Comparing \(\frac { 1 }{ 4 } \)th of an inch and \(\frac { 3 }{ 8 } \)th of an inch.
\(\frac { 1 }{ 4 } =\frac { 2 }{ 8 } <\frac { 3 }{ 8 } \)
\(\therefore\) Second plant grew more.

\(\frac { 8 }{ 5 } =\frac { 5\times 10 }{ 8\times 10 } =\frac { 50 }{ 80 } \)
\(\frac { 1 }{ 10 } =\frac { 1\times 8 }{ 10\times 8 } =\frac { 8 }{ 80 } \)
Here \(\frac { 50 }{ 80 } >\frac { 8 }{ 80 } \)  
\(\therefore \frac { 5 }{ 8 } >\frac { 1 }{ 10 } \)

0˚

straight angle

right angle

Parallel and Perpendicular lines

Parallel lines

One is Multiplicative Identity

Product of extremes = 6 \(\times\) 15 = 90
\(\therefore\) Product of means = 90 = 1 \(\times\) 90
The required sets are 1 and 30, 2 and 45, 3 and 30, 5 and 18, 6 and 15, 9 and 10
= 1 \(\times\) 90
= 2 \(\times\)45
= 3 \(\times\) 30
= 5 \(\times\) 18
= 6 \(\times\) 15
= 9 \(\times\) 10
So, 6 : 1 : : 90 : 15.

We have to round off 4065 to hundreds
The place value is hundred
The digit in hundreds place is 0
The digit to the right is 6 > 5
Adding 1 to 0 \(\Rightarrow\) 0 + 1 = 1
changing the digits to the right of 41 to zeros
4065 \(\simeq \) 4100 \(\Rightarrow\) 4100

\(i) \ \angle \mathrm{ABD}=180^{\circ}-25=155^{\circ}\)
\(ii) \ \angle \mathrm{ABD}=90^{\circ}-30^{\circ}=60^{\circ}\)
\(iii)\ \angle \mathrm{CBE}=180^{\circ}-67^{\circ}=113^{\circ}\)
\(iv)\ \angle \mathrm{ABD}=90^{\circ}-46^{\circ}=44^{\circ}\)

(i)

(ii)

(iii)

(v)

(i) 3, 9, 4, 12 .
Here product of extremes = 3 \(\times\) 12 = 36
Product of means = 9 \(\times\) 4 = 36
∴ 3 : 9 : : 4: 12
(ii) Also if we take 9, 3, 12, 4
Product of extremes = 9 \(\times\) 4 = 36
Product of means = 3 \(\times\) 12 = 36
∴ 9 : 3 : : 12: 4.

(i) vertex : \(D,\) Sides : \(\overrightarrow{DE} ,\overrightarrow{DF}\)
(ii) vertex : \(D\), Sides : \(\overrightarrow{DE} ,\overrightarrow{DC}\)

Place value chart is given by

\(\Rightarrow\) The number with more digits is the greater number
Step 1: \(\therefore\) 128435 is the larger number and 6348 is the least number
Step 2:  For the remaining 5 digit numbers we can compare the left most digits and find 25840 > 21354 > 10835
\(\therefore\)  The descending order:
128435> 25840 > 21354 > 10835> 6348

56 + 2x

4q

14 days, 9 weeks

Step 1: Express the quantity in the same unit. (Hint : 1 Hour = 60 minutes)
Step 2: Now, the ratio of 40 minutes to 60 minutes is 40:60 \(\Rightarrow {40\over 60}={40\div 20\over 60\div 20}={2\over 3}=2:3\)
This is the ratio in the simplest form.
20 \(\times\) 1 = 20
20 \(\times\) 2 = 40
20 \(\times\) 3 = 60
1 hour = 60 minutes

We know that the place value increases from right to left
[ \(\therefore\) Arranging the digits in ascending order from right to left we get the largest number]
Largest number is 75320
Smallest number is  20357
[ \(\therefore\) Reverse order of 75320 is 02357. It becomes four digit number 2357]

(i) 3n
(ii) 4n

75 : 100 
Fraction = \(\frac{75}{100} \div \frac{25}{25}=\frac{3}{4}\)
Simplest form = 3 : 4

7 : 15
Fraction = \(​​\frac {7 \div 1}{15 \div 1}=\frac{7}{15}\)
Simplest form = 7 : 15