Mathematical Operations on Expressions

Q. The shifting of a number from one side of an equation to the other is called as _____.

1. transposition
2. distributivity
3. associativity
4. commutativity

Q.

Question 3

Which of the following is not allowed in a given equation?

(a) Adding the same number to both sides of the equation.

(b) Subtracting the same number from both sides of the equation.

(c) Multiplying both sides of the equation by the same non-zero number.

(d) Dividing both sides of the equation by the same number.

Q. Set up an equation in the following cases:
The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. ( Take the lower score to be $l$).

Q.

Classify the following into constants and variables.

Q.

$3x+15=10$ is a simple equation. If $5$ is added to the left-hand side of the equation, the equation remains the same as the given equation.

1. True

2. False

Q. Which of the following operation is not allowed in an equation?

1. Adding the same number to both sides of the equation
2. Subtracting the same number from both sides of the equation
3. Multiplying both sides of the equation by the same non-zero number
4. Dividing both sides of the equation by zero

Q. Which of the following equations has $x=2$ as a solution?

1. $x+2=5$
2. $x-2=0$
3. $2x+1=0$
4. $x+3=6$

Q. Kaushlaya can do a work in $20$ days, while Kaikeyi can do the same work in $25$ days. They started the work jointly. A few days later Sumitra joined them and thus all of them completed the whole work in $10$ days. All of them were paid a total $Rs.700$. What is the share of Sumitra?

1. Can't be determined
2. $Rs.185$
3. $Rs.130$
4. $Rs.70$

Q. If we assign a variable x to the number of '8's that can be made using 42 matchsticks, then what would be the equation relating the number of matchsticks and the number of '8's that can be made using those many matchsticks?

1. $x=7\times 42$
2. $7+x=42$
3. $7+42=x$
4. $7x=42$

Q. Solve linear equation

Q.

What is the mean of the numbers 5, 6 and 7

1. 4

2. 5

3. 6

4. 18

Q. What is the mean of the numbers 5, 6 and 7?

1. 4
2. 5
3. 6
4. 18

Q. Organize the following marks in a class assessment, in a tabular form:
4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7.
Find the arithmetic mean

Q. Give the steps you will use to separate the variable and then solve the equation:
5m + 7 = 17

Q. State which of the following are equation (with a variable) given reason and tell your answer. identify the variable from the equation with a variable.
$7=(11\times 2)÷p$

Q. Organize the following marks in a class assessment, in a tabular form:
4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7.
Find the arithmetic mean

Q. What remains after 4 is subtracted on both sides is $2x=6$ Which of the following operations can I perform next?

1. Divide both sides of the equation by 2
2. Shift 2 to the right hand side
3. Multiply 2 on both sides of the equation
4. Both A and B

Q. Find the mean of first six natural numbers.

1. None of these
2. $3.6$
3. $7$
4. $3.5$

Q. For which equation(s) is $x=3$ a solution?
(I) $2x-5+3x=10$ (II) $\frac{-x+7}{2}=2$
(III) $4x-11=17$ (IV) $9=-(x-1)+11$

1. I only
2. I and II
3. I, II and III
4. I, II and IV

Q.

Question 26

An autorickshaw charges ₹ 10 for the first kilometre, then ₹ 8 for each such subsequent kilometre. The total charge (in ₹) for $d$ kilometres is ___ .

Q. What is the value of x in the equation
$2x+4=10?$

1. 4
2. 3
3. 6
4. 1

Q. What do we get when we multiply both the sides of the equation $\frac{2m}{5}=6$ with $\frac{5}{2}$ ?

1. $\frac{m}{5}=15$
2. $m=30$
3. $m=15$
4. $5m=6$

Q. Give the the step you will use to separate the variable and then solve the equations
$20r=-10$

Q. What do we get on adding 5 on both sides of the equation $x+5=10$?

1. $x+20=15$
2. $x+10=15$
3. $x+5=15$
4. $x+10=5$

Q. Give first the step you will use to separate the variable and then solve the equations
$\frac{3p}{10}=6$

Q.

What is the mean of the numbers 5, 6 and 7

1. 5

2. 4

3. 18

4. 6

Q. Give first the step you will use to separate the variable and then solve the equations
$\frac{20p}{3}=40$

Q.

Find the mean of all factors of $10$.

Q. A marathon runner completes a full marathon of $42km$ in $4$ hours and $30$ minutes. What is his speed in $m/sec$ (rounded to one decimal place)

Q.

Karan spends ₹ 5000 on food which is $\frac{5}{8}$th of his income. Karan's income is ___ (in rupess).