From the tree diagrams, algebraic expressions are
c / (a / b) and a / (b / c)
c / (a / b) \(\neq\) a / (b / c)
No, they are not equal.

(i) 8 + (6 \(\times\) 2)

(ii) 9 − (2 \(\times\) 3)

(iii) (3 \(\times\) 5) − (4 \(\div \) 2)

(iv) [(2 \(\times\) 4)+2] \(\times\) (8 \(\div \) 2)

(v) [(6 +4) \(\times\) 7] \(\div \) [2 \(\times\) (10 −5)]

(vi) [(4 \(\times\) 3) \(\div \) 2] + [8 \(\times\) (5 − 3)]

(i) 3.15 a.m. = 3.15 hours
(ii) 12.35 p.m. = 12.35 hours
(iii) 12.00 noon = 12.00 hours
(iv) 12.00 midnight = 00.00 or 24.00 hours

1km = 1000m
Maran Walks = 1.5 km
= 1.5 \(\times\)1000 = 1500m
Mahizhan walks = 1400m
Difference = 1500 - 1400 = 100m
Maran walks more distance and by 100m

(i) name a pair of complementary angles:
∠FAE;∠EAD
(ii) name a pair of supplementary angles:
∠FAD;∠DAC
∠BAC;∠CAE
∠FAB;∠BAC
∠FAB;∠FAE
∠EAD;∠DAB

Number of bags of apples = 25
Number of apples in each bag = 9
\(\therefore\) Total apples   = 25 \(\times\) 9 = 225
Number of friends = 6
Number of apples each friend get = 225 \(\div\) 6 = 37
Number of apples each get = 37
Remaining apples = 3.

5p

Total no. of days = 7
first 3 days (c.p) (10 Kgs)
1 kg = Rs. 10 
1 kg of tomatoes got smashed everyday
1^st day = 9kg \(\times\) 10 = Rs. 90
2^nd day = 8kg \(\times\) 10 = Rs. 80
3^rd day = 7kg \(\times\) 10 = Rs. 70
Total = Rs. 240
Next 4 days (c.p) (15 kgs)
1 kg = Rs. 8
1^st day = 15 \(\times\) 8 = Rs. 120
2^nd day = 15 \(\times\) 8 = Rs. 120
3^rd day = 15 \(\times\) 8 = Rs. 120
4^th day = 15 \(\times\) 8 = Rs. 120
Total = Rs. 480
c.p of 1 week = Rs. 240 + Rs. 480 = Rs. 720
Next 3 days (s.p) (15 kgs)
1 kg = Rs. 20
1^st day = 9 \(\times\) 20 = Rs. 180
2^nd day = 8 \(\times\)20 = Rs. 160
3^rd day = 7 \(\times\) 20 = Rs. 140
Total = Rs. 480
Next 4 days (s.p) (15 kgs)
1^st day = 15 \(\times\) 20 = Rs. 300
2^nd day = 15 \(\times\) 20 = Rs. 300
3^rd day = 15 \(\times\) 20 = Rs. 300
4^th day = 15 \(\times\) 20 = Rs. 300
= Rs. 1200
s.p = Rs. 480 + Rs. 1,200
= Rs. 1680 - Rs. 720
= Rs. 960

Given: 40 seconds, 60 seconds and 72 seconds

LCM = \(2 \times 2 \times 5 \times 2 \times 3 \times 3\) = 360 seconds
Also given, they changed simultaneously together at 8 a.m.
Therefore 360 seconds = 6 min
⇒ 1 hour = 60 min
Therefore 8 a.m. + 6 min = 8.00 + 0.06
Time = 8.06 a.m.
After 360 seconds, therefore 8.06 a.m. will they simultaneously change together again.

Parallel lines

Distance covered in 1 hr ie., 60 minutes = 6 km
Distance covered in 1 minutes = \(\frac { 6 }{ 10 } \)km
Distance covered in 20 minutes = \(\frac { 6 }{ 60 } \) \(\times\) 20 = 2 km
∴ Cholan cover 2 km in 20 minutes.

567,456,345
Place value of 7 is 7 \(\times\) 1,000,000
= 7,000,000
= Seven Million.

(a) 3500 people visited Mahabalipuram in April
(b) 500 more people
(c) January
(d) April
(e) 11,500 people

(i) Indian System :Two crore fifty nine lakh forty one thousand nine hundred
International System : Twenty five million nine hundred forty one thousand nine hundred
(ii) 5,50,500
(iii) Eighty six crore forty lakh seven hundred thirty
(iv) Ninteen million eight hundred eighty eight thousand eight hundred
(v) Indian System : 60,53,100 - Sixty lakh fifty three thousand one hundred
International System : 6,053,100 - Six million fifty three thousand one hundred

(i) Yes
(ii) 5
(iii) 
     
Sums are 17, 19, 20, 21 and 23.

Ratio of red beads: blue beads = 35: 30
Fraction of 35 : 30  \(=\frac{35}{30}\)
= 7:6
Also given that the bracelet made is smaller in size
∴ The possible ways are red beads: blue beads
The equivalent ways are
\( \frac{7 \times 2}{6 \times 2}=\frac{14}{12}=14: 12 \)
\( \frac{7 \times 3}{6 \times 3}=\frac{21}{18}=21: 18 \)
\( \frac{7 \times 4}{6 \times 4}=\frac{28}{24}=28: 24\)
= 7 : 6 (or) 14: 12 (or) 21 : 18 (or) 28 : 24
In 4 different way can she made.

(i) Length of wire = '12 s' cm 
Sum of 3 sides of equilateral triangle = '12 s'
3 \(\times\) side = 12 s
The length of a side = \(\frac{12 \mathrm{~s}}{3}=\) '4 s' cm
(ii) Sum of 4 sides of square = '12 s'
The length of a side = \(\frac{12 \mathrm{~s}}{4}=\) '3 s' cm