Algebra is the study of mathematical symbols and the rules for manipulating these symbols. Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. Here we have given NCERT Solutions for Class 6 Mathematics, Chapter 11 Algebra, Exercise 11.1 which is solved by subject experts as per NCERT (CBSE) Book guidelines.
|Algebra Exercise 11.1
NCERT Answers for Class 6 Maths Chapter 11 Algebra Exercise 11.1
Ex 11.1 Class 6 Maths Question 1. Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
(a) 2 matchsticks are required to make a letter T. Hence, the pattern is 2n
(b) 3 matchsticks are required to make a letter Z. Hence, the pattern is 3n
(c) 3 matchsticks are required to make a letter U. Hence, the pattern is 3n
(d) 2 matchsticks are required to make a letter V. Hence, the pattern is 2n
(e) 5 matchsticks are required to make a letter E. Hence, the pattern is 5n
(f) 5 matchsticks are required to make a letter S. Hence, the pattern is 5n
(g) 6 matchsticks are required to make a letter A. Hence, the pattern is 6n
Ex 11.1 Class 6 Maths Question 2. We already know the rule for the pattern of letters L, C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?
We know that L require only two matchsticks. So, the pattern for letter L is 2n. Among all the letters given in question 1, only L and V are the letters which require two matchsticks. Hence, (a) and (d).
Ex 11.1 Class 6 Maths Question 3. Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows.)
Let n be the number of rows
Number of cadets in a row = 5
Total number of cadets = number of cadets in a row × number of rows
Ex 11.1 Class 6 Maths Question 4. If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)
Let b be the number of boxes
Number of mangoes in a box = 50
Total number of mangoes = number of mangoes in a box × number of boxes
Ex 11.1 Class 6 Maths Question 5. The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)
Let s be the number of students
Pencils given to each student = 5
Total number of pencils = number of pencils given to each student × number of students
Ex 11.1 Class 6 Maths Question 6. A bird flies 1 kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use t for flying time in minutes.)
Let t minutes be the flying times
Distance covered in one minute = 1 km
Distance covered in t minutes = Distance covered in one minute × Flying time
= 1 × t
= t km
Ex 11.1 Class 6 Maths Question 7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?
Number of dots in a row = 9
Number of rows = r
Total number of dots in r rows = Number of dots in a row × number of rows
Number of dots in 8 rows = 8 × 9
Number of dots in 10 rows = 10 × 9
Ex 11.1 Class 6 Maths Question 8. Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Can you write Leela’s age in terms of Radha’s age? Take Radha’s age to be x years.
Let Radha’s age be x years
Leela’s age = 4 years younger than Radha
= (x – 4) years
Ex 11.1 Class 6 Maths Question 9. Mother has made laddus. She gives some laddus to guests and family members; still 5 laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?
Number of laddus mother gave = l
Remaining laddus = 5
Total number of laddus = number of laddus given away by mother + number of laddus remaining
= (l + 5) laddus
Ex 11.1 Class 6 Maths Question 10. Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be x, what is the number of oranges in the larger box?
Number of oranges in a small box = x
Number of oranges in two small boxes = 2x
Number of oranges remained = 10
Number of oranges in large box = number of oranges in two small boxes + number of oranges remained
= 2x + 10
Ex 11.1 Class 6 Maths Question 11. (a) Look at the following matchstick pattern of squares (Fig 11.6). The squares are not separate. Two neighbouring squares have a common matchstick.
Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint : If you remove the vertical stick at the end, you will get a pattern of Cs.)
(b) Fig 11.7 gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.
(a) We may observe that in the given matchstick pattern, the number of matchsticks are 4, 7, 10 and 13, which is 1 more than the thrice of the number of squares in the pattern
Therefore the pattern is 3x + 1, where x is the number of squares
(b) We may observe that in the given matchstick pattern, the number of matchsticks are 3, 5, 7 and 9 which is 1 more than the twice of the number of triangles in the pattern.
Therefore the pattern is 2x + 1, where x is the number of triangles.