4; 147 = 4×37−1 → row 37, col 3; 201 = 4×51−3 → row 51, col 1
(c)
number = 4(r − 1) + c