In division as the inverse of multiplication, let a and b be two whole numbers. Dividing a by b means finding a whole number which when multiplied by b gives a and we writea ÷ b = c.
Thus, a ÷ b = c or a = b × c
For example:
Divide 28 by 7 means finding a whole number which when multiplied by 7 gives 28. Clearly, such a number is 4. So, we write 28 ÷ 7 = 4.
Similarly, 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 Fact 24 ÷ 4 = 6 |
→ |
Multiplication fact = 6 × 4 = 24 or 4 × 6 = 24 |
Multiplication Fact 6 × 3 = 18 |
→ |
Division Fact = 18 ÷ 3 = 6 or 18 ÷ 6 = 3 |
Note:
If a and b are two whole numbers, then a ÷ b is also expressed as a/b.
Thus, a ÷ b = c or a = bc, which can also be written as
\(\frac{a}{b}\) = c or a = b × c.
Questions and Answers on Division as The Inverse of Multiplication:
I. Write division facts: One has been done 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 ___________________ ..... ÷ ..... = ..... ..... ÷ ..... = ..... |
Answer:
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 Facts: One has been done 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 ___________________ ..... × ..... = ..... ..... × ..... = ..... |
Answer:
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
Representation of Whole Numbers on Number Line
Division as The Inverse of Multiplication
Numbers Page
6th Grade Page
From Division as The Inverse of Multiplication to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Apr 15, 24 01:29 AM
Apr 15, 24 01:13 AM
Apr 14, 24 03:06 PM
Apr 14, 24 02:23 PM
Apr 14, 24 02:01 PM