Division as The Inverse of Multiplication
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In division because the inverse of multiplication, let a and b be two complete numbers. Dividing a by b means discovering a complete quantity which when multiplied by b offers a and we writea ÷ b = c.
Thus, a ÷ b = c or a = b × c
For instance:
Divide 28 by 7 means discovering a complete quantity which when multiplied by 7 offers 28. Clearly, such a quantity is 4. So, we write 28 ÷ 7 = 4.
Equally, now we have
12 ÷ 4 = 3, since 4 × 3 = 12
35 ÷ 5 = 7, since 5 × 7 = 35
2 ÷ 1 = 2, since 2 × 1 = 2
15 ÷ 15 = 1, since 15 × 1 = 15
42 ÷ 6 = 7, since 6 × 7 = 42
Division by Inverse of Multiplication:
Division Reality 24 ÷ 4 = 6 |
→ |
Multiplication truth = 6 × 4 = 24 or 4 × 6 = 24 |
Multiplication Reality 6 × 3 = 18 |
→ |
Division Reality = 18 ÷ 3 = 6 or 18 ÷ 6 = 3 |
Be aware:
If a and b are two complete numbers, then a ÷ b can be expressed as a/b.
Thus, a ÷ b = c or a = bc, which will also be written as
(frac{a}{b}) = c or a = b × c.
Questions and Solutions on Division as The Inverse of Multiplication:
I. Write division details: One has been achieved for you.
(i) 6 × 8 = 48 ___________________ 48 ÷ 6 = 8 48 ÷ 8 = 6 |
(ii) 9 × 5 = 45 ___________________ ….. ÷ ….. = ….. ….. ÷ ….. = ….. |
(iii) 12 × 7 = 84 ___________________ ….. ÷ ….. = ….. ….. ÷ ….. = ….. |
(iv) 14 × 4 = 56 ___________________ ….. ÷ ….. = ….. ….. ÷ ….. = ….. |
(v) 16 × 2 = 32 ___________________ ….. ÷ ….. = ….. ….. ÷ ….. = ….. |
(vi) 6 × 9 = 54 ___________________ ….. ÷ ….. = ….. ….. ÷ ….. = ….. |
Reply:
I. (ii) 45 ÷ 9 = 5; 45 ÷ 5 = 9
(iii) 72 ÷ 12 = 6; 72 ÷ 6 = 12
(iv) 30 ÷ 15 = 2; 30 ÷ 2 = 15
(v) 84 ÷ 12 = 7; 84 ÷ 7 = 12
(vi) 56 ÷ 14 = 4; 56 ÷ 4 = 14
(vii) 32 ÷ 16 = 2; 32 ÷ 2 = 16
(viii) 45 ÷ 9 = 5; 45 ÷ 5 = 9
II. Write Multiplication Information: One has been achieved for you.
(i) 27 ÷ 9 = 3 ___________________ 3 × 9 = 27 9 × 3 = 27 |
(ii) 45 ÷ 3 = 15 ___________________ ….. × ….. = ….. ….. × ….. = ….. |
(iii) 15 ÷ 3 = 5 ___________________ ….. × ….. = ….. ….. × ….. = ….. |
(iv) 12 ÷ 4 = 3 ___________________ ….. × ….. = ….. ….. × ….. = ….. |
(v) 16 ÷ 2 = 8 ___________________ ….. × ….. = ….. ….. × ….. = ….. |
(vi) 49 ÷ 7 = 7 ___________________ ….. × ….. = ….. ….. × ….. = ….. |
(vii) 54 ÷ 6 = 9 ___________________ ….. × ….. = ….. ….. × ….. = ….. |
(viii) 48 ÷ 8 = 6 ___________________ ….. × ….. = ….. ….. × ….. = ….. |
Reply:
II. (ii) 15 × 3 = 45; 3 × 15 = 45
(iii) 5 × 3 = 15; 3 × 5 = 15
(iv) 3 × 4 = 12; 4 × 3 = 15
(v) 8 × 2 = 16; 2 × 8 = 16
(vi) 7 × 7 = 49; 7 × 7 = 49
(vii) 9 × 6 = 54; 6 × 9 = 54
(viii) 6 × 8 = 48; 8 × 6 = 48
Illustration of Entire Numbers on Quantity Line
Division as The Inverse of Multiplication
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