Problem 1 :
A chemist mixed 6.35 grams of one compound with 2.45 grams of another compound. How many grams were there in the mixture?
Solution :
Amount of compound in the mixture is
= 6.35 + 2.45
= 8.8 grams
Problem 2 :
If the cost of a pencil is $1.25, find the cost of 10 pencils.
Solution :
To find the cost of 10 pencils, we have to multiply the cost of one pencil by 10.
= 100 ⋅ 1.25
Since 1.25 is multiplied by 10, the decimal point has to be moved to the right by one digit.
= 12.5
The cost of 10 pencils is $12.50.
Problem 3 :
Mr. James walks a distance of 365.7 ft. of distance in 100 minutes. Find the distance he walks in one minute.
Solution :
To find the distance that Mr. James walks in one minute, we have to divide the distance walked in 10 minutes by 10.
= 365.7/100
Since 365.7 is divided by 100, the decimal point has to be moved to the left by two digits.
= 3.657
James walks a distance of 3.657 ft. in one minute.
Problem 4 :
If the cost of a pen is $10.50, a book is $25.75 and a bag is $45.50, then find the total cost of 2 books, 3 pens and 1 bag.
Solution :
Total cost of 2 books, 3 pens and 1 bag is
= 2(25.75) + 3(10.50) + 1(45.50)
= 51.50 + 31.50 + 45.50
= $128.50
Problem 5 :
John wants to buy a bicycle that cost $ 450.75. He has saved $ 125.35. How much more money must John save in order to have enough money to buy the bicycle ?
Solution :
Amount of money that John still has to save is
= 450.75 - 125.35
= $325.40
Problem 6 :
Jennifer bought 6.5 kg of sugar. she used 3750 grams. How many kilograms of sugar were left ?
Solution :
3750 grams = 3750/1000 kg
3750 grams = 3.75 grams
Amount of sugar left (in kilograms) is
= 6.5 - 3.75
= 2.75 kg
Problem 7 :
The inner radius of a pipe is 12.625 mm and the outer radius is 18.025 mm. Find the thickness of the pipe.
Solution :
Thickness of the pipe is
= Outer radius - Inner radius
= 18.025 - 12.625
= 5.40 mm
Problem 8 :
A copy of English book weighs 0.45 kg. What is the weight of 20 copies ?
Solution :
Weight of 20 copies of English book is
= 20 ⋅ 0.45
= 9 kg
Problem 9 :
Find the weight of 25.5 meters of copper wire in kilograms, if one meter weighs 10 grams.
Solution :
Weight of 25.5 meters of copper wire is
= 25.5 ⋅ 10
= 255 grams
= 255/1000 kilograms
= 0.255 kilograms
Problem 10 :
Robert paid $140 for 2.8 kg of cooking oil. How much did 1 kg of the cooking oil cost ?
Solution :
The cost of 1 kg of cooking oil is
= 140/2.8
= $50
Problem 11 :
If $20.70 is earned in 6 hours, how much money will be earned in 5 hours ?
Solution :
Amount of money earned in 1 hour is
= 20.70/6
= 3.45
Amount of money earned in 5 hours is
= 5 ⋅ 3.45
= $17.25
Problem 12 :
A pipe is 76.8 meters long. What will be the greatest number of pieces of pipe each 8 meters long that can be cut from this pipe ?
Solution :
Greatest number of pieces can be cut from the pipe is
= 76.8/8
= 9.6
So, 9 pieces of pipe each 8 meters long can be cut from the pipe of length 76.8 meters.
Problem 13 :
When the decimal number 2.78A is multiplied by 100, the answer is 278.5 Find the value of A.
Solution :
When the decimal number 2.78A is multiplied by 100, the decimal point has to be moved to the right by two digits.
2.78A x 100 = 278.A ----(1)
It is given that dividing the decimal number 2.78A by 100 results 278.5.
2.78A x 100 = 278.5 ----(2)
Comparing (1) and (2),
278.A = 278.5
If two decimal numbers are equal, then the digits at tenths places must be equal.
Therefore,
A = 5
Problem 14 :
If ten-thousandth of a number is 0.0005, find the number.
Solution :
It is given that ten-thousandth of the decimal number is 0.0005.
Let k be the number.
Then, from the given information, we get
(1/10000) x k = 0.0005
Multiply both sides by 10000.
k = 0.0005 x 10000
Since 0.0005 is multiplied by 10000, the decimal point has to be moved to the right by four digits.
k = 5
Therefore, the number is 5.
Problem 15 :
Evaluate the following expression with the conditions given below.
a.b + b.a
Conditions :
(i) Both a and b are positive integers.
(ii) Both a and b are prime numbers and a is an even number.
Solution :
From the given conditions,
a = 2 and b = 3
a.b + b.a :
= 2.3 + 3.2
= 5.5
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