To do:We have to find the ratio of: (a) Number of triangles to the number of circles inside the rectangle. (b) Number of squares to all the figures inside the rectangle. (c) Number of circles to all the figures inside the rectangle.Solution: From the figure we have, $3$ triangles, $2$ squares ... Read More

To do:We have to express the given property in a general way, by using variables \( a, b \) and \( c \).Solution:$(14+27)+13=41+13=54$$14+(27+13)=14+40=54$Let $a=14, b=27, c=13$This implies,$(a+b)+c=a+(b+c)$Therefore,For any three whole numbers $a, b$ and $c$$(a + b) + c = a + (b + c)$

Given:The diameter of a circle is a line which joins two points on the circle and also passes through the centre of the circle.In the given figure \( \mathrm{AB} \) is a diameter of the circle; \( \mathrm{C} \) is its centre.To do:We have to express the diameter of the ... Read More

To do:We have to make up as many expressions with numbers (no variables) as we can from three numbers 5,7 and 8.Solution:Some of the expressions formed by 5, 7 and 8 are as follows:$5+(8-7)$$5-(8-7)$$5-(8+7)$$(5 \times 8)+7$$(5 \times8) - 7)$$5 \times (8 + 7)$$(7 + 5) \times 8$$(8 – 5) \times 7$$(8 + 5) \times 7$$(7 – 5) \times 8$

To do:We have to find expressions with only numbers.Solution:Variable:A variable is denoted by a symbol that can take any real value. The value of a variable is not fixed.The letters $x, y$ and $z$ are generally used for variables.Therefore, (a) $y+3$ is an expression with the variable $y$.(b) $(7\times 20)-8z$ is ... Read More

To do:We have to identify the operations (addition, subtraction, division, multiplication) in forming the given expressions and tell how the expressions have been formed.Solution:(a) $z + 1$ --> 1 is added to $z$ Addition operation is used$z - 1$ --> 1 is subtracted from $z$  Subtraction operation is used$y + ... Read More

To do:We have to write the given statements as expressions.Solutions:(a) 7 added to $p$ is $p+7$.(b) 7 subtracted from $p$ is $p-7$.(c) $p$ multiplied by 7 is $7p$(d) $p$ divided by 7 is $\frac{p}{7}$(e) 7 subtracted from $-m$ is $(-m-7)$(f) $-p$ multiplied by 5 is $(-5p)$(g) $-p$ divided by 5 ... Read More

To do:We have to give expressions in the given cases.Solutions:(a) 11 added to $2m$ is $(2m + 11)$(b) 11 subtracted from $2m$ is $(2m - 11)$(c) 5 times $y$ to which 3 is added is $(5y + 3)$(d) 5 times $y$ from which 3 is subtracted is $(5y - 3)$(e) ... Read More

To do:We have to form expressions using the given details.Solutions:(a) $(t + 4), (t - 4), 4t, (4 - t), (4 + t), (\frac{t}{4}), (\frac{4}{t})$ are the expressions using $t$ and $4$.(b) $2y + 7, 2y - 7, 7y + 2, 7y-2$ are few expressions using $y, 2$ and $7$

Given:There are 20 girls and 15 boys in a class.To do:We have to find:(a) The ratio of the number of girls to the number of boys.(b) The ratio of number of girls to the total number of students in the class.Solution:Number of girls in the class$ =20$ Number of boys ... Read More