Now the HCF of 16, 28
16 = 2 \(\times\) 2 \(\times\)2 \(\times\) 2
28 = 2 \(\times\)2 \(\times\) 7
HCF of (16, 28) = 2 \(\times\)2 = 4
Now the HCF of (16 , 28 -16)
16 = 2 \(\times\) 2 \(\times\)2 \(\times\) 2
12 = 2 \(\times\) 2 \(\times\) 3
HCF of (16, 12) = 2 \(\times\) 2 = 4
Therefore HCF of (16, 28) = HCF of (16, 28 - 16).
Hence, HCF of two numbers a and b, a > b, is same as the HCF of a and a – b.

a = 3 cm
b = 4 cm
c = 5 cm
P = (a + b + c) units
= 3 + 4 + 5 = 12 cm
Perimeter of the triangle is 12 cm.

s = 5 cm
P = (4 × s) units
= 4 × 5
= 20 cm
Perimeter of the square is 20 cm

l = 12 cm
b = 10 cm
P = 2 (l + b) units
= 2(12 + 10)
= 2× 22
= 44 cm
Perimeter of the rectangle is 44 cm.

Step 1: First, separate the positive integers as 12, 3, 1, 25, 18 and the negative integers as −15, −7, −5, −20
Step 2: We can easily arrange positive integers in ascending order as 1, 3, 12, 18, 25 and negative integers in ascending order as −20, −15, −7, −5.
Step 3: As 0 is neither positive nor negative, it stays at the middle and now the arrangement −20, −15, −7, −5, 0, 1, 3, 12, 18 and 25 is in ascending order.

\(4{1\over2}\div 3{1\over2}={9\over2}\div {7\over 2}\)
\(={9\over2}\times{2\over7}\) (reciprocal of \(\frac{7}{2} \text { is } \frac{2}{7}\))
\(={9\over7}\)

Here 9 > 3 and \({11\over 4}<{5\over6}\)So we proceed as follows:
We convert the mixed fraction into improper fraction and then subtract
\(9{1\over4}={(9\times4)+1\over4}={37\over 4}\)
and \(3{5\over6}={(3\times4)+5\over 6}={23\over6}\)
Common multiple of 4 and 6 is 12
Now, \({37\over 4}-{23\over 6}={37\times3\over12}-{23\times2\over12}\)
\(={111\over12}-{46\over 12}={65\over 12}=5{5\over12}\)

\(3{2\over4}+7{2\over5}=3+{2\over4}+7+{2\over5}\)
\(=3+7+\left({2\over4}+{2\over5}\right)\)
\(=10+\left({10\over20}+{8\over20}\right)\)
\(=10+{18\over20}=10+{9\over10}=10{9\over10}\)

i) 74
ii) -258
iii) -830

400, -300, -150, 0, 50

-99, -345, -354, -567, -777, -990

\( a) \ 8 \div \frac{8}{9}=8 \times \frac{9}{8}=9 \)
\(b) \ \frac{11}{12} \div \frac{3}{4}=\frac{11}{12} \times \frac{4}{3}=\frac{11}{9}\)

LCM of 5, 7 = 35
\(\frac{4}{5}=\frac{4 \times 7}{5 \times 7}=\frac{28}{35}\)
\( \frac{3}{7}=\frac{3 \times 5}{7 \times 5}=\frac{15}{35}\)
\( \frac{28}{35}+\frac{15}{35}=\frac{43}{35} \)

\(a) \ 3 \frac{5}{6}=\frac{(6 \times 3)+5}{6}=\frac{23}{6}=\frac{18+5}{6} \)
\(b) \ 17 \frac{1}{4}=\frac{(17 \times 4)+1}{4}=\frac{68+1}{4}=\frac{69}{4}\)

(i) 50, 51, 53, 56, 60 
The next three numbers will be 65, 71, 78 .......
(ii) 77, 69, 61, 53 
The next three numbers will be 45, 37, 29 .....
(iii) 10, 20, 40, 80
The next three numbers will be 160, 320, 640 .....
(iv) \(\cfrac { 21 }{ 33 } ,\cfrac { 321 }{ 444 } ,\cfrac { 4321 }{ 5555 } \)
The next three numbers will be \(\cfrac { 54321 }{ 66666 } ,\cfrac { 654321 }{ 777777 } ,\cfrac { 7654321 }{ 888888 } ,\)

(i) Hidden word isDECODE
(ii) Hidden word is KICK
(iii) Hidden word is BED
(iv) Hidden word WAY
(v) Hidden word MAT H
(vi) Hidden word TOM A T 0

Side of the Square (s) = 8 cm
P = 4s
P = 4 \(\times\) 8 = 32 cm
Area = S²
= 82 = 64 cm²

Length (l) = 6 m
breadth (b) = 4 m
Perimeter of the rectangle (P) = 2 (1+b) units
= 2 (6 + 4)
= 2(10) = 20m
Area(A) = l\(\times\)b = (6 \(\times\) 4)m²
= 24m
\(\therefore\) P = 20 m, A = 24 m²

The depth of 10 feet from the ground level and its opposite

Opposite number of - 10 feet is 10 feet.

(i)
 
\(\therefore\) Number is : -3
(ii)

\(\therefore\) Number is : -2

(i) The integer that represent a profit is + 45
(ii) An integer on the profit or loss in, 2016 is 0
(iii) Loss in 2011 is -10, Loss in 2012 is - 20
(iv) False
(v) Fill in : The amount of loss in 2011 is the same as profit in 2013.

C3: The opposite to the second negative integer.
C5: The additive identity in whole numbers.
C6: The successor of the integer in C2.
C8: The predecessor of the integer in C7.
C9: The opposite to the integer in C5.