CBSE Class 7 Mathematics Expressions using Letter Numbers MCQs Set 11

Answer: (b) letter-numbers

Explanation:
1. A letter that stands for a number, like a for Aftab's age, is called a letter-number.
2. A coefficient is the number that multiplies a letter-number, and a constant is a term with no letter at all.
3. So such letters are called letter-numbers.

Teacher's Note:
1. Letter-numbers are also called variables in higher classes.
2. Any letter can be chosen as a letter-number.

Answer: (c) 7 × k

Explanation:
1. In algebra we do not write the multiplication sign between a number and a letter-number.
2. So 7 × k is written simply as 7k.
3. Hence 7k is short for 7 × k.

Teacher's Note:
1. A number written next to a letter always means multiplication.
2. It never means addition.

Answer: (d) m − 4

Explanation:
1. Younger means Jaya's age is less than Meera's age by 4.
2. So we take 4 away from m.
3. Jaya's age = m − 4 years.

Teacher's Note:
1. 'Younger' means subtract; 'older' means add.
2. Check with a number: if Meera is 12, Jaya is 8.

Answer: (a) 13

Explanation:
1. 5m means 5 × m.
2. Put m = 2: 5 × 2 + 3 = 10 + 3.
3. So the value is 13.

Teacher's Note:
1. Multiply first, then add.
2. 25 comes from wrongly working out 5 × (2 + 3).

Answer: (c) 6a

Explanation:
1. A regular hexagon has 6 equal sides.
2. Perimeter = a + a + a + a + a + a = 6 × a.
3. So the perimeter is 6a units.

Teacher's Note:
1. Hexagon means six sides.
2. Number of sides × side gives the perimeter of a regular figure.

Answer: (b) 3p and 7p

Explanation:
1. Like terms have exactly the same letter-number.
2. 5c and 5d have different letters; 2x and 2 do not both have a letter; 9m and 9n have different letters.
3. Only 3p and 7p both have the same letter p.

Teacher's Note:
1. Look at the letters, not at the numbers.
2. Same number in front does not make terms alike.

Answer: (a) 4p

Explanation:
1. Adding p four times is the same as 4 times p.
2. p + p + p + p = (1 + 1 + 1 + 1) × p = 4p.
3. So the simplest form is 4p.

Teacher's Note:
1. Repeated addition is multiplication.
2. p + 4 changes the meaning completely.

Answer: (d) Both Statement I and Statement II are true

Explanation:
1. The expression has two terms, 9x and 4.
2. 4 has no letter-number, so it is the constant term. Statement I is true.
3. The number multiplying x is 9, so 9 is the coefficient of x. Statement II is true.
4. So both Statement I and Statement II are true.

Teacher's Note:
1. Constant term: no letter. Coefficient: the number in front of the letter.
2. Check each statement on its own.

Answer: (a) (i)-(r), (ii)-(p), (iii)-(q), (iv)-(s)

Explanation:
1. 5 more than x is x + 5 (r); 5 times x is 5x (p).
2. 5 less than x is x − 5 (q); x less than 5 means x is taken away from 5, so 5 − x (s).
3. So the match is (i)-(r), (ii)-(p), (iii)-(q), (iv)-(s).

Teacher's Note:
1. 'Less than' reverses the order of writing.
2. Try x = 10 to test each expression.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. The number multiplying a letter-number is its coefficient, so A is true.
2. A letter-number can take any value, so R is also true.
3. But R does not tell us why 4 is called the coefficient, so R is not the correct explanation of A.

Teacher's Note:
1. Both true does not mean one explains the other.
2. Ask: does R give the reason for A?

Answer: (c) A is true, but R is false.

Explanation:
1. 18c and 11d have different letter-numbers, so they cannot be joined into one term. A is true.
2. Terms with different letter-numbers are unlike terms, not like terms. R is false.
3. So A is true but R is false.

Teacher's Note:
1. Only like terms can be added into a single term.
2. c and d are different letters.

Answer: (d) 2n

Explanation:
1. Each L is made of 2 matchsticks.
2. So n Ls need 2 × n = 2n matchsticks.
3. Check with the picture: 3 Ls need 2 × 3 = 6 matchsticks. The answer is 2n.

Teacher's Note:
1. The Ls do not share any matchstick.
2. Always check the rule with the picture.

Answer: (a) 6p + 3q

Explanation:
1. 6p and 3q are unlike terms, so 6p + 3q cannot be simplified.
2. The others can be simplified: 7p − p + 5q − 2q = 6p + 3q, 3b − 2b − b = 0 and 2y + (3y − 6) = 5y − 6.
3. So 6p + 3q is already in its simplest form.

Teacher's Note:
1. Simplest form has no two like terms left.
2. Remove brackets before deciding.

Answer: (c) 6x + 15

Explanation:
1. A minus sign before a bracket changes the sign of every term inside: −(2x − 3) = −2x + 3.
2. So the expression is 8x − 2x + 3 + 12.
3. = 6x + 15, so the answer is 6x + 15.
4. Check with x = 1: 8 − (−1) + 12 = 21 and 6 + 15 = 21.

Teacher's Note:
1. −(−3) becomes +3.
2. Check the answer by putting x = 1.

Answer: (b) 8r + 12s + 20

Explanation:
1. By the distributive property, 4 multiplies every term inside the bracket.
2. 4 × 2r + 4 × 3s + 4 × 5 = 8r + 12s + 20.
3. So the answer is 8r + 12s + 20.

Teacher's Note:
1. Multiply each term inside the bracket.
2. A common mistake is to multiply only the first term.

Answer: (d) Both Statement I and Statement II are true

Explanation:
1. p + q − (p + q) = p + q − p − q = 0. Statement I is true.
2. p − q − p − q = (p − p) + (−q − q) = −2q. Statement II is true.
3. So both Statement I and Statement II are true.

Teacher's Note:
1. Group like terms together before adding.
2. Check with p = 5, q = 2.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Rearranging, l + b + l + b = l + l + b + b = 2l + 2b, so the two always take the same value. A is true.
2. For example, with l = 3 and b = 4 both give 14.
3. R states exactly the test for equal expressions, so R is true and explains A.

Teacher's Note:
1. Equal expressions give equal values for every choice of numbers.
2. One example is a check, not a proof.

Answer: (c) 8n

Explanation:
1. The whole length AB is 12 units and EB is 4 units, so AE = 12 − 4 = 8 units.
2. The width AD is n units.
3. Area of AEFD = 8 × n = 8n square units.
4. Check: 12n − 4n = 8n.

Teacher's Note:
1. Find the missing length first.
2. Area of a rectangle = length × breadth.

Answer: (b) 10y − 3

Explanation:
1. 10 times y is 10y.
2. 3 less than it means take 3 away from 10y.
3. So the expression is 10y − 3.

Teacher's Note:
1. Build the expression in the order of the words.
2. 10(y − 3) means 10 times '3 less than y'.

Answer: (d) Neither Statement I nor Statement II is true

Explanation:
1. 5 − (2 − 6z) = 5 − 2 + 6z = 3 + 6z, not 3 − 6z. Statement I is false.
2. 6(p + 2) = 6p + 12, not 6p + 8. Statement II is false.
3. So neither statement is true.

Teacher's Note:
1. A minus before a bracket flips every sign inside.
2. The number outside multiplies every term inside.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. In a calendar, the date to the right is 1 more and the date below is 7 more.
2. So the square is a, a + 1, a + 7, a + 8, and both diagonal sums are 2a + 8. R is true.
3. Since this works for every a, A is true, and R gives exactly the reason. So R explains A.

Teacher's Note:
1. Letter-numbers prove a pattern for all cases at once.
2. Check with a real calendar.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. We leave out the multiplication sign, so 4 × n is written 4n. A is true.
2. 4 × 7 = 28, so R is true.
3. R is only one value; it does not explain the rule of leaving out the sign. So R is not the correct explanation of A.

Teacher's Note:
1. A single numerical check does not explain a rule.
2. Both statements are true here.

Answer: (c) (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q)

Explanation:
1. (i) 2d − d − d − c = −c (r). (ii) 2d − d − d − d = −d (p).
2. (iii) 2d − d − (d − c) = 2d − d − d + c = c (s). (iv) 2d − (d − d) − c = 2d − 0 − c = 2d − c (q).
3. So the match is (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q).

Teacher's Note:
1. Remove brackets carefully, flipping signs after a minus.
2. Simplify all four before choosing.

Answer: (d) Only Statement I is true

Explanation:
1. 4(x + y) − y = 4x + 4y − y = 4x + 3y. Statement I is true.
2. 10(y − 3) = 10y − 30, which is not the same as 10y − 3. For y = 0 they give −3 and −30. Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. One value that gives different answers is enough to show two expressions are not equal.
2. Open the bracket to compare.

Answer: (a) 105 + 21z

Explanation:
1. Week 1: 7 × 5 = 35 km.
2. Week 2: she cycles 5 + z km a day, so 7(5 + z) = 35 + 7z km.
3. Week 3: she cycles 5 + 2z km a day, so 7(5 + 2z) = 35 + 14z km.
4. Total = 35 + 35 + 7z + 35 + 14z = 105 + 21z km.

Teacher's Note:
1. A week has 7 days.
2. In week 3 the increase is 2z, not z.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. 3 + 2(y − 1) = 3 + 2y − 2 = 2y + 1, so the two expressions are always equal. A is true.
2. Each new triangle shares one stick, so 2 sticks are added at each step. R is true.
3. R explains why the pattern goes up by 2, but the equality in A comes from opening the bracket. So R is not the correct explanation of A.

Teacher's Note:
1. Read carefully what R is explaining.
2. Opening the bracket proves A.

Answer: (d) Only Statement I is true

Explanation:
1. Design C is at positions 3, 6, 9, …, that is 3n. B is one place before, at 3n − 1. Statement I is true.
2. 122 = 3 × 41 − 1, so position 122 has design B, not C. Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. Divide the position by 3 and look at the remainder.
2. Remainder 0 means C, 2 means B, 1 means A.

Answer: (c) 4(r − 1) + c

Explanation:
1. Rows 1 to r − 1 use up 4(r − 1) numbers.
2. In row r, the number in column c comes c places after that.
3. So the number is 4(r − 1) + c. Check: row 2, column 3 gives 4 × 1 + 3 = 7.

Teacher's Note:
1. Count how many numbers come before the row.
2. Test the formula with a number you can see.

Answer: (a) (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s)

Explanation:
1. (i) 2 sticks per L gives 2n (q). (ii) A regular pentagon has 5 sides, so 5n (r).
2. (iii) Design C is at positions 3, 6, 9, …, so 3n (p). (iv) 3, 5, 7, … sticks give 2n + 1 (s).
3. So the match is (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s).

Teacher's Note:
1. Test each rule with n = 1 and n = 2.
2. Every pair must fit for the option to be right.

Answer: (b) 3w + 1

Explanation:
1. The first square needs 4 matchsticks.
2. Each extra square shares one stick, so it needs only 3 more.
3. For w squares: 4 + 3(w − 1) = 4 + 3w − 3 = 3w + 1.
4. Check: for w = 4, 3 × 4 + 1 = 13, which matches the picture.

Teacher's Note:
1. Count the shared sticks only once.
2. Check the formula with the drawing.