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?
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.
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.
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.
To find the distance that Mr. James walks in one minute, we have to divide the distance walked in 10 minutes by 10.
Since 365.7 is divided by 100, the decimal point has to be moved to the left by two digits.
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.
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
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 ?
Amount of money that John still has to save is
= 450.75 - 125.35
Problem 6 :
Jennifer bought 6.5 kg of sugar. she used 3750 grams. How many kilograms of sugar were left ?
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.
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 ?
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.
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 ?
The cost of 1 kg of cooking oil is
Problem 11 :
If $20.70 is earned in 6 hours, how much money will be earned in 5 hours ?
Amount of money earned in 1 hour is
Amount of money earned in 5 hours is
= 5 ⋅ 3.45
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 ?
Greatest number of pieces can be cut from the pipe is
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.
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.
A = 5
Problem 14 :
If ten-thousandth of a number is 0.0005, find the number.
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
(i) Both a and b are positive integers.
(ii) Both a and b are prime numbers and a is an even number.
From the given conditions,
a = 2 and b = 3
a.b + b.a :
= 2.3 + 3.2
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