Problems 1-17 : Evaluate each of the following division.
Problem 1 :
2.1 ÷ 0.7
Problem 2 :
4.8 ÷ 0.6
Problem 3 :
2.7 ÷ 0.03
Problem 4 :
0.72 ÷ 0.006
Problem 5 :
35 ÷ 0.007
Problem 6 :
4325.78 ÷ 10
Problem 7 :
4325.78 ÷ 100
Problem 8 :
4325.78 ÷ 1000
Problem 9 :
3.96 ÷ 10
Problem 10 :
7.89 ÷ 100
Problem 11 :
5.9 ÷ 1000
Problem 12 :
0.4 ÷ 100
Problem 13 :
0.09 ÷ 100
Problem 14 :
0.001 ÷ 1000
Problem 15 :
0.15 ÷ 0.5
Problem 16 :
14.7 ÷ 7
Problem 17 :
106.9 ÷ 25
Problem 18 :
A car travelled for 4.5 hours and covered a distance of 290.25 miles. Find the speed of the car in miles per hour.
Problem 19 :
Jasmine was preparing a design to decorate her classroom. She needed a few colored strips of paper of length 1.8 cm each. She had a strip of colored paper of length 7.2 cm. How many pieces of the required length will she get out of this strip?
Problem 20 :
There are 54.25 liters of oil in 4 cans. First three cans are completely filled and in the fourth can, only half of it is filled. How much oil can be filled in one can?
1. Answer :
= 2.1 ÷ 0.7
= ²¹⁄₁₀ ÷ ⁷⁄₁₀
Change division to multiplication and take reciprocal of the fraction ⁷⁄₁₀.
= ²¹⁄₁₀ x ¹⁰⁄₇
Simplify.
= ³⁄₁ x ¹⁄₁
= ³⁄₁
= 3
2. Answer :
= 4.8 ÷ 0.6
= ⁴⁸⁄₁₀ ÷ ⁶⁄₁₀
Change division to multiplication and take reciprocal of the fraction ⁶⁄₁₀.
= ⁴⁸⁄₁₀ x ¹⁰⁄₆
Simplify.
= ⁸⁄₁ x ¹⁄₁
= ⁸⁄₁
= 8
3. Answer :
= 2.7 ÷ 0.03
= ²⁷⁄₁₀ ÷ ³⁄₁₀₀
Change division to multiplication and take reciprocal of the fraction ³⁄₁₀₀.
= ²⁷⁄₁₀ x ¹⁰⁰⁄₃
Simplify.
= ⁹⁄₁ x ¹⁰⁄₁
= 9 x 10
= 90
4. Answer :
= 0.72 ÷ 0.006
= ⁷²⁄₁₀₀ ÷ ⁶⁄₁₀₀₀
Change division to multiplication and take reciprocal of the fraction ⁶⁄₁₀₀₀.
= ⁷²⁄₁₀₀ x ¹⁰⁰⁰⁄₆
Simplify.
= ¹²⁄₁ x ¹⁰⁄₁
= 12 x 10
= 120
5. Answer :
= 35 ÷ 0.007
= 35 ÷ ⁷⁄₁₀₀₀
Change division to multiplication and take reciprocal of the fraction ⁷⁄₁₀₀₀.
= 35 x ¹⁰⁰⁰⁄₇
= 5 x ¹⁰⁰⁰⁄₁
= 5 x 1000
= 5000
6. Answer :
Since we divide 4325.78 by 10, we have to move the decimal point one digit to the left.
4325.78 ÷ 10 = 432.578
7. Answer :
Since we divide 4325.78 by 100, we have to move the decimal point two digits to the left.
4325.78 ÷ 100 = 43.2578
8. Answer :
Since we divide 4325.78 by 1000, we have to move the decimal point three digits to the left.
4325.78 ÷ 1000 = 4.32578
9. Answer :
Since we divide 3.96 by 10, we have to move the decimal point one digit to the left.
3.96 ÷ 10 = 0.396
10. Answer :
Since we divide 7.89 by 100, we have to move the decimal point two digits to the left.
But, we have only one digit '7' to the left of the decimal point in 7.89. To get one more digit to the left of the decimal point, we have to add one zero.
7.89 ÷ 100 = 0.0789
11. Answer :
Since we divide 5.9 by 1000, we have to move the decimal point three digits to the left.
But, we have only one digit to the left of the decimal point in 5.9. To get two more digits to the left of the decimal point, we have to add two zeros.
5.9 ÷ 1000 = 0.0059
12. Answer :
Since we divide 0.4 by 100, we have to move the decimal point two digits to the left.
But, we have no digit to the left of the decimal point in 0.4. To get two digits to the left of the decimal point, we have add two zeros.
0.4 ÷ 100 = 0.004
13. Answer :
Since we divide 0.09 by 100, we have to move the decimal point two digits to the left.
But, we have no digit to the left of the decimal point in 0.4. To get two digits to the left of the decimal point, we have add two zeros.
0.09 ÷ 100 = 0.0009
14. Answer :
Since we divide 0.001 by 1000, we have to move the decimal point three digits to the left.
But, we have no digit to the left of the decimal point in 0.4. To get two digits to the left of the decimal point, we have add three zeros.
0.001 ÷ 1000 = 0.000001
15. Answer :
= 0.15 ÷ 0.5
= ¹⁵⁄₁₀₀ ÷ ⁵⁄₁₀
Change division to multiplication and take reciprocal of the fraction ⁵⁄₁₀.
= ¹⁵⁄₁₀₀ x ¹⁰⁄₅
Simplify.
= ³⁄₁₀x ¹⁄₁
= ³⁄₁₀
Since we divide 3 by 10, there should be one digit to the right of the decimal point in the answer.
= 0.3
16. Answer :
= 14.7 ÷ 7
= ¹⁴⁷⁄₁₀ ÷ ⁷⁄₁
Change division to multiplication and take reciprocal of the fraction ⁷⁄₁.
= ¹⁴⁷⁄₁₀ x ⅐
Simplify.
= ¹⁴⁷⁄₁₀ x ⅐
= ²¹⁄₁₀ x ¹⁄₁
= ²¹⁄₁₀
Since we divide 21 by 10, there should be one digit to the right of the decimal point in the answer.
= 2.1
17. Answer :
= 1069 ÷ 25
= ¹⁰⁶⁹⁄₁₀ ÷ ²⁵⁄₁
Change division to multiplication and take reciprocal of the fraction ²⁵⁄₁.
= ¹⁰⁶⁹⁄₁₀ x ¹⁄₂₅
Multiply both numerator and denominator of the fraction ¹⁄₂₅ by 4 to make the denominator as 100.
= ¹⁰⁶⁹⁄₁₀ x ⁽¹ˣ⁴⁾⁄₍₂₅ₓ₄₎
= ¹⁰⁶⁹⁄₁₀ x ⁴⁄₁₀₀
= ⁽¹⁰⁶⁹ˣ⁴⁾⁄₍₁₀ₓ₁₀₀₎
= ⁴²⁷⁶⁄₁₀₀₀
Since we divide 4276 by 1000, there should be three digits to the right of the decimal point in the answer.
= 4.276
18. Answer :
The time is given in hours and the distance is given in miles.
To find the speed of the car, we have to divide the given distance in miles by the time in hours.
Speed of the car :
= 290.25 ÷ 4.5
= ²⁹⁰²⁵⁄₁₀₀ ÷ ⁴⁵⁄₁₀
Change division to multiplication and take reciprocal of the fraction ⁴⁵⁄₁₀.
= ²⁹⁰²⁵⁄₁₀₀ x ¹⁰⁄₄₅
= ⁵⁸⁰⁵⁄₁₀ x ⅑
= ¹⁹³⁵⁄₁₀ x ⅓
= ⁶⁴⁵⁄₁₀ x ¹⁄₁
= ⁶⁴⁵⁄₁₀
Since 645 is divided by 10, there should be one digit to the right of the decimal point in the answer.
= 64.5
Therefore, the speed of the car was 64.5 miles per hour.
19. Answer :
Number of pieces of the required length :
= 7.2/1.8
= 7.2 ÷ 1.8
= ⁷²⁄₁₀ ÷ ¹⁸⁄₁₀
Change division to multiplication and take reciprocal of the fraction ¹⁸⁄₁₀.
= ⁷²⁄₁₀ x ¹⁰⁄₁₈
Simplify.
= ⁴⁄₁ x ¹⁄₁
= 4 x 1
= 4
20. Answer :
From the given information, it is clear that 54.25 liters of oil is filled in 3.5 cans.
Amount of oil can be filled in one can :
= 54.25/3.5
= ⁵⁴²⁵⁄₁₀₀ ÷ ³⁵⁄₁₀
Change division to multiplication and take reciprocal of the fraction ³⁵⁄₁₀.
= ⁵⁴²⁵⁄₁₀₀ x ¹⁰⁄₃₅
Simplify.
= ⁵⁴²⁵⁄₁₀₀ x ¹⁰⁄₃₅
= ¹⁰⁸⁵⁄₁₀ x ⅐
= ¹⁵⁵⁄₁₀ x ¹⁄₁
= ¹⁵⁵⁄₁₀
Since 155 is divided by 10, there should be one digit to the right of the decimal point in the answer.
= 15.5
Therefore, 15.5 liters of oil can be filled in one can.
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