Problem 1 :
Find the area of the following shape :
Solution :
By drawing a vertical line, we can divide the given shape in to shapes.
Area of rectangle in the left + area of rectangle in the right
= 8 x 4 + (8 x 3)
= 32 + 24
= 56 cm^{2}
Problem 2 :
Max has more than 4 apples but fewer than 7 apples. Alex has more than 5 apples and fewer than eight apples. How many apples do Max and Alex have altogether?
Circle all the possible values
4 5 6 7 8 9 10 11 12 13 14 15
Solution :
Given information :
4 < number of apples Max has < 7
5 < number of apples Alex has < 8
Let M be the number of apples and A be number of apples Alex has.
Then the total number of apples altogether is 11, 12 and 13.
Problem 3 :
Suki saves £12 in January, £18 in February and £5 in March. What is her mean (average) monthly saving?
Solution :
Mean = Total savings / 3
= (12 + 18 + 5) / 3
= 35/3
= 11.6
So, the mean is £11.6.
Problem 4 :
What is 1/2 of 4/5 of 35 ?
Solution :
1/2 of 4/5 of 35
Problem 5 :
Put the following numbers in order from smallest to largest :
Solution :
Here two quantities are in the form of fraction and the other quantity is in the form of percentage.
Converting everything into decimal, we can do the comparison simply.
3/5 = 0.6
5/8 = 0.625
62% = 62/100 = 0.62
Arranging from least to greatest,
0.508, 0.58, 0.6, 0.620, 0.625,
0.508, 0.58, 3/5, 62%, 5/8
Problem 6 :
You are told that 82 × 107 = 8774 Use this to work out the value of the following:
a. 8200 × 107
b. 8774 ÷ 107
c. 8774 ÷ 41
Solution :
82 × 107 = 8774
a) 8200 x 107 = 82 x 100 x 107
= (82 x 107) x 100
= 8774 x 100
= 877400
b. 8774 ÷ 107 = 82
c. 8774 ÷ 41
Given : 82 x 107 = 8774
2 x 41 x 107 = 8774
8774 ÷ 41 = 2 x 107
= 214
Problem 7 :
A bus can seat 82 people. 8770 people travel to a football match by bus. How many buses are needed?
Solution :
Number of seats in the bus = 82
Number of people has to travel to a foot ball match = 8770
Number of buses needed = 8770/82
= 106.9
So, 107 buses are needed.
Problem 8 :
B + A + T = 17
C + A + T = 25
C + O + A + T = 29
What is the value of B + O + A + T?
Solution :
B + A + T = 17 ----(1)
C + A + T = 25 ----(2)
C + O + A + T = 29 ----(3)
Applying (2) in (3), we get
O + 25 = 29
O = 29 - 25
O = 4
We should find the value of, B + O + A + T
= (B + A + T) + O
= 17+4
= 21
So, the value of B + O + A + T is 21.
Problem 9 :
A rectangle is 6cm longer than it is wide. Its perimeter is 32cm. Find its area.
Solution :
Let x be the width of the rectangle. Then length of the rectangle will be x + 6.
Perimeter = 32 cm
2(x + x + 6) = 32
2x + 6 = 32/2
2x + 6 = 16
2x = 16 - 6
2x = 10
x = 5
Width of the rectangle = 5 cm, length of the rectangle = 11 cm
Area = length x width
= 5 x 11
= 55 cm^{2}
Problem 10 :
On Planet Pythagoras, the people use a different money system to us. One pog is worth four pings Three pings are worth five paz Convert the following:
A. 3 pog = _____ pings
B. 40 paz = ____________ pog
C. 3 paz = ____________ pog
Solution :
1 pog is = 4 pings
3 pings = 5 paz
A)
3 pog = 3 x 4
= 12 pings
B)
40 paz = ____________ pog
1 paz = 3/5 pings
40 paz = (3/5) x 40
= 24 pings
1 ping = 1/4 pog
24 pings = 24 x (1/4)
= 6 pog
C.
3 paz = ____________ pog
1 paz = 3/5 pings
3 paz = 3 x (3/5)
= 9/5 pings
3 pings = 5 paz
1 ping = 5/3 paz
9/5 pings = 9/5 x (5/3)
= 3 paz
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM