Question 12 Marks
The successor of an integer.
AnswerLet the integer be $n.$
Successor of $n = n + 1$
$\therefore$ Required expression $= n + 1$
Note: If $7$ is added to a number, we get its successor.
View full question & answer→Question 22 Marks
On my last birthday, I weighed $40\ kg.$ If I put on $m \ kg$ of weight after a year, what is my present weight?
AnswerGiven, my weight on my last birthday $= 40\ kg$
Weight increase after a year $= m \ kg$
Present weight $= 40\ kg + m \ kg = (40 + m)kg$
View full question & answer→Question 32 Marks
$z$ is multiplied by $-3$ and the result is subtracted from $13.$
AnswerAccording to the question, $z$ is multiplied by $-3 = (-3) \times z$
Now, result is subtracted from $13 = 13 - (-3)$
$z = 13 + 3z $
Hence, the required expression is $13 + 3z.$
View full question & answer→Question 42 Marks
$x$ times of $3$ is added to the smallest natural number.
AnswerAccording to the question, $x$ times of $3 = 3x$ and smallest natural number $= 1$
Now, according to question,
Resulting expression $= 3x + 1$
Hence, the required expression is $3x + 1$.
View full question & answer→Question 52 Marks
Multiple of $5.$
AnswerThe multiples of a whole number are found by taking the product of any counting number and that whole number.
Multiples of $ 5$ are Multiply $5$ by $1 = 5 \times 1 = 5$ Multiply $5$ by $2 = 5 \times 2 = 10$ and so on.
Hence, multiple of $5 = 5n,$ where n is any whole number.
View full question & answer→Question 62 Marks
Translate the following statements into an equation, using $x$ as the variable$: 13$ subtracted from twice a number gives $3.$
AnswerLet the number be $x$
Twice the number $= 2x$
According to the question,
$2x - 13 = 3$
Hence, the required equation is $ 2x - 13 = 3.$
View full question & answer→Question 72 Marks
$p$ is divided by $11$ and the result is added to $10.$
AnswerAccording to the question, $p$ is divided by $11=\frac{\text{p}}{11}$ Now, result is added to $10,$ i.e. $10+\frac{\text{p}}{11}$ Hence, the required expression is $10+\frac{\text{p}}{11}.$
View full question & answer→Question 82 Marks
Translate the following statements into an equation, using $x$ as the variable:$1$ subtracted from one-third of a number gives $1.$
AnswerLet the number be $x.$
Twice of this number $=\frac{\text{x}}{3}$
According to the question, $\frac{\text{x}}{3}-1=1$
Hence, the required equation is $\frac{\text{x}}{3}-1=1.$
View full question & answer→Question 92 Marks
Area of the rectangle with length $k$ units and breadth $n$ units.
AnswerGiven, length of rectangle $= k$ units
Breadth of rectangle $= n$ units
Now, area of rectangle $=$ Length $\times $ Breadth $= k \times n = kn$ units
Hence, area of the rectangle is $kn$ sq units.
View full question & answer→Question 102 Marks
Perimeter of a rectangle is found by using the formula $P = 2(l + w),$ where $l$ and $w$ are respectively the length and breadth of the rectangle. Write the rule that is expressed by this formula in words.
AnswerPerimeter of a rectangle $= 2($Length of the rectangle $+$ Breadth of the rectangle$)$
i.e. The perimeter of a rectangle is twice the sum of its length and breadth.
View full question & answer→Question 112 Marks
The perimeter of an equilateral triangle, if side of the triangle is $m.$
AnswerGiven, side of triangle is $m.$
In equilateral triangle, all sides are equal.
$\therefore$ Perimeter of an equilateral triangle $=$ Sum of all the sides $= m + m + m = 3m$
Hence, the perimeter of an equilateral triangle is $3m.$
View full question & answer→Question 122 Marks
Translate the following statements into an equation, using $x$ as the variable: One fifth of a number is $5$ less than that number.
AnswerLet the number be $x$
One-fifth of this number $=\frac{\text{x}}{5}$
According to the question, $\frac{\text{x}}{5}=\text{x}-5$
So, the required equation is $\frac{\text{x}}{5}=\text{x}-5$
View full question & answer→Question 132 Marks
Length and breadth of a bulletin board are $r \ cm$ and $t \ cm,$ respectively. If $x$ nails are used to repair one board, how many nails will be required to repair $15$ such boards$?$
AnswerGiven, length of bulletin board $= r \ cm$ and breadth of bulletin board $= t \ cm$
Then, perimeter of bulletin board $= 2(r + f)cm $ and area of bulletin board $= rt \ cm$ To repair one board, number of nails required $= x$ For $15$ boards, number of nails required $= 15x$
View full question & answer→Question 142 Marks
Translate the following statements into an equation, using $x$ as the variable: Two-third of number is $12.$
AnswerLet the number be $x.$
Two-third of this number $=\frac{2}{3}\text{x}$
According to the question, $\frac{2\text{x}}{3}=12$
Hence, the required equation is $\frac{2\text{x}}{3}=12.$
View full question & answer→Question 152 Marks
Perimeter of a triangle is found by using the formula $P = a + b + c,$ where $a, b$ and $c$ are the sides of the triangle. Write the rule that is expressed by this formula in words.
AnswerIn this question, given formula for getting perimeter of triangle is $p = a + b + c.$
Here, $a, b $ and $c$ are the length of sides of the triangle. Hence, the perimeter of a triangle is equal to the sum of all sides of a triangle.
View full question & answer→Question 162 Marks
Translate the following statements into an equation, using $x$ as the variable: $9$ added to twice a number gives $13.$
AnswerLet the number be $x.$
Twice of this number $= 2x$
According to the question, $2x + 9 = 13$
Hence, the required equation is $2x + 9 = 13.$
View full question & answer→Question 172 Marks
Two consecutive even integers.
AnswerAny even integer can be written as $2n,$ where $n$ is an integer.
So, next even integer will be $2n + 2.$
Hence, two consecutive even integers are $2n$ and $2n + 2.$
View full question & answer→Question 182 Marks
Omar helps his mother $1$ hour more than his sister does.
AnswerLet sister’s helping hours $= x$ years
Then, Omar’s helping hour $=$ Sister’s helping hour $+\ 1 = (x + 1)$years
$\therefore$ Required expression $= (x + 1)$ years
View full question & answer→Question 192 Marks
Length and breadth of a bulletin board are $r \ cm$ and $t \ cm,$ respectively. What will be the expenditure for making $23$ boards, if the carpenter charges $Rs.x$ per board.
AnswerGiven, length of bulletin board $= r \ cm$ and breadth of bulletin board $= t \ cm$ Then, perimeter of bulletin board $= 2(r + f) \ cm$ and area of bulletin board $= rt \ cm$ Charges for one board $= Rs. x$ Charges of $23$ boards $= Rs. 23x$
Hence, expenditure for making $23$ boards is $T\ 23x.$
View full question & answer→Question 202 Marks
Length and breadth of a bulletin board are $r \ cm$ and $t \ cm,$ respectively. What will be the length (in \ cm) of the aluminium strip required to frame the board, if $10\ cm$ extra strip is required to fix it properly.
AnswerGiven, length of bulletin board $= r \ cm$ and breadth of bulletin board $= t \ cm$ Then, perimeter of bulletin board $= 2(r + f)cm$ and area of bulletin board $= rt \ cm$ Required length of aluminium strip $= [2 (r + 1) + 10]cm$
View full question & answer→Question 212 Marks
One more than twice the number.
AnswerLet the number be $x$ and twice the number $x = 2x$ Now, according to question, The expression $= 2x + 1$ Hence, required expression is $2x + 1.$
View full question & answer→Question 222 Marks
The denominator of a fraction is $1$ more than its numerator.
AnswerLet the numerator be $x.$
Then, denominator $= x + 1$
Now, fraction $=\frac{\text{Numerator}}{\text{Denominator}}$
$=\frac{\text{x}}{\text{x}+1}$
Hence, the required expression is $\frac{\text{x}}{\text{x}+1}.$
View full question & answer→Question 232 Marks
Write an equation for which $0$ is a solution.
AnswerLet the one number be $x$ which have solution $0$ in equation.
Now, for getting equation, the number $x$ is multiplied by $2,$ then the number is $2x$.
After that, it will be added to $3$ which results into $3.$
Hence, $2x + 3 = 3$
On solving $2x = 3 - 3 = 0 [$transposing $+3$ to $RHS]$
$\Rightarrow\frac{2\text{x}}{2}=\frac{0}{2}[$ dividing both sides by $2]$
$\Rightarrow x = 0$
Hence, required equation is $2x + 3 = 3.$
View full question & answer→Question 242 Marks
If a note book costs $Rs.p$ and a pencil costs $Rs.3,$ then the total cost $($in $Rs)$ of two note books and one pencil.
AnswerGiven, Cost of one notebook $= Rs. p$
Cost of $2$ notebooks $= 2 \times p = Rs.2p$
Similarly, cost of one pencil $= Rs. 3$
Now, total cost $=$ Cost of $2$ notebooks $+$ Cost of one pencil $= Rs.(2p + 3) $
Hence, the required expression is $2p + 3.$
View full question & answer→Question 252 Marks
Length and breadth of a bulletin board are $r \ cm$ and $t \ cm,$ respectively. If 500sqcm extra cloth per board is required to cover the edges, what will be the total area of the cloth required to cover $8$ such boards$?$
AnswerGiven, length of bulletin board $= r \ cm$ and breadth of bulletin board $= t \ cm$
Then, perimeter of bulletin board $= 2(r + f)cm$ and area of bulletin board $= rt \ cm$
Area of one board $= rt$ sq-cm Area of eight boards $= 8\ \times $ Area of one board $= 8$ rt sq-cm
Extra cloth for one board $= 500sq-cm [$given$]$
Extra cloth for $8$ boards $= 500 \times 8 = 4000 sq \ cm$
Required area of the cloth to cover 8 boards $= (8rt + 4000)sq-cm$
View full question & answer→Question 262 Marks
$6$ times $q$ is subtracted from the smallest two digit number.
Answer$6$ times of $q = 6g$ and smallest two digit number $= 10$ Then,
according to question, resulting expression $= 10 - 6g$
Hence, the required expression $= 10 - 6g$
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