Division Chart Printable - Paper Trail Design - Free Printable
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Step-by-step solution for: Division Chart Printable - Paper Trail Design
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Show Answer Key & Explanations
Step-by-step solution for: Division Chart Printable - Paper Trail Design
The image you provided is a division table that covers division facts for numbers 1 through 12. Each column represents division by a specific number (e.g., "ONES" for dividing by 1, "TWOS" for dividing by 2, etc.). Below, I will solve the problems and explain the solution process.
---
Division is the inverse operation of multiplication. It involves splitting a number (the dividend) into equal parts based on another number (the divisor). The result is called the quotient.
For example:
- \( 6 \div 3 = 2 \) because \( 3 \times 2 = 6 \).
---
#### Column 1: ONES
Dividing any number by 1 results in the number itself.
\[
\begin{aligned}
1 \div 1 &= 1 \\
2 \div 1 &= 2 \\
3 \div 1 &= 3 \\
4 \div 1 &= 4 \\
5 \div 1 &= 5 \\
6 \div 1 &= 6 \\
7 \div 1 &= 7 \\
8 \div 1 &= 8 \\
9 \div 1 &= 9 \\
10 \div 1 &= 10 \\
11 \div 1 &= 11 \\
12 \div 1 &= 12 \\
\end{aligned}
\]
#### Column 2: TWOS
Dividing by 2 means splitting the number into two equal parts.
\[
\begin{aligned}
2 \div 2 &= 1 \\
4 \div 2 &= 2 \\
6 \div 2 &= 3 \\
8 \div 2 &= 4 \\
10 \div 2 &= 5 \\
12 \div 2 &= 6 \\
14 \div 2 &= 7 \\
16 \div 2 &= 8 \\
18 \div 2 &= 9 \\
20 \div 2 &= 10 \\
22 \div 2 &= 11 \\
24 \div 2 &= 12 \\
\end{aligned}
\]
#### Column 3: THREES
Dividing by 3 means splitting the number into three equal parts.
\[
\begin{aligned}
3 \div 3 &= 1 \\
6 \div 3 &= 2 \\
9 \div 3 &= 3 \\
12 \div 3 &= 4 \\
15 \div 3 &= 5 \\
18 \div 3 &= 6 \\
21 \div 3 &= 7 \\
24 \div 3 &= 8 \\
27 \div 3 &= 9 \\
30 \div 3 &= 10 \\
33 \div 3 &= 11 \\
36 \div 3 &= 12 \\
\end{aligned}
\]
#### Column 4: FOURS
Dividing by 4 means splitting the number into four equal parts.
\[
\begin{aligned}
4 \div 4 &= 1 \\
8 \div 4 &= 2 \\
12 \div 4 &= 3 \\
16 \div 4 &= 4 \\
20 \div 4 &= 5 \\
24 \div 4 &= 6 \\
28 \div 4 &= 7 \\
32 \div 4 &= 8 \\
36 \div 4 &= 9 \\
40 \div 4 &= 10 \\
44 \div 4 &= 11 \\
48 \div 4 &= 12 \\
\end{aligned}
\]
#### Column 5: FIVES
Dividing by 5 means splitting the number into five equal parts.
\[
\begin{aligned}
5 \div 5 &= 1 \\
10 \div 5 &= 2 \\
15 \div 5 &= 3 \\
20 \div 5 &= 4 \\
25 \div 5 &= 5 \\
30 \div 5 &= 6 \\
35 \div 5 &= 7 \\
40 \div 5 &= 8 \\
45 \div 5 &= 9 \\
50 \div 5 &= 10 \\
55 \div 5 &= 11 \\
60 \div 5 &= 12 \\
\end{aligned}
\]
#### Column 6: SIXES
Dividing by 6 means splitting the number into six equal parts.
\[
\begin{aligned}
6 \div 6 &= 1 \\
12 \div 6 &= 2 \\
18 \div 6 &= 3 \\
24 \div 6 &= 4 \\
30 \div 6 &= 5 \\
36 \div 6 &= 6 \\
42 \div 6 &= 7 \\
48 \div 6 &= 8 \\
54 \div 6 &= 9 \\
60 \div 6 &= 10 \\
66 \div 6 &= 11 \\
72 \div 6 &= 12 \\
\end{aligned}
\]
#### Column 7: SEVENS
Dividing by 7 means splitting the number into seven equal parts.
\[
\begin{aligned}
7 \div 7 &= 1 \\
14 \div 7 &= 2 \\
21 \div 7 &= 3 \\
28 \div 7 &= 4 \\
35 \div 7 &= 5 \\
42 \div 7 &= 6 \\
49 \div 7 &= 7 \\
56 \div 7 &= 8 \\
63 \div 7 &= 9 \\
70 \div 7 &= 10 \\
77 \div 7 &= 11 \\
84 \div 7 &= 12 \\
\end{aligned}
\]
#### Column 8: EIGHTS
Dividing by 8 means splitting the number into eight equal parts.
\[
\begin{aligned}
8 \div 8 &= 1 \\
16 \div 8 &= 2 \\
24 \div 8 &= 3 \\
32 \div 8 &= 4 \\
40 \div 8 &= 5 \\
48 \div 8 &= 6 \\
56 \div 8 &= 7 \\
64 \div 8 &= 8 \\
72 \div 8 &= 9 \\
80 \div 8 &= 10 \\
88 \div 8 &= 11 \\
96 \div 8 &= 12 \\
\end{aligned}
\]
#### Column 9: NINES
Dividing by 9 means splitting the number into nine equal parts.
\[
\begin{aligned}
9 \div 9 &= 1 \\
18 \div 9 &= 2 \\
27 \div 9 &= 3 \\
36 \div 9 &= 4 \\
45 \div 9 &= 5 \\
54 \div 9 &= 6 \\
63 \div 9 &= 7 \\
72 \div 9 &= 8 \\
81 \div 9 &= 9 \\
90 \div 9 &= 10 \\
99 \div 9 &= 11 \\
108 \div 9 &= 12 \\
\end{aligned}
\]
#### Column 10: TENS
Dividing by 10 means splitting the number into ten equal parts.
\[
\begin{aligned}
10 \div 10 &= 1 \\
20 \div 10 &= 2 \\
30 \div 10 &= 3 \\
40 \div 10 &= 4 \\
50 \div 10 &= 5 \\
60 \div 10 &= 6 \\
70 \div 10 &= 7 \\
80 \div 10 &= 8 \\
90 \div 10 &= 9 \\
100 \div 10 &= 10 \\
110 \div 10 &= 11 \\
120 \div 10 &= 12 \\
\end{aligned}
\]
#### Column 11: ELEVENS
Dividing by 11 means splitting the number into eleven equal parts.
\[
\begin{aligned}
11 \div 11 &= 1 \\
22 \div 11 &= 2 \\
33 \div 11 &= 3 \\
44 \div 11 &= 4 \\
55 \div 11 &= 5 \\
66 \div 11 &= 6 \\
77 \div 11 &= 7 \\
88 \div 11 &= 8 \\
99 \div 11 &= 9 \\
110 \div 11 &= 10 \\
121 \div 11 &= 11 \\
132 \div 11 &= 12 \\
\end{aligned}
\]
#### Column 12: TWELVES
Dividing by 12 means splitting the number into twelve equal parts.
\[
\begin{aligned}
12 \div 12 &= 1 \\
24 \div 12 &= 2 \\
36 \div 12 &= 3 \\
48 \div 12 &= 4 \\
60 \div 12 &= 5 \\
72 \div 12 &= 6 \\
84 \div 12 &= 7 \\
96 \div 12 &= 8 \\
108 \div 12 &= 9 \\
120 \div 12 &= 10 \\
132 \div 12 &= 11 \\
144 \div 12 &= 12 \\
\end{aligned}
\]
---
The completed division table is as follows:
\[
\boxed{
\begin{array}{c|c|c|c|c|c|c|c|c|c|c|c}
\text{ONES} & \text{TWOS} & \text{THREES} & \text{FOURS} & \text{FIVES} & \text{SIXES} & \text{SEVENS} & \text{EIGHTS} & \text{NINES} & \text{TENS} & \text{ELEVENS} & \text{TWELVES} \\
\hline
1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 \\
3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 \\
4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 \\
5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 \\
6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 \\
7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 \\
8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 \\
9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 \\
10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 \\
11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 \\
12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 \\
\end{array}
}
\]
---
Explanation of Division
Division is the inverse operation of multiplication. It involves splitting a number (the dividend) into equal parts based on another number (the divisor). The result is called the quotient.
For example:
- \( 6 \div 3 = 2 \) because \( 3 \times 2 = 6 \).
---
Solving the Problems
#### Column 1: ONES
Dividing any number by 1 results in the number itself.
\[
\begin{aligned}
1 \div 1 &= 1 \\
2 \div 1 &= 2 \\
3 \div 1 &= 3 \\
4 \div 1 &= 4 \\
5 \div 1 &= 5 \\
6 \div 1 &= 6 \\
7 \div 1 &= 7 \\
8 \div 1 &= 8 \\
9 \div 1 &= 9 \\
10 \div 1 &= 10 \\
11 \div 1 &= 11 \\
12 \div 1 &= 12 \\
\end{aligned}
\]
#### Column 2: TWOS
Dividing by 2 means splitting the number into two equal parts.
\[
\begin{aligned}
2 \div 2 &= 1 \\
4 \div 2 &= 2 \\
6 \div 2 &= 3 \\
8 \div 2 &= 4 \\
10 \div 2 &= 5 \\
12 \div 2 &= 6 \\
14 \div 2 &= 7 \\
16 \div 2 &= 8 \\
18 \div 2 &= 9 \\
20 \div 2 &= 10 \\
22 \div 2 &= 11 \\
24 \div 2 &= 12 \\
\end{aligned}
\]
#### Column 3: THREES
Dividing by 3 means splitting the number into three equal parts.
\[
\begin{aligned}
3 \div 3 &= 1 \\
6 \div 3 &= 2 \\
9 \div 3 &= 3 \\
12 \div 3 &= 4 \\
15 \div 3 &= 5 \\
18 \div 3 &= 6 \\
21 \div 3 &= 7 \\
24 \div 3 &= 8 \\
27 \div 3 &= 9 \\
30 \div 3 &= 10 \\
33 \div 3 &= 11 \\
36 \div 3 &= 12 \\
\end{aligned}
\]
#### Column 4: FOURS
Dividing by 4 means splitting the number into four equal parts.
\[
\begin{aligned}
4 \div 4 &= 1 \\
8 \div 4 &= 2 \\
12 \div 4 &= 3 \\
16 \div 4 &= 4 \\
20 \div 4 &= 5 \\
24 \div 4 &= 6 \\
28 \div 4 &= 7 \\
32 \div 4 &= 8 \\
36 \div 4 &= 9 \\
40 \div 4 &= 10 \\
44 \div 4 &= 11 \\
48 \div 4 &= 12 \\
\end{aligned}
\]
#### Column 5: FIVES
Dividing by 5 means splitting the number into five equal parts.
\[
\begin{aligned}
5 \div 5 &= 1 \\
10 \div 5 &= 2 \\
15 \div 5 &= 3 \\
20 \div 5 &= 4 \\
25 \div 5 &= 5 \\
30 \div 5 &= 6 \\
35 \div 5 &= 7 \\
40 \div 5 &= 8 \\
45 \div 5 &= 9 \\
50 \div 5 &= 10 \\
55 \div 5 &= 11 \\
60 \div 5 &= 12 \\
\end{aligned}
\]
#### Column 6: SIXES
Dividing by 6 means splitting the number into six equal parts.
\[
\begin{aligned}
6 \div 6 &= 1 \\
12 \div 6 &= 2 \\
18 \div 6 &= 3 \\
24 \div 6 &= 4 \\
30 \div 6 &= 5 \\
36 \div 6 &= 6 \\
42 \div 6 &= 7 \\
48 \div 6 &= 8 \\
54 \div 6 &= 9 \\
60 \div 6 &= 10 \\
66 \div 6 &= 11 \\
72 \div 6 &= 12 \\
\end{aligned}
\]
#### Column 7: SEVENS
Dividing by 7 means splitting the number into seven equal parts.
\[
\begin{aligned}
7 \div 7 &= 1 \\
14 \div 7 &= 2 \\
21 \div 7 &= 3 \\
28 \div 7 &= 4 \\
35 \div 7 &= 5 \\
42 \div 7 &= 6 \\
49 \div 7 &= 7 \\
56 \div 7 &= 8 \\
63 \div 7 &= 9 \\
70 \div 7 &= 10 \\
77 \div 7 &= 11 \\
84 \div 7 &= 12 \\
\end{aligned}
\]
#### Column 8: EIGHTS
Dividing by 8 means splitting the number into eight equal parts.
\[
\begin{aligned}
8 \div 8 &= 1 \\
16 \div 8 &= 2 \\
24 \div 8 &= 3 \\
32 \div 8 &= 4 \\
40 \div 8 &= 5 \\
48 \div 8 &= 6 \\
56 \div 8 &= 7 \\
64 \div 8 &= 8 \\
72 \div 8 &= 9 \\
80 \div 8 &= 10 \\
88 \div 8 &= 11 \\
96 \div 8 &= 12 \\
\end{aligned}
\]
#### Column 9: NINES
Dividing by 9 means splitting the number into nine equal parts.
\[
\begin{aligned}
9 \div 9 &= 1 \\
18 \div 9 &= 2 \\
27 \div 9 &= 3 \\
36 \div 9 &= 4 \\
45 \div 9 &= 5 \\
54 \div 9 &= 6 \\
63 \div 9 &= 7 \\
72 \div 9 &= 8 \\
81 \div 9 &= 9 \\
90 \div 9 &= 10 \\
99 \div 9 &= 11 \\
108 \div 9 &= 12 \\
\end{aligned}
\]
#### Column 10: TENS
Dividing by 10 means splitting the number into ten equal parts.
\[
\begin{aligned}
10 \div 10 &= 1 \\
20 \div 10 &= 2 \\
30 \div 10 &= 3 \\
40 \div 10 &= 4 \\
50 \div 10 &= 5 \\
60 \div 10 &= 6 \\
70 \div 10 &= 7 \\
80 \div 10 &= 8 \\
90 \div 10 &= 9 \\
100 \div 10 &= 10 \\
110 \div 10 &= 11 \\
120 \div 10 &= 12 \\
\end{aligned}
\]
#### Column 11: ELEVENS
Dividing by 11 means splitting the number into eleven equal parts.
\[
\begin{aligned}
11 \div 11 &= 1 \\
22 \div 11 &= 2 \\
33 \div 11 &= 3 \\
44 \div 11 &= 4 \\
55 \div 11 &= 5 \\
66 \div 11 &= 6 \\
77 \div 11 &= 7 \\
88 \div 11 &= 8 \\
99 \div 11 &= 9 \\
110 \div 11 &= 10 \\
121 \div 11 &= 11 \\
132 \div 11 &= 12 \\
\end{aligned}
\]
#### Column 12: TWELVES
Dividing by 12 means splitting the number into twelve equal parts.
\[
\begin{aligned}
12 \div 12 &= 1 \\
24 \div 12 &= 2 \\
36 \div 12 &= 3 \\
48 \div 12 &= 4 \\
60 \div 12 &= 5 \\
72 \div 12 &= 6 \\
84 \div 12 &= 7 \\
96 \div 12 &= 8 \\
108 \div 12 &= 9 \\
120 \div 12 &= 10 \\
132 \div 12 &= 11 \\
144 \div 12 &= 12 \\
\end{aligned}
\]
---
Final Answer
The completed division table is as follows:
\[
\boxed{
\begin{array}{c|c|c|c|c|c|c|c|c|c|c|c}
\text{ONES} & \text{TWOS} & \text{THREES} & \text{FOURS} & \text{FIVES} & \text{SIXES} & \text{SEVENS} & \text{EIGHTS} & \text{NINES} & \text{TENS} & \text{ELEVENS} & \text{TWELVES} \\
\hline
1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 \\
3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 \\
4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 \\
5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 \\
6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 \\
7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 & 7 \\
8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 \\
9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 & 9 \\
10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 \\
11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 & 11 \\
12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 & 12 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of division table worksheet.
