Mathematics
Fill in the blanks:
(i) In algebra, we use ….. to represent variables (generalized numbers).
(ii) A symbol or letter which can be given various numerical values is called a …..
(iii) If Jaggu's present age is x years, then his age 7 years from now is …..
(iv) If one pen costs ₹x, then the cost of 9 pens is …..
(v) An equation is a statement that the two expressions are ……
(vi) The numerical coefficient of the monomial −5x2y3 is …..
(vii) 7 less than thrice a number y is …..
(viii) If 3x + 4 = 19, then the value of x is …..
(ix) The number of pencils bought for ₹x at the rate of ₹2 per pencil is ……… .
(x) 3p2q and −5pq2 are ….. terms.
(xi) The value of the expression 3 − 5x for x = 4 is …..
Algebra Basics
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Answer
(i) In algebra, we use letters (literals) to represent variables.
(ii) A symbol or letter which can be given various numerical values is called a variable.
(iii) Jaggu's age 7 years from now = (x + 7) years.
(iv) Cost of 9 pens at ₹x each = ₹9x.
(v) An equation is a statement that the two expressions are equal.
(vi) Numerical coefficient of −5x2y3 is −5.
(vii) Thrice y = 3y. 7 less than this = 3y − 7.
(viii) 3x + 4 = 19 ⇒ 3x = 15 ⇒ x = 5.
(ix) Number of pencils = = .
(x) 3p2q and −5pq2 have different powers of p and q, so they are unlike terms.
(xi) Value of 3 − 5x at x = 4 = 3 − 5(4) = 3 − 20 = −17.
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Related Questions
Solve the following linear equations:
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Solve the following linear equations:
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(ii)
(iii) 5p + 7 = 19 − 2p
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(v)
(vi)
State whether the following statements are true (T) or false (F):
(i) If x is variable then 5x is also variable.
(ii) If y is variable then y − 5 is also variable.
(iii) The number of angles in a triangle is a variable.
(iv) The value of an algebraic expression changes with the change in the value of the variable.
(v) If the length of a rectangle is twice its breadth, then its area is a constant.
(vi) An equation is satisfied only for a definite value of the variable.
(vii) If x toffees are distributed equally among 5 children, then each child gets 5x toffees.
(viii) t minutes are equal to 60t seconds.
(ix) If x is a negative integer, then −x is a positive integer.
(x) x = 5 is a solution of the equation 3x + 2 = 13.
(xi) 2y - 7 > 13 is an equation.
(xii) 'One third of a number x added to itself gives 8' can be expressed as .
(xiii) The difference between the ages of two sisters Lata and Asha is a variable.
I think of a number x, add 5 to it. The result is then multiplied by 2 and the final result is 24. The correct algebraic statement is
x + 5 × 2 = 24
(x + 5) × 2 = 24
2 × x + 5 = 24
x + 5 = 2 × 24