Division Facts
Grade 3 · Mathematics · Worksheet 1
- 2 ÷ 2 = ? Answer: ______________
- 20 ÷ 5 = ? Answer: ______________
- 3 ÷ 1 = ? Answer: ______________
- 12 ÷ 6 = ? Answer: ______________
- 30 ÷ 5 = ? Answer: ______________
- 20 ÷ 4 = ? Answer: ______________
- 63 ÷ 7 = ? Answer: ______________
- 8 ÷ 1 = ? Answer: ______________
- 21 ÷ 3 = ? Answer: ______________
- 77 ÷ 7 = ? Answer: ______________
Answer Key & Explanations
Division Facts · Grade 3 · Worksheet 1
- 2 ÷ 2 = ? Answer: 1 Solution: We are asked to divide 2 by 2. Division is the process of splitting a number into equal parts. Interpret the division.
Full step-by-step solution
Step 1: Understand the problem.
We are asked to divide 2 by 2. Division is the process of splitting a number into equal parts.
Step 2: Interpret the division.
The expression 2 ÷ 2 asks: "How many groups of 2 can we make from the number 2?"
Step 3: Visualize the division.
Imagine you have 2 objects. You want to put them into groups, with each group containing exactly 2 objects.
Step 4: Perform the grouping.
If you take your 2 objects and put them into one group, that one group contains all 2 objects. You have no objects left over.
Step 5: State the result.
Since you can make exactly 1 full group of 2 from the number 2, the answer is 1.
Step 6: Write the final answer.
2 ÷ 2 = 1
- 20 ÷ 5 = ? Answer: 4 Solution: We are solving: 20 ÷ 5 = ? Division means splitting a number into equal parts. Here, we are splitting 20 into 5 equal groups.
Full step-by-step solution
We are solving: 20 ÷ 5 = ?
Step 1: Understand the division.
Division means splitting a number into equal parts.
Here, we are splitting 20 into 5 equal groups.
Step 2: Think of it as repeated subtraction.
How many times can we subtract 5 from 20 until we reach 0?
20 - 5 = 15 (1 time)
15 - 5 = 10 (2 times)
10 - 5 = 5 (3 times)
5 - 5 = 0 (4 times)
We subtracted 5 a total of 4 times.
Step 3: Alternatively, think of multiplication.
Division is the inverse of multiplication.
We ask: "What number multiplied by 5 gives 20?"
That is: ? × 5 = 20.
We know 4 × 5 = 20, so the answer is 4.
Step 4: Conclusion.
Therefore, 20 ÷ 5 = 4.
ANSWER: 4
- 3 ÷ 1 = ? Answer: 3 Solution: We are asked to divide 3 by 1. This means we need to find how many times the number 1 fits into the number 3. Recall the concept of division.
Full step-by-step solution
Step 1: Understand the problem.
We are asked to divide 3 by 1. This means we need to find how many times the number 1 fits into the number 3.
Step 2: Recall the concept of division.
Division is the process of splitting a number into equal parts. For example, 6 ÷ 2 = 3 means splitting 6 into 2 equal groups, with 3 in each group.
Step 3: Apply the concept to our problem.
We are splitting the number 3 into 1 equal group. If we have one group containing all 3 items, then that one group contains 3 items.
Step 4: Perform the calculation.
3 ÷ 1 = 3
Step 5: Verify the answer using multiplication (the inverse operation).
Division and multiplication are opposites. If 3 ÷ 1 = 3 is correct, then multiplying the answer (3) by the divisor (1) should give us the original number (3).
Check: 3 (answer) × 1 (divisor) = 3 (original number). This confirms our answer is correct.
Step 6: State the final answer.
Therefore, 3 divided by 1 equals 3.
- 12 ÷ 6 = ? Answer: 2 Solution: We are solving: 12 ÷ 6 = ? Division means splitting a number into equal parts. Here, we are dividing 12 by 6, which means we want to know how many groups of 6 are in 12.
Full step-by-step solution
We are solving: 12 ÷ 6 = ?
Step 1: Understand the division.
Division means splitting a number into equal parts.
Here, we are dividing 12 by 6, which means we want to know how many groups of 6 are in 12.
Step 2: Think of it as repeated subtraction.
Start with 12.
Subtract 6: 12 - 6 = 6 (1 group)
Subtract 6 again: 6 - 6 = 0 (2 groups)
We subtracted 6 exactly 2 times until we reached 0.
Step 3: Use multiplication to check.
If 12 ÷ 6 = ?, then ? × 6 should equal 12.
We know 2 × 6 = 12, so ? must be 2.
Step 4: Conclusion.
Therefore, 12 ÷ 6 = 2.
ANSWER: 2
- 30 ÷ 5 = ? Answer: 6 Solution: We are solving: 30 ÷ 5 = ? Division means splitting a number into equal parts. Here, we are splitting 30 into 5 equal groups.
Full step-by-step solution
We are solving: 30 ÷ 5 = ?
Step 1: Understand the division.
Division means splitting a number into equal parts.
Here, we are splitting 30 into 5 equal groups.
Step 2: Think of it as: how many times does 5 fit into 30?
We can count: 5, 10, 15, 20, 25, 30.
That is 6 times.
Step 3: Check with multiplication.
If 30 ÷ 5 = x, then 5 × x = 30.
We know 5 × 6 = 30, so x = 6.
Step 4: Conclusion.
30 divided by 5 equals 6.
ANSWER: 6
- 20 ÷ 4 = ? Answer: 5 Solution: We are solving: 20 ÷ 4 = ? Division means splitting a number into equal parts. Here, we are splitting 20 into 4 equal groups.
Full step-by-step solution
We are solving: 20 ÷ 4 = ?
Step 1: Understand the division.
Division means splitting a number into equal parts. Here, we are splitting 20 into 4 equal groups.
Step 2: Think of it as repeated subtraction.
We subtract 4 repeatedly from 20 until we reach 0, and count how many times we subtract.
20 - 4 = 16 (1 time)
16 - 4 = 12 (2 times)
12 - 4 = 8 (3 times)
8 - 4 = 4 (4 times)
4 - 4 = 0 (5 times)
We subtracted 4 a total of 5 times to reach 0.
Step 3: Check with multiplication.
Division is the opposite of multiplication. If 20 ÷ 4 = ?, then 4 × ? = 20.
We know 4 × 5 = 20, so the answer is 5.
Step 4: Conclusion.
Therefore, 20 ÷ 4 = 5.
- 63 ÷ 7 = ? Answer: 9 Solution: We are solving 63 ÷ 7. Division asks: how many times does 7 fit into 63? Recall multiplication facts related to 7.
Full step-by-step solution
We are solving 63 ÷ 7.
Step 1: Understand the division.
Division asks: how many times does 7 fit into 63?
Step 2: Recall multiplication facts related to 7.
7 × 9 = 63.
This means 7 fits into 63 exactly 9 times.
Step 3: Write the answer.
Since 7 × 9 = 63, then 63 ÷ 7 = 9.
Final Answer: 9
- 8 ÷ 1 = ? Answer: 8 Solution: We have 8 ÷ 1. This means we are dividing the number 8 into 1 equal part. Interpret what division means.
Full step-by-step solution
Step 1: Understand the division problem.
We have 8 ÷ 1. This means we are dividing the number 8 into 1 equal part.
Step 2: Interpret what division means.
Division asks the question: "How many times does the divisor (the number after the division sign) fit into the dividend (the number before the division sign)?" Here, we are asking: "How many times does 1 fit into 8?"
Step 3: Perform the calculation.
If you have 8 items and you put them into 1 group, that one group will contain all 8 items. Another way to think about it is: What number, when multiplied by the divisor (1), gives us the dividend (8)? We can write this as:
? x 1 = 8
Step 4: Apply the identity property of multiplication.
Any number multiplied by 1 remains itself. So, the number that fits in the blank is 8.
8 x 1 = 8
Step 5: State the final answer.
Therefore, 8 ÷ 1 = 8.
- 21 ÷ 3 = ? Answer: 7 Solution: We are solving: 21 ÷ 3 = ? Division means splitting a number into equal parts. Here, we are splitting 21 into 3 equal groups.
Full step-by-step solution
We are solving: 21 ÷ 3 = ?
Step 1: Understand the division.
Division means splitting a number into equal parts.
Here, we are splitting 21 into 3 equal groups. We want to know how many are in each group.
Step 2: Think of it as repeated subtraction.
If we have 21 and repeatedly subtract 3, how many times can we do that until we reach 0?
21 - 3 = 18 (1 time)
18 - 3 = 15 (2 times)
15 - 3 = 12 (3 times)
12 - 3 = 9 (4 times)
9 - 3 = 6 (5 times)
6 - 3 = 3 (6 times)
3 - 3 = 0 (7 times)
We subtracted 3 a total of 7 times.
Step 3: Relate to multiplication.
Division is the inverse of multiplication.
We ask: 3 times what number equals 21?
3 × 7 = 21.
So 21 ÷ 3 = 7.
Step 4: Conclusion.
The number 21 divided into 3 equal parts gives 7 in each part.
ANSWER: 7
- 77 ÷ 7 = ? Answer: 11 Solution: We are dividing 77 by 7. This means we want to know how many times 7 fits into 77. Recall multiplication facts for 7.
Full step-by-step solution
Let's solve 77 ÷ 7 step by step.
Step 1: Understand the division.
We are dividing 77 by 7. This means we want to know how many times 7 fits into 77.
Step 2: Recall multiplication facts for 7.
7 × 10 = 70.
77 is 7 more than 70.
Step 3: Find how many more 7s fit into the remaining part.
77 − 70 = 7.
7 × 1 = 7.
So 7 fits into the remaining 7 exactly 1 time.
Step 4: Add up the total number of 7s.
From Step 2: 10 times.
From Step 3: 1 time.
Total: 10 + 1 = 11.
Step 5: Check the result.
7 × 11 = 77, which matches the original number.
Therefore, 77 ÷ 7 = 11.