CBSE Class 7 Mathematics Expressions using Letter Numbers Worksheet Set 01

Very Short Answer Questions

Question 1. What are letter-numbers? Give one example.
Answer:
Letters used in place of numbers in a mathematical relation are called letter-numbers. For example, n in the expression 2n.

Teacher's Note:
1. Any letter can be used.
2. A letter-number can take many values.

Question 2. Write an algebraic expression for “7 more than a number x”.
Answer:
7 more than x is x + 7.

Teacher's Note:
1. 'More than' means add.
2. 7 + x is also correct, since addition can be done in any order.

Question 3. The side of a square is q cm. Write an expression for its perimeter.
Answer:
A square has 4 equal sides, so its perimeter is q + q + q + q = 4q cm.

Teacher's Note:
1. Perimeter is the sum of all sides.
2. Write the unit cm.

Question 4. Write 9 × m in the short form used in algebra.
Answer:
We drop the multiplication sign and write the number first: 9 × m = 9m.

Teacher's Note:
1. Number first, then the letter.
2. We write 9m, not m9.

Question 5. Find the value of 8k when k = 6.
Answer:
8k = 8 × k = 8 × 6 = 48.

Teacher's Note:
1. 8k means 8 × k.
2. It does not mean 86.

Question 6. Name the coefficient of y in the term 15y.
Answer:
The number multiplying y is 15, so the coefficient of y is 15.

Teacher's Note:
1. The coefficient is the number in front of the letter.
2. Here it is 15, not 15y.

Question 7. Write the constant term in the expression 7h − 4.
Answer:
The term without a letter-number is −4, so the constant term is −4.

Teacher's Note:
1. The sign in front belongs to the term.
2. So the constant is −4, not 4.

Question 8. Give one example of a pair of unlike terms and say why they are unlike.
Answer:
7x and 7y are unlike terms, because they have different letter-numbers, so they cannot be added into a single term.

Teacher's Note:
1. Like terms need the same letter-number.
2. Same coefficient does not make terms alike.

Question 9. Simplify: 5c + 3c + 10c.
Answer:
All are like terms, so add the coefficients: (5 + 3 + 10)c = 18c.

Teacher's Note:
1. Add the numbers; keep the letter.
2. Answer is 18c, not 18.

Question 10. How many terms are there in the expression 4a − 3b + 9? Name them.
Answer:
There are 3 terms: 4a, −3b and 9.

Teacher's Note:
1. Terms are separated by + and − signs.
2. The minus sign goes with 3b.

Question 11. Write the next two numbers of the sequence 4, 8, 12, 16, … and the expression for its nth term.
Answer:
The next two numbers are 20 and 24.
These are multiples of 4, so the nth term is 4n.

Teacher's Note:
1. The numbers go up by 4 each time.
2. Check: n = 3 gives 12.

Question 12. In a border the designs A, B, C repeat as A, B, C, A, B, C, … from position 1. At which position does design C occur for the 5th time?
Answer:
Design C is at positions 3, 6, 9, …, that is 3n.
For the 5th time: 3 × 5 = position 15.

Teacher's Note:
1. C is always at a multiple of 3.
2. List the first few positions to check.

Question 13. Simplify: p + q + p − q.
Answer:
p + q + p − q = p + p + q − q = 2p.

Teacher's Note:
1. q − q = 0.
2. Group like terms first.

Question 14. Simplify: 8h − (5 + 7h) + 9.
Answer:
8h − (5 + 7h) + 9 = 8h − 5 − 7h + 9 = h + 4.
Check with h = 1: 8 − 12 + 9 = 5 and 1 + 4 = 5.

Teacher's Note:
1. The minus sign before the bracket changes both signs inside.
2. Check by putting a value.

Question 15. Find the value of 7p − 3q when p = 4 and q = 1.
Answer:
7p − 3q = 7 × 4 − 3 × 1 = 28 − 3 = 25.

Teacher's Note:
1. Replace each letter by its own value.
2. Multiply before subtracting.

Question 16. Are the expressions 5u and 5 + u equal? Support your answer using one value of u.
Answer:
No, they are not equal.
For u = 2: 5u = 10 but 5 + u = 7. Equal expressions must give the same value for every value of u.

Teacher's Note:
1. 5u means 5 × u, not 5 + u.
2. One value that differs is enough.

Question 17. Munirathna joins a pipe of k metres to a pipe of 20 m. Write an expression for the combined length.
Answer:
Combined length = (20 + k) metres.

Teacher's Note:
1. Joining lengths means adding.
2. Write the unit.

Question 18. A flour mill takes 10 seconds to start and then 8 seconds to grind each kilogram of grain. Write an expression for the time in seconds taken to grind y kg of grain.
Answer:
Starting time 10 s, plus 8 s for each of the y kg.
Time = 10 + 8y seconds.

Teacher's Note:
1. The starting time is added only once.
2. The 8 seconds is repeated y times.

Question 19. Add the expressions 4d − 7c + 9 and 8c − 11 + 9d.
Answer:
Grouping like terms: (4d + 9d) + (−7c + 8c) + (9 − 11)
= 13d + c − 2.

Teacher's Note:
1. Collect d-terms, c-terms and numbers separately.
2. Keep each sign with its term.

Question 20. Subtract 9a − 6b + 14 from 6a + 9b − 18.
Answer:
(6a + 9b − 18) − (9a − 6b + 14) = 6a + 9b − 18 − 9a + 6b − 14
= −3a + 15b − 32.

Teacher's Note:
1. 'Subtract A from B' means B − A.
2. Every sign inside the second bracket changes.

Question 21. In a 2 × 2 square of dates taken from a calendar, the top-left date is a. Write the other three dates in terms of a.
Answer:
Date to the right: a + 1; date below: a + 7; date diagonally below to the right: a + 8.

Teacher's Note:
1. Going right adds 1; going down adds 7.
2. A week has 7 days.

Question 22. A straight rope folded r times is cut once across. Write an expression for the number of pieces obtained.
Answer:
Each fold adds one more piece after the cut.
So the number of pieces is r + 2.
Check: with 1 fold, one cut gives 3 pieces.

Teacher's Note:
1. Try with a real piece of string.
2. With no fold, one cut gives 2 pieces.

Question 23. A row of triangles is made with matchsticks using 3, 5, 7, 9, … sticks at Steps 1, 2, 3, 4, … Write an expression for the number of matchsticks at Step y.
Answer:
The count starts at 3 and goes up by 2 at each step.
Step y: 3 + 2(y − 1) = 2y + 1 matchsticks.

Teacher's Note:
1. Check: Step 4 gives 9.
2. Add 2 for each step after the first.

Question 24. Reena wrote: “If d = 6, then 3d = 36.” Find her mistake and give the correct value.
Answer:
She multiplied 6 by 6 instead of by 3.
3d means 3 × d, so 3d = 3 × 6 = 18.

Teacher's Note:
1. The number in front is the multiplier.
2. Read 3d as 3 times d.

Question 25. Simplify: 23 + 4(6m − 3n) − 8n − 3m − 18.
Answer:
= 23 + 24m − 12n − 8n − 3m − 18
= (24m − 3m) + (−12n − 8n) + (23 − 18)
= 21m − 20n + 5.

Teacher's Note:
1. Open the bracket first.
2. Then collect like terms.

Question 26. A snail climbs u cm up a wall during the day and slips d cm down during the night, for 10 days and 10 nights. Write an expression for its distance from the starting position, and state what happens if d > u.
Answer:
In one day and night it gains (u − d) cm, so after 10 days and nights it is 10(u − d) cm from the start.
If d > u, it slips more than it climbs, so it ends up below its starting position.

Teacher's Note:
1. Find the change for one day and night first.
2. A negative gain means going down.

Question 27. A number machine takes two inputs. It turns 6 and 3 into 9, turns 10 and 4 into 16, and turns 7 and 5 into 9. Write its formula using the letter-numbers a and b.
Answer:
2 × 6 − 3 = 9, 2 × 10 − 4 = 16, 2 × 7 − 5 = 9.
So the formula is 2a − b (twice the first number minus the second).

Teacher's Note:
1. Test your rule on every pair given.
2. One pair alone can fit many rules.

Question 28. In an endless 4-column grid the numbers are written row by row, so that the number in row r and column c is 4(r − 1) + c. In which row and column does 147 appear?
Answer:
147 = 4 × 36 + 3.
Comparing with 4(r − 1) + c: r − 1 = 36 and c = 3.
So 147 is in row 37, column 3.

Teacher's Note:
1. Divide by 4 and look at the quotient and remainder.
2. Check: 4 × 36 + 3 = 147.

Question 29. Five dates of a calendar form a plus shape with the date a at the centre. Show that their sum is always 5 times the centre date.
Answer:
Above: a − 7, below: a + 7, left: a − 1, right: a + 1.
Sum = (a − 7) + (a − 1) + a + (a + 1) + (a + 7) = 5a, which is 5 times the centre date for every a.

Teacher's Note:
1. The +7 and −7 cancel, and so do +1 and −1.
2. Check with a real calendar.

Question 30. After three rounds of a quiz, the score of Charu is 21p − 9q and that of Krishita is 23p − 7q. By how much is the score of Krishita more than that of Charu?
Answer:
(23p − 7q) − (21p − 9q) = 23p − 7q − 21p + 9q
= 2p + 2q. So Krishita scores 2p + 2q more than Charu.

Teacher's Note:
1. 'More than' means subtract the smaller score.
2. −(−9q) becomes +9q.