Problem 1 :
If 10 people share 24.73 lbs. of food, how many lbs. of food does each person get?
Problem 2 :
100 people have been administered vaccine with 325.6 ml of a particular medicine. Find the amount of medicine used to administer vaccine for one person.
Problem 3 :
436.5 ml of cough syrup is filled in 9 bottles. Find the amount of syrup in each bottle.
Problem 4 :
If Amy walks walk 10.5 miles in 3 hours, find her speed in miles per hour.
Problem 5 :
If 5.25 gigabytes of data is copied from a USB drive to a laptop in 7 minutes, find the amount data copied in 1 minute.
Problem 6 :
James is selling apple juice in bottles. Yesterday, he sold of 26 bottles of apple juice for $93.60. For how much did he sell each bottle?
Problem 7 :
To donate food for the kids in an orphanage, Liam packed food in containers. She has 37.5 lbs. of food and each container can hold 1.25 lbs. How many containers does Liam need to pack 37.5 lbs. of food?
Problem 8 :
On dividing the decimal number 253.K6 by 100, Lucas gets the answer 2.5376. Find the value of K.
Problem 9 :
Dividing the decimal number 3.5 by A results 0.00035. Find the value of K.
Problem 10 :
A car covers a distance of 125.4 miles in 2 hours 45 minutes. Find the distance covered by the car in 1 hour.
1. Answer :
10 people ----> 24.73 pounds
1 person ----> (24.73/10) pounds
= 24.73/10
Since we divide 24.73 by 10, we have to move the decimal point to the left by one digit.
= 2.473
Each person gets 2.473 pounds of food.
2. Answer :
100 people ----> 325.6 ml
1 person ----> (325.6/100) ml
= 325.6/100
Since we divide 325.6 by 100, we have to move the decimal point to the left by two digits.
= 3.256
3.256 ml of medicine used to administer vaccine for one person.
3. Answer :
9 bottles ----> 436.5 ml
1 bottle ----> (436.5/9) ml
= 436.5/9
= 436.5 ÷ 9
= ⁴³⁶⁵⁄₁₀ ÷ ⁹⁄₁
Division can be changed to multiplication by taking reciprocal of ⁹⁄₁.
= ⁴³⁶⁵⁄₁₀ x ¹⁄9
Simplify.
= ¹⁴⁵⁵⁄₁₀ x ¹⁄3
= ⁴⁸⁵⁄₁₀ x ¹⁄₁
= ⁴⁸⁵⁄₁₀
Since 485 is divided by 10, there should be one digit to the right of the decimal point in the answer.
= 48.5
Amount of syrup in each bottle is 48.5 ml.
4. Answer :
Speed = Distance/Time
= 10.5/3
= 10.5 ÷ 3
= ¹⁰⁵⁄₁₀ ÷ ³⁄₁
Division can be changed to multiplication by taking reciprocal of ³⁄₁.
= ¹⁰⁵⁄₁₀ x ⅓
Simplify.
= ³⁵⁄₁₀ x ¹⁄₁
= ³⁵⁄₁₀
Since we divide 35 by 10, there should be one digit to the right of the decimal point.
= 3.5
Amy walks at a speed of 3.5 miles per hour.
5. Answer :
7 minutes ----> 5.25 gigabytes
1 minute ----> (5.25/7) gigabytes
= 5.25/7
= 5.25 ÷ 7
= ⁵²⁵⁄₁₀₀ ÷ ⁷⁄₁
Division can be changed to multiplication by taking reciprocal of ⁷⁄₁.
= ⁵²⁵⁄₁₀₀ x ⅐
Simplify.
= ⁷⁵⁄₁₀₀ x ¹⁄₁
= ⁷⁵⁄₁₀₀
Since 75 is divided by 100, there should be two digits to the right of the decimal point in the answer.
= 0.75
0.75 gigabytes of data copied in 1 minute.
6. Answer :
26 bottles ----> $93.60
1 bottle ----> $(93.60/26)
= 93.6/26
= 93.6 ÷ 26
= ⁹³⁶⁄₁₀ ÷ ²⁶⁄₁
Division can be changed to multiplication by taking reciprocal of ²⁶⁄₁.
= ⁹³⁶⁄₁₀ x ¹⁄₂₆
Simplify.
= ⁴⁶⁸⁄₁₀ x ¹⁄13
= ³⁶⁄₁₀ x ¹⁄₁
= ³⁶⁄₁₀
Since 36 is divided by 10, there should be one digit to the right of the decimal point in the answer.
= 3.6
He sold each bottle for $3.60.
7. Answer :
To find the number of containers, divide the total amount of food by the amount of food that each container can hold.
= 37.5/1.25
= 37.5 ÷ 1.25
= ³⁷⁵⁄₁₀ ÷ ¹²⁵⁄₁₀₀
Division can be changed to multiplication by taking reciprocal of ¹²⁵⁄₁₀₀.
= ³⁷⁵⁄₁₀ x ¹⁰⁰⁄₁₂₅
Simplify.
= ³⁷⁵⁄₁₀ x ⅘
= ⁷⁵⁄₁₀ x ⁴⁄₁
= ³⁰⁰⁄₁₀
= 30
Liam needs 30 containers to pack 37.5 lbs. of food.
8. Answer :
253.K6 ÷ 100 = ?
Since we divide 253.K6 by 100, we have to move the decimal point two digits to the left.
253.K6 ÷ 100 = 2.53K6 ---(1)
Given : Dividing 253.K6 by 100 results 2.5376.
253.K6 ÷ 100 = 2.5376 ----(2)
Comparing (1) and (2),
2.53K6 = 2.5376
If two decimal numbers are equal, then the digits at thousandths places also must be equal.
K = 7
9. Answer :
3.5 ÷ A = 0.00035
When 3.5 is divided by A, the decimal point in 3.5 has been moved to the left by four digits and it is 0.00035.
When a decimal number is divided by 10000, the decimal point is moved to the left by four digits.
It is clear that 3.5 is divided by 10000.
Therefore,
A = 10000
10. Answer :
The time 2 hours 45 minutes is in two units, hours and minutes. Convert it to hours completely.
2 hours 45 minutes = 2 hours + ⁴⁵⁄₆₀ hours
= 2 hours + ¾ hours
= 2 hours + ⁽³ˣ²⁵⁾⁄₍₄ₓ₂₅₎ hours
= 2 hours + ⁷⁵⁄₁₀₀ hours
= 2 hours + 0.75 hours
= 2.75 hours
Given : 125.4 miles of distance covered in 2 hours 45 minutes.
2 hours 45 minutes ----> 125.4 miles
2.75 hours ----> 125.4 miles
1 hour ----> (125.4/2.75) miles
= 125.4/2.75
= 125.4 ÷ 2.75
= ¹²⁵⁴⁄₁₀ ÷ ²⁷⁵⁄₁₀₀
Division can be changed to multiplication by taking reciprocal of ²⁷⁵⁄₁₀₀.
= ¹²⁵⁴⁄₁₀ x ¹⁰⁰⁄₂₇₅
= ¹²⁵⁴⁄₁ x ¹⁰⁄₂₇₅
= ¹²⁵⁴⁄₁ x ⅖₅
= ¹¹⁴⁄₁ x ⅖
= ²²⁸⁄₅
= ⁽²²⁸ˣ²⁾⁄₍₅ₓ₂₎
= ⁴⁵⁶⁄₁₀
Since 456 is divided by 10, there should be one digit to the right of the decimal point in the answer.
= 45.6
The distance covered by the car in 1 hour is 45.6 miles.
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