AP SCERT Class 7 Maths Unit 4 – Expressions Using Letter-Numbers – Solutions (Pages 205–256): This post gives complete, easy-to-understand answers for Unit 4: Expressions Using Letter-Numbers from the AP SCERT Class 7 Mathematics textbook. It covers all "Figure it Out" exercises (4.1, 4.2, 4.3) and "Mind the Mistake, Mend the Mistake" activities, including algebraic expressions, letter-numbers, like and unlike terms, simplifying expressions, the distributive property, perimeter formulas, number patterns, and real-life word problems. These Class 7 Maths Unit 4 solutions are perfect for AP students, parents, and teachers preparing for exams, and are useful reference material for AP TET / DSC Mathematics Pedagogy aspirants as well. Keywords: AP SCERT Class 7 Maths solutions, Expressions using letter numbers answers, algebraic expressions Class 7, AP Board Maths Unit 4, Figure it Out 4.1 4.2 4.3 answers.
📘 Figure it Out - 4.1 (Page 213–215)
1. Write formulas for the perimeter of:
(a) Triangle with all sides equal (side = a): Perimeter = 3 × a = 3a
(b) A regular pentagon (side = a): Perimeter = 5 × a = 5a
(c) A regular hexagon (side = a): Perimeter = 6 × a = 6a
2. Munirathna has a 20 m pipe and joins another pipe of length 'k' metres to it.
Expression for combined length = 20 + k metres.
3. Krithika's total amount table:
| No. of ₹100 notes | No. of ₹20 notes | No. of ₹5 notes | Expression and Total Amount |
|---|---|---|---|
| 3 | 5 | 6 | 3 × 100 + 5 × 20 + 6 × 5 = 430 |
| 6 | 4 | 3 | 6 × 100 + 4 × 20 + 3 × 5 = 695 |
| 8 | 4 | z | 8 × 100 + 4 × 20 + z × 5 = 880 + 5z |
| x | y | z | 100x + 20y + 5z |
4. Time to grind y kg grain (10 sec to start, 8 sec per kg): (d) 10 + 8 × y
5. Algebraic expressions:
(a) 5 more than a number (n): n + 5
(b) 4 less than a number (n): n − 4
(c) 2 less than 13 times a number (n): 13n − 2
(d) 13 less than 2 times a number (n): 2n − 13
6. Describe situations for the expressions:
(a) 8 × x + 3 × y — Suma buys x notebooks priced ₹8 each and y pens priced ₹3 each. This expression gives the total money she spends.
(b) 15 × j − 2 × k — In a quiz, a student gets 15 points for every correct answer (j correct answers) and loses 2 points for every wrong answer (k wrong answers). This expression gives the student's total score.
7. Calendar 2×3 grid — bottom middle cell = w. Filling the grid:
| w − 8 | w − 7 | w − 6 |
| w − 1 | w | w + 1 |
🔍 Mind the Mistake, Mend the Mistake (Page 220)
| No. | Statement Given | Mistake? | Correct Value |
|---|---|---|---|
| 1 | If a = −4, then 10 − a = 6 | Yes | 10 − (−4) = 14 |
| 2 | If d = 6, then 3d = 36 | Yes | 3 × 6 = 18 |
| 3 | If s = 7, then 3s − 2 = 15 | Yes | 3×7−2 = 19 |
| 4 | If r = 8, then 2r + 1 = 29 | Yes | 2×8+1 = 17 |
| 5 | If j = 5, then 2j = 10 | No mistake | 10 (correct) |
| 6 | If m = −6, then 3(m+1) = 19 | Yes | 3×(−5) = −15 |
| 7 | If f = 3, g = 1, then 2f − 2g = 2 | Yes | 6 − 2 = 4 |
| 8 | If t = 4, b = 3, then 2t + b = 24 | Yes | 8+3 = 11 |
| 9 | If h = 5, n = 6, then h − (3 − n) = 4 | Yes | 5−(−3) = 8 |
📗 Figure it Out - 4.2 (Page 231–233)
1. Add the numbers in each picture (unknown values as letter-numbers) and simplify:
Picture 1 — Row 1: 5y, −6, x | Row 2: x, 2, 5y
Expression = 5y + (−6) + x + x + 2 + 5y = 10y + 2x − 4
Picture 2 — Row 1: 2p, 3q, −2, 3 | Row 2: 3q, 2p, 3, −2 | Row 3: 2p, 3q | Row 4: 3q, 2p
Expression = (2p+2p+2p+2p) + (3q+3q+3q+3q) + (−2+3+3−2) = 8p + 12q + 2
Picture 3 — Row 1: −5g, 5k, 5k, −5g | Row 2 & 3: 5k, 5k, 5k, 5k each | Row 4: −5g, 5k, 5k, −5g
Expression = (−10g+10k) + 20k + 20k + (−10g+10k) = −20g + 60k
2. Simplify each of the following expressions:
(a) p+p+p+p = 4p; p+p+p+q = 3p + q; p+q+p−q = 2p
(b) p−q+p−q = 2p − 2q; p+q−p+q = 2q
(c) p+q−(p+q) = 0; p−q−p−q = −2q
(d) 2d−d−d−d = −d; 2d−d−d−c = −c
(e) 2d−d−(d−c) = c; 2d−(d−d)−c = 2d − c
(f) 2d−d−c−c = d − 2c
🔍 Mind the Mistake, Mend the Mistake (Page 234)
| No. | Expression | Given "Simplest Form" | Mistake? | Correct Simplest Form |
|---|---|---|---|---|
| 1 | 3a + 2b | 5 | Yes | 3a + 2b (unlike terms, cannot combine) |
| 2 | 3b − 2b − b | 0 | No mistake | 0 (correct) |
| 3 | 6(p + 2) | 6p + 8 | Yes | 6p + 12 |
| 4 | (4x+3y) − (3x+4y) | x + y | Yes | x − y |
| 5 | 5 − (2 − 6z) | 3 − 6z | Yes | 3 + 6z |
| 6 | 2 + (x + 3) | 2x − 6 | Yes | x + 5 |
| 7 | 2y + (3y − 6) | −y + 6 | Yes | 5y − 6 |
| 8 | 7p − p + 5q − 2q | 7p + 3q | Yes | 6p + 3q |
| 9 | 5(2w + 3x + 4w) | 10w + 15x + 20w | Yes (not fully combined) | 30w + 15x |
| 10 | 3j + 6k + 9h + 12 | 3(j + 2k + 3h + 4) | No mistake | 3(j+2k+3h+4) (correct) |
| 11 | 4(2r + 3s + 5) | −20 − 8r − 12s | Yes | 8r + 12s + 20 |
📙 Figure it Out - 4.3 (Page 249–253)
1. One Jowar roti plate = ₹30, Pulao plate = ₹20; x plates Jowar, y plates Pulao sold. Correct expression(s):
(a) 30x + 20y
2. Pushpita gives one flag to every customer (p only champak + q only marigold + r both):
(a) p + q + r
3. Snail climbs u cm up by day, slips d cm down by night, for 10 days & 10 nights.
(a) Distance from starting position = 10u − 10d = 10(u − d)
(b) If d > u, the snail slips down more than it climbs each day, so its net position keeps going below the starting point — the snail never reaches the top and keeps sliding further down the well.
4. Radha's cycling distance over 3 weeks (Week 1: 5 km/day; increases by z km/day each week):
Week 1 = 7 × 5 = 35 km
Week 2 = 7 × (5+z) = 35 + 7z km
Week 3 = 7 × (5+2z) = 35 + 14z km
Total after 3 weeks = 105 + 21z km
5. Number-path diagram starting from w + 2:
| Path | Steps | Result |
|---|---|---|
| Top-left | (w+2) −5 → (w−3) ×3 → | 3w − 9 |
| Top-right | (w+2) +3 → (w+5) ×4 → | 4w + 20 (given) |
| Bottom-left | (w+2) −8 → (w−6) −4 → | w − 10 |
| Bottom-right | (w+2) −4 → (w−2) ×3 → | 3w − 6 (given) |
6. Train from Yahapur to Vahapur — 3 stops (4 equal segments of t minutes each), stopping 2 minutes at each of the 3 stations.
(a) If t = 4: Time = 4×4 + 3×2 = 16 + 6 = 22 minutes
(b) Algebraic expression: 4t + 6
7. Simplify the following expressions:
(a) 3a+9b−6+8a−4b−7a+16 = 4a + 5b + 10
(b) 3(3a−3b)−8a−4b−16 = a − 13b − 16
(c) 2(2x−3)+8x+12 = 12x + 6
(d) 8x−(2x−3)+12 = 6x + 15
(e) 8h−(5+7h)+9 = h + 4
(f) 23+4(6m−3n)−8n−3m−18 = 21m − 20n + 5
8. Add the expressions:
(a) 4d−7c+9 and 8c−11+9d = 13d + c − 2
(b) −6f+19−8s and −23+13f+12s = 7f + 4s − 4
(c) 8d−14c+9 and 16c−(11+9d) = −d + 2c − 2
(d) 6f−20+8s and 23−13f−12s = −7f − 4s + 3
(e) 13m−12n and 12n−13m = 0
(f) −26m+24n and 26m−24n = 0
9. Subtract the expressions:
(a) 9a−6b+14 from 6a+9b−18 = −3a + 15b − 32
(b) −15x+13−9y from 7y−10+3x = 18x + 16y − 23
(c) 17g+9−7h from 11−10g+3h = −27g + 10h + 2
(d) 9a−6b+14 from 6a−(9b+18) = −3a − 3b − 32
(e) 10x+2+10y from −3y+8−3x = −13x − 13y + 6
(f) 8g+4h−10 from 7h−8g+20 = −16g + 3h + 30
10. Describe situations for the expressions:
(a) 8x + 3y — Ravi buys x kg of rice at ₹8 per kg and y kg of sugar at ₹3 per kg. This gives the total amount spent.
(b) 15x − 2x — A shopkeeper had 15x mangoes packed in boxes of x each, and 2x mangoes got spoiled and removed. This expression gives the number of good mangoes left (=13x).
11. Rope cut pattern: straight cut → 2 pieces; folded once & cut → 3 pieces.
Each fold doubles the number of layers (2r layers for r folds); cutting through all layers of a folded rope gives 2r + 1 pieces.
Folded 10 times and cut: 210 + 1 = 1025 pieces
Expression for r folds: 2r + 1
12. Matchstick squares pattern (each new square adds 3 sticks after the first, which needs 4):
Formula: 3n + 1 (n = number of squares)
For 10 squares: 3×10+1 = 31 matchsticks
For w squares: 3w + 1
13. Traffic signal colour sequence (Red, Yellow, Green, Yellow repeating, period 4):
Position 90 → Yellow Position 190 → Yellow Position 343 → Green
Expressions (n = 1, 2, 3, ...): Red positions = 4n − 3; Yellow positions = 4n − 2 and 4n; Green positions = 4n − 1
14. X-shaped square pattern (each step adds 4 more squares to the previous X):
Formula for number of squares at Step n: 4n + 1
Step 4 = 17 squares; Step 10 = 41 squares; Step 50 = 201 squares
Since each square has 4 vertices, total vertices ≈ 4 × (4n+1) = 16n + 4
15. 4-column endless number grid (Column 1: 1,5,9,13,…; Column 2: 2,6,10,14,…; Column 3: 3,7,11,15,…; Column 4: 4,8,12,16,…):
(a) Expressions for row n: Column 1 = 4n − 3; Column 2 = 4n − 2; Column 3 = 4n − 1; Column 4 = 4n
(b) Row and column of:
(i) 124 → Row 31, Column 4
(ii) 147 → Row 37, Column 3
(iii) 201 → Row 51, Column 1
(c) Number in row r, column c: 4(r − 1) + c
(d) Multiples of 3 shift by one column in each successive row (since 3 and 4 have no common factor, the pattern of multiples of 3 repeats fully only after every 3 rows / 12 numbers — this is because LCM(3,4) = 12).
📌 Chapter Summary
- Algebraic expressions use letter-numbers along with numbers to describe patterns and relationships, and are used to make predictions.
- The same rules used for arithmetic expressions (swapping, grouping, distributive property) apply to algebraic expressions too, and help simplify them to their simplest form.
- Algebraic expressions can be written in words and vice versa. Algebra often gives a short and elegant way to describe relationships that would otherwise need long sentences.
