E.4.1. Use the fractions in the middle of the image. When you move upwards, multiply each pair to fill in the blanks and when you go downwards, fill in the blanks by dividing the left fraction by the right fraction of each pair. Like this, find the last fraction of both the top and bottom positions.
Solution:
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E.4.2. Ria is interested to put up a fence on three sides of her garden. The lengths of these three sides are 15 meter, 13.5 meter and 12.3 meter. It costs Ria 75.75 taka per meter of fencing to put up the fence.
a. How many meters of fencing will Ria need to put up?
b. How much would the fence cost Ria?
Solution:
To find out how many meters of fencing Ria needs, she simply needs to add up the lengths of the three sides of her garden:
a. Total length of fencing needed = 15 meters + 13.5 meters + 12.3 meters
Total length of fencing needed = 40.8 meters
So, Ria needs 40.8 meters of fencing.
b. To calculate the cost, we multiply the total length of fencing needed by the cost per meter:
Cost of fencing = (Total length of fencing ✕ Cost per meter) Taka
= (40.8 ✕ 75.75) taka
≈ 3084.6 taka
So, the fence would cost Ria approximately 3084.6 taka.
E.4.3. Determine the range and area of the following diagrams:
a)
b)
c)
Solution:
Let's calculate the range and area for each of the given shapes:
a) Rectangle:
Length = 5.5 cm
Width = 2.3 cm
Range of a rectangle = 2 ✖ (length + width)
= 2 ✖ (5.5 cm + 2.3 cm)
= 2 ✖ 7.8 cm
= 15.6 cm
Area of a rectangle = length ✖ width
= 5.5 cm ✖ 2.3 cm
= 12.65 cm²
b) Square:
Length = 3.6 cm
Range of a square = 4 ✖ length
= 4 ✖ 3.6 cm
= 14.4 cm
Area of a square = length ✖ length
= 3.6 cm ✖ 3.6 cm
= 12.96 cm²
c) Rhombus:
Height = 4.2 cm
Length = 6.8 cm
Range of a rhombus = 4 ✖ length
= 4 ✖ 6.8 cm
= 27.2 cm
Area of a rhombus = height ✖ length
= 4.2 cm ✖ 6.8 cm
= 28.56 cm²
So, the ranges and areas of the given diagrams are:
a) Rectangle: Range: 15.6 cm Area: 12.65 cm²
b) Square: Range: 14.4 cm Area: 12.96 cm²
c) Rhombus: Range: 27.2 cm Area: 28.56 cm²
E.4.4.
Observe the above diagram and think about our body.
a. What is the mass of your head?
b. How many kgs of water does our body need to remain healthy?
Solution:
a. To find the mass of our head, we'll need to know the total mass of our body.
Let's represent the total mass of our body as M kg.
Given that the mass of our head is 145 of our total mass, we can calculate it using the following formula:
Mass of head = 145 ✕ M kg
Let's assume a typical total body mass, say 70 kg, for the calculations.
Mass of head: Mass of head = 145 ✕ 70 kg
Mass of head ≈ 1.56 kg
b. To determine the amount of water needed to remain healthy, we'll use the fact that about 23 of our body mass is water. So, if we denote the total mass of our body as M, then the mass of water in our body would be:
Mass of water = 23✕ M
Let's assume a typical total body mass, say 70 kg, for the calculations.
Mass of water needed:
Mass of water = 23 ✕ 70 kg
Mass of water ≈ 46.67 kg
So, our head would have a mass of approximately 1.56 kg, and our body would need around 46.67 kg of water to remain healthy, given a total body mass of 70 kg.
E.4.5. Ratul planted some young flower saplings along the length and width of his rectangular garden, planting four and three saplings in each row, respectively. The distance between two consecutive saplings is meter. Draw a picture and think about it.
a. Find the area of Ratul’s garden?
b. How many flower saplings did Ratul plant? How many bones do you have?
Solution:
Let's visualize Ratul's garden and the arrangement of the flower saplings:
a. To find the area of Ratul's garden, we need to multiply the length by the width. Let's denote the length as L and the width as W. Each row of saplings contributes 4 + 3 = 7 meters to the total width.
So, the total width (W) of the garden = 2 rows of saplings ✕ 7 meters = 14 meters.
Given the distance between two consecutive saplings is 1 meter, we can calculate the length (L) of the garden. It will be the same as the number of saplings in each row.
Thus, the total length (L) of the garden = 4 saplings.
Now, the area (A) of the garden can be calculated as follows:
A = Length ✕ Width
A = 4 meters ✕ 14 meters
A = 56 square meters
b. Ratul planted a total of 4 + 3 = 7 saplings in each row. As there are 2 rows, the total number of saplings planted is 2 ✕ 7 = 14 saplings.
As for the second question, a typical human adult has 206 bones in their body.
E.4.6. Ria’s family has 8 members. Ria made 0.56 liters of tea to serve equally amongst all. But Ria does not drink tea. How many liters of tea will be in each cup?
Solution:
If Ria made 0.56 liters of tea to serve equally among the 8 members of her family, including herself, but she does not drink tea, then the tea will be distributed among 7 people.
To find out how many liters of tea each person will get, we need to divide the total amount of tea by the number of people:
Tea per cup = Total amount of teaNumber of people
= 0.56 7 liters
≈ 0.08 liters
So, each cup will contain approximately 0.08 liters of tea.
E.4.7. Ratul bought 1.5 kg of lentils at Tk 105 per kg, 5 kg onions at Tk 45.50 per kg from the market. How much will he pay the shopkeeper?
Solution:
To find out how much Ratul will pay the shopkeeper, we need to calculate the total cost of the lentils and onions separately, and then add them together.
For lentils:
Cost of lentils = (Weight of lentils ✕ Price per kg)
= (1.5 ✕ 105) Taka
= 157.50 Taka
For onions:
Cost of onions = (Weight of onions ✕ Price per kg)
= (5 ✕ 45.50) Taka
= 227.50 Taka
Now, let's add the costs of lentils and onions to find the total amount Ratul will pay:
Total cost = Cost of lentils + Cost of onions
= (157.50 + 227.50) Taka
= 385 Taka
So, Ratul will pay the shopkeeper Tk 385.00 in total.
E.4.8. Shumon can travel 8 km distance per hour by a cycle.
a) How many km of distance can Shumon go in 6 hours?
b) How many hours will Shumon take to travel a distance of 30 km?
Solution:
a) To find out how many kilometers Shumon can travel in 6 hours, we multiply his speed by the time traveled:
Distance = Speed × Time
Given that Shumon can travel 8 km per hour and he travels for 6 hours:
Distance = 8 km/h × 6 hours
Distance = 48 km
So, Shumon can travel 48 kilometers in 6 hours.
b) To determine how many hours Shumon will take to travel a distance of 30 km, we can rearrange the formula for distance to solve for time:
Time = Distance Speed
Given that Shumon is traveling a distance of 30 km and his speed is 8 km/h:
Time = 30 km8 km/h
Time ≈ 3.75 hours
So, Shumon will take approximately 3.75 hours to travel a distance of 30 km.
E.4.9. Auhona used the following ingredients of salad to make salad for her younger brother and herself:
a) Determine the total weight of Auhona’s salad in kg.
b) If you have to make the salad for 5 members of the family, including the parents, present the necessary ingredients of the salad in a Table form and find out the total weight in kg, of the salad made.
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