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← 3-1 · Division as repeated subtraction · Division as the Inverse of Multiplication

Division as repeated subtraction · 11 practice problems

3.OA.A.23.OA.A.3

Generated variants — 11

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 12 div 4 = 3; 16 div 4 = 4; 28 div 4 = 7

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

8÷4=28 \div 4 = 2
12÷4=312 \div 4 = 3
20÷4=5‾\overline{20 \div 4 = 5}

Using the same method, find the number for each box below.

12÷4=□12 \div 4 = \square
□÷4=□\square \div 4 = \square
28÷4=□‾\overline{28 \div 4 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 12 div 4 plus another fact equals 28 div 4.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 12 div 4 = box, then box div 4 = box, summing to 28 div 4 = box.
  • All three facts use divisor 4.
Unknowns
  • The quotient of 12 div 4.
  • The middle dividend and its quotient.
  • The quotient of 28 div 4.
Constraints
  • All three facts use divisor 4.
  • The first two dividends must add to 28, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 28 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 12 by 4. Since 4 times 3 is 12, the quotient is 3.
12÷4=312 \div 4 = 3
Grade 3 division: 12 split into groups of 4 makes 3 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 12 plus the middle dividend equals 28. So the middle dividend is 28 minus 12 = 16.
28−12=1628 - 12 = 16
Grade 3 subtraction: since the dividends must add to 28, the missing one is 28 take away 12.
#5 Look for a Pattern 3.OA.A.2
Divide 16 by 4: 4 times 4 is 16, so 16 div 4 = 4.
16÷4=416 \div 4 = 4
Grade 3 division: 16 split into groups of 4 makes 4 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 28 by 4 to get 7. This matches the pattern because the top two quotients add: 3 plus 4 equals 7.
28÷4=7,3+4=728 \div 4 = 7, \quad 3 + 4 = 7
Grade 3: the quotients add the same way the dividends do, confirming 7 is right.
Answer: 12 div 4 = 3; 16 div 4 = 4; 28 div 4 = 7

Review

Dividends: 12 + 16 = 28 (correct total). Quotients: 3 + 4 = 7, and 28 div 4 is indeed 7. Both sums line up with the example's rule.

Skip-count by 4 to fill the boxes: reach 12 in 3 steps, continue to 16 in 4 steps, and 28 in 7 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 12 and 16 by 4 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 28 minus 12.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 3, 16, 4, and 7!
Variant 2 answer: 12 div 6 = 2; 24 div 6 = 4; 36 div 6 = 6

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

12÷6=212 \div 6 = 2
18÷6=318 \div 6 = 3
30÷6=5‾\overline{30 \div 6 = 5}

Using the same method, find the number for each box below.

12÷6=□12 \div 6 = \square
□÷6=□\square \div 6 = \square
36÷6=□‾\overline{36 \div 6 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 12 div 6 plus another fact equals 36 div 6.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 12 div 6 = box, then box div 6 = box, summing to 36 div 6 = box.
  • All three facts use divisor 6.
Unknowns
  • The quotient of 12 div 6.
  • The middle dividend and its quotient.
  • The quotient of 36 div 6.
Constraints
  • All three facts use divisor 6.
  • The first two dividends must add to 36, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 36 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 12 by 6. Since 6 times 2 is 12, the quotient is 2.
12÷6=212 \div 6 = 2
Grade 3 division: 12 split into groups of 6 makes 2 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 12 plus the middle dividend equals 36. So the middle dividend is 36 minus 12 = 24.
36−12=2436 - 12 = 24
Grade 3 subtraction: since the dividends must add to 36, the missing one is 36 take away 12.
#5 Look for a Pattern 3.OA.A.2
Divide 24 by 6: 6 times 4 is 24, so 24 div 6 = 4.
24÷6=424 \div 6 = 4
Grade 3 division: 24 split into groups of 6 makes 4 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 36 by 6 to get 6. This matches the pattern because the top two quotients add: 2 plus 4 equals 6.
36÷6=6,2+4=636 \div 6 = 6, \quad 2 + 4 = 6
Grade 3: the quotients add the same way the dividends do, confirming 6 is right.
Answer: 12 div 6 = 2; 24 div 6 = 4; 36 div 6 = 6

Review

Dividends: 12 + 24 = 36 (correct total). Quotients: 2 + 4 = 6, and 36 div 6 is indeed 6. Both sums line up with the example's rule.

Skip-count by 6 to fill the boxes: reach 12 in 2 steps, continue to 24 in 4 steps, and 36 in 6 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 12 and 24 by 6 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 36 minus 12.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 2, 24, 4, and 6!
Variant 3 answer: 14 div 7 = 2; 21 div 7 = 3; 35 div 7 = 5

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

14÷7=214 \div 7 = 2
21÷7=321 \div 7 = 3
35÷7=5‾\overline{35 \div 7 = 5}

Using the same method, find the number for each box below.

14÷7=□14 \div 7 = \square
□÷7=□\square \div 7 = \square
35÷7=□‾\overline{35 \div 7 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 14 div 7 plus another fact equals 35 div 7.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 14 div 7 = box, then box div 7 = box, summing to 35 div 7 = box.
  • All three facts use divisor 7.
Unknowns
  • The quotient of 14 div 7.
  • The middle dividend and its quotient.
  • The quotient of 35 div 7.
Constraints
  • All three facts use divisor 7.
  • The first two dividends must add to 35, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 35 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 14 by 7. Since 7 times 2 is 14, the quotient is 2.
14÷7=214 \div 7 = 2
Grade 3 division: 14 split into groups of 7 makes 2 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 14 plus the middle dividend equals 35. So the middle dividend is 35 minus 14 = 21.
35−14=2135 - 14 = 21
Grade 3 subtraction: since the dividends must add to 35, the missing one is 35 take away 14.
#5 Look for a Pattern 3.OA.A.2
Divide 21 by 7: 7 times 3 is 21, so 21 div 7 = 3.
21÷7=321 \div 7 = 3
Grade 3 division: 21 split into groups of 7 makes 3 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 35 by 7 to get 5. This matches the pattern because the top two quotients add: 2 plus 3 equals 5.
35÷7=5,2+3=535 \div 7 = 5, \quad 2 + 3 = 5
Grade 3: the quotients add the same way the dividends do, confirming 5 is right.
Answer: 14 div 7 = 2; 21 div 7 = 3; 35 div 7 = 5

Review

Dividends: 14 + 21 = 35 (correct total). Quotients: 2 + 3 = 5, and 35 div 7 is indeed 5. Both sums line up with the example's rule.

Skip-count by 7 to fill the boxes: reach 14 in 2 steps, continue to 21 in 3 steps, and 35 in 5 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 14 and 21 by 7 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 35 minus 14.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 2, 21, 3, and 5!
Variant 4 answer: 18 div 6 = 3; 24 div 6 = 4; 42 div 6 = 7

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

12÷6=212 \div 6 = 2
18÷6=318 \div 6 = 3
30÷6=5‾\overline{30 \div 6 = 5}

Using the same method, find the number for each box below.

18÷6=□18 \div 6 = \square
□÷6=□\square \div 6 = \square
42÷6=□‾\overline{42 \div 6 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 18 div 6 plus another fact equals 42 div 6.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 18 div 6 = box, then box div 6 = box, summing to 42 div 6 = box.
  • All three facts use divisor 6.
Unknowns
  • The quotient of 18 div 6.
  • The middle dividend and its quotient.
  • The quotient of 42 div 6.
Constraints
  • All three facts use divisor 6.
  • The first two dividends must add to 42, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 42 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 18 by 6. Since 6 times 3 is 18, the quotient is 3.
18÷6=318 \div 6 = 3
Grade 3 division: 18 split into groups of 6 makes 3 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 18 plus the middle dividend equals 42. So the middle dividend is 42 minus 18 = 24.
42−18=2442 - 18 = 24
Grade 3 subtraction: since the dividends must add to 42, the missing one is 42 take away 18.
#5 Look for a Pattern 3.OA.A.2
Divide 24 by 6: 6 times 4 is 24, so 24 div 6 = 4.
24÷6=424 \div 6 = 4
Grade 3 division: 24 split into groups of 6 makes 4 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 42 by 6 to get 7. This matches the pattern because the top two quotients add: 3 plus 4 equals 7.
42÷6=7,3+4=742 \div 6 = 7, \quad 3 + 4 = 7
Grade 3: the quotients add the same way the dividends do, confirming 7 is right.
Answer: 18 div 6 = 3; 24 div 6 = 4; 42 div 6 = 7

Review

Dividends: 18 + 24 = 42 (correct total). Quotients: 3 + 4 = 7, and 42 div 6 is indeed 7. Both sums line up with the example's rule.

Skip-count by 6 to fill the boxes: reach 18 in 3 steps, continue to 24 in 4 steps, and 42 in 7 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 18 and 24 by 6 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 42 minus 18.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 3, 24, 4, and 7!
Variant 5 answer: 15 div 5 = 3; 25 div 5 = 5; 40 div 5 = 8

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

10÷5=210 \div 5 = 2
15÷5=315 \div 5 = 3
25÷5=5‾\overline{25 \div 5 = 5}

Using the same method, find the number for each box below.

15÷5=□15 \div 5 = \square
□÷5=□\square \div 5 = \square
40÷5=□‾\overline{40 \div 5 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 15 div 5 plus another fact equals 40 div 5.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 15 div 5 = box, then box div 5 = box, summing to 40 div 5 = box.
  • All three facts use divisor 5.
Unknowns
  • The quotient of 15 div 5.
  • The middle dividend and its quotient.
  • The quotient of 40 div 5.
Constraints
  • All three facts use divisor 5.
  • The first two dividends must add to 40, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 40 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 15 by 5. Since 5 times 3 is 15, the quotient is 3.
15÷5=315 \div 5 = 3
Grade 3 division: 15 split into groups of 5 makes 3 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 15 plus the middle dividend equals 40. So the middle dividend is 40 minus 15 = 25.
40−15=2540 - 15 = 25
Grade 3 subtraction: since the dividends must add to 40, the missing one is 40 take away 15.
#5 Look for a Pattern 3.OA.A.2
Divide 25 by 5: 5 times 5 is 25, so 25 div 5 = 5.
25÷5=525 \div 5 = 5
Grade 3 division: 25 split into groups of 5 makes 5 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 40 by 5 to get 8. This matches the pattern because the top two quotients add: 3 plus 5 equals 8.
40÷5=8,3+5=840 \div 5 = 8, \quad 3 + 5 = 8
Grade 3: the quotients add the same way the dividends do, confirming 8 is right.
Answer: 15 div 5 = 3; 25 div 5 = 5; 40 div 5 = 8

Review

Dividends: 15 + 25 = 40 (correct total). Quotients: 3 + 5 = 8, and 40 div 5 is indeed 8. Both sums line up with the example's rule.

Skip-count by 5 to fill the boxes: reach 15 in 3 steps, continue to 25 in 5 steps, and 40 in 8 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 15 and 25 by 5 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 40 minus 15.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 3, 25, 5, and 8!
Variant 6 answer: 8 div 2 = 4; 12 div 2 = 6; 20 div 2 = 10

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

4÷2=24 \div 2 = 2
6÷2=36 \div 2 = 3
10÷2=5‾\overline{10 \div 2 = 5}

Using the same method, find the number for each box below.

8÷2=□8 \div 2 = \square
□÷2=□\square \div 2 = \square
20÷2=□‾\overline{20 \div 2 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 8 div 2 plus another fact equals 20 div 2.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 8 div 2 = box, then box div 2 = box, summing to 20 div 2 = box.
  • All three facts use divisor 2.
Unknowns
  • The quotient of 8 div 2.
  • The middle dividend and its quotient.
  • The quotient of 20 div 2.
Constraints
  • All three facts use divisor 2.
  • The first two dividends must add to 20, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 20 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 8 by 2. Since 2 times 4 is 8, the quotient is 4.
8÷2=48 \div 2 = 4
Grade 3 division: 8 split into groups of 2 makes 4 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 8 plus the middle dividend equals 20. So the middle dividend is 20 minus 8 = 12.
20−8=1220 - 8 = 12
Grade 3 subtraction: since the dividends must add to 20, the missing one is 20 take away 8.
#5 Look for a Pattern 3.OA.A.2
Divide 12 by 2: 2 times 6 is 12, so 12 div 2 = 6.
12÷2=612 \div 2 = 6
Grade 3 division: 12 split into groups of 2 makes 6 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 20 by 2 to get 10. This matches the pattern because the top two quotients add: 4 plus 6 equals 10.
20÷2=10,4+6=1020 \div 2 = 10, \quad 4 + 6 = 10
Grade 3: the quotients add the same way the dividends do, confirming 10 is right.
Answer: 8 div 2 = 4; 12 div 2 = 6; 20 div 2 = 10

Review

Dividends: 8 + 12 = 20 (correct total). Quotients: 4 + 6 = 10, and 20 div 2 is indeed 10. Both sums line up with the example's rule.

Skip-count by 2 to fill the boxes: reach 8 in 4 steps, continue to 12 in 6 steps, and 20 in 10 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 8 and 12 by 2 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 20 minus 8.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 4, 12, 6, and 10!
Variant 7 answer: 10 div 5 = 2; 35 div 5 = 7; 45 div 5 = 9

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

10÷5=210 \div 5 = 2
15÷5=315 \div 5 = 3
25÷5=5‾\overline{25 \div 5 = 5}

Using the same method, find the number for each box below.

10÷5=□10 \div 5 = \square
□÷5=□\square \div 5 = \square
45÷5=□‾\overline{45 \div 5 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 10 div 5 plus another fact equals 45 div 5.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 10 div 5 = box, then box div 5 = box, summing to 45 div 5 = box.
  • All three facts use divisor 5.
Unknowns
  • The quotient of 10 div 5.
  • The middle dividend and its quotient.
  • The quotient of 45 div 5.
Constraints
  • All three facts use divisor 5.
  • The first two dividends must add to 45, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 45 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 10 by 5. Since 5 times 2 is 10, the quotient is 2.
10÷5=210 \div 5 = 2
Grade 3 division: 10 split into groups of 5 makes 2 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 10 plus the middle dividend equals 45. So the middle dividend is 45 minus 10 = 35.
45−10=3545 - 10 = 35
Grade 3 subtraction: since the dividends must add to 45, the missing one is 45 take away 10.
#5 Look for a Pattern 3.OA.A.2
Divide 35 by 5: 5 times 7 is 35, so 35 div 5 = 7.
35÷5=735 \div 5 = 7
Grade 3 division: 35 split into groups of 5 makes 7 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 45 by 5 to get 9. This matches the pattern because the top two quotients add: 2 plus 7 equals 9.
45÷5=9,2+7=945 \div 5 = 9, \quad 2 + 7 = 9
Grade 3: the quotients add the same way the dividends do, confirming 9 is right.
Answer: 10 div 5 = 2; 35 div 5 = 7; 45 div 5 = 9

Review

Dividends: 10 + 35 = 45 (correct total). Quotients: 2 + 7 = 9, and 45 div 5 is indeed 9. Both sums line up with the example's rule.

Skip-count by 5 to fill the boxes: reach 10 in 2 steps, continue to 35 in 7 steps, and 45 in 9 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 10 and 35 by 5 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 45 minus 10.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 2, 35, 7, and 9!
Variant 8 answer: 12 div 3 = 4; 15 div 3 = 5; 27 div 3 = 9

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

6÷3=26 \div 3 = 2
9÷3=39 \div 3 = 3
15÷3=5‾\overline{15 \div 3 = 5}

Using the same method, find the number for each box below.

12÷3=□12 \div 3 = \square
□÷3=□\square \div 3 = \square
27÷3=□‾\overline{27 \div 3 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 12 div 3 plus another fact equals 27 div 3.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 12 div 3 = box, then box div 3 = box, summing to 27 div 3 = box.
  • All three facts use divisor 3.
Unknowns
  • The quotient of 12 div 3.
  • The middle dividend and its quotient.
  • The quotient of 27 div 3.
Constraints
  • All three facts use divisor 3.
  • The first two dividends must add to 27, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 27 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 12 by 3. Since 3 times 4 is 12, the quotient is 4.
12÷3=412 \div 3 = 4
Grade 3 division: 12 split into groups of 3 makes 4 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 12 plus the middle dividend equals 27. So the middle dividend is 27 minus 12 = 15.
27−12=1527 - 12 = 15
Grade 3 subtraction: since the dividends must add to 27, the missing one is 27 take away 12.
#5 Look for a Pattern 3.OA.A.2
Divide 15 by 3: 3 times 5 is 15, so 15 div 3 = 5.
15÷3=515 \div 3 = 5
Grade 3 division: 15 split into groups of 3 makes 5 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 27 by 3 to get 9. This matches the pattern because the top two quotients add: 4 plus 5 equals 9.
27÷3=9,4+5=927 \div 3 = 9, \quad 4 + 5 = 9
Grade 3: the quotients add the same way the dividends do, confirming 9 is right.
Answer: 12 div 3 = 4; 15 div 3 = 5; 27 div 3 = 9

Review

Dividends: 12 + 15 = 27 (correct total). Quotients: 4 + 5 = 9, and 27 div 3 is indeed 9. Both sums line up with the example's rule.

Skip-count by 3 to fill the boxes: reach 12 in 4 steps, continue to 15 in 5 steps, and 27 in 9 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 12 and 15 by 3 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 27 minus 12.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 4, 15, 5, and 9!
Variant 9 answer: 9 div 3 = 3; 21 div 3 = 7; 30 div 3 = 10

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

6÷3=26 \div 3 = 2
9÷3=39 \div 3 = 3
15÷3=5‾\overline{15 \div 3 = 5}

Using the same method, find the number for each box below.

9÷3=□9 \div 3 = \square
□÷3=□\square \div 3 = \square
30÷3=□‾\overline{30 \div 3 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 9 div 3 plus another fact equals 30 div 3.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 9 div 3 = box, then box div 3 = box, summing to 30 div 3 = box.
  • All three facts use divisor 3.
Unknowns
  • The quotient of 9 div 3.
  • The middle dividend and its quotient.
  • The quotient of 30 div 3.
Constraints
  • All three facts use divisor 3.
  • The first two dividends must add to 30, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 30 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 9 by 3. Since 3 times 3 is 9, the quotient is 3.
9÷3=39 \div 3 = 3
Grade 3 division: 9 split into groups of 3 makes 3 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 9 plus the middle dividend equals 30. So the middle dividend is 30 minus 9 = 21.
30−9=2130 - 9 = 21
Grade 3 subtraction: since the dividends must add to 30, the missing one is 30 take away 9.
#5 Look for a Pattern 3.OA.A.2
Divide 21 by 3: 3 times 7 is 21, so 21 div 3 = 7.
21÷3=721 \div 3 = 7
Grade 3 division: 21 split into groups of 3 makes 7 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 30 by 3 to get 10. This matches the pattern because the top two quotients add: 3 plus 7 equals 10.
30÷3=10,3+7=1030 \div 3 = 10, \quad 3 + 7 = 10
Grade 3: the quotients add the same way the dividends do, confirming 10 is right.
Answer: 9 div 3 = 3; 21 div 3 = 7; 30 div 3 = 10

Review

Dividends: 9 + 21 = 30 (correct total). Quotients: 3 + 7 = 10, and 30 div 3 is indeed 10. Both sums line up with the example's rule.

Skip-count by 3 to fill the boxes: reach 9 in 3 steps, continue to 21 in 7 steps, and 30 in 10 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 9 and 21 by 3 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 30 minus 9.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 3, 21, 7, and 10!
Variant 10 answer: 16 div 8 = 2; 24 div 8 = 3; 40 div 8 = 5

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

16÷8=216 \div 8 = 2
24÷8=324 \div 8 = 3
40÷8=5‾\overline{40 \div 8 = 5}

Using the same method, find the number for each box below.

16÷8=□16 \div 8 = \square
□÷8=□\square \div 8 = \square
40÷8=□‾\overline{40 \div 8 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 16 div 8 plus another fact equals 40 div 8.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 16 div 8 = box, then box div 8 = box, summing to 40 div 8 = box.
  • All three facts use divisor 8.
Unknowns
  • The quotient of 16 div 8.
  • The middle dividend and its quotient.
  • The quotient of 40 div 8.
Constraints
  • All three facts use divisor 8.
  • The first two dividends must add to 40, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 40 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 16 by 8. Since 8 times 2 is 16, the quotient is 2.
16÷8=216 \div 8 = 2
Grade 3 division: 16 split into groups of 8 makes 2 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 16 plus the middle dividend equals 40. So the middle dividend is 40 minus 16 = 24.
40−16=2440 - 16 = 24
Grade 3 subtraction: since the dividends must add to 40, the missing one is 40 take away 16.
#5 Look for a Pattern 3.OA.A.2
Divide 24 by 8: 8 times 3 is 24, so 24 div 8 = 3.
24÷8=324 \div 8 = 3
Grade 3 division: 24 split into groups of 8 makes 3 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 40 by 8 to get 5. This matches the pattern because the top two quotients add: 2 plus 3 equals 5.
40÷8=5,2+3=540 \div 8 = 5, \quad 2 + 3 = 5
Grade 3: the quotients add the same way the dividends do, confirming 5 is right.
Answer: 16 div 8 = 2; 24 div 8 = 3; 40 div 8 = 5

Review

Dividends: 16 + 24 = 40 (correct total). Quotients: 2 + 3 = 5, and 40 div 8 is indeed 5. Both sums line up with the example's rule.

Skip-count by 8 to fill the boxes: reach 16 in 2 steps, continue to 24 in 3 steps, and 40 in 5 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 16 and 24 by 8 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 40 minus 16.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 2, 24, 3, and 5!
Variant 11 answer: 20 div 4 = 5; 16 div 4 = 4; 36 div 4 = 9

Do the division using the same method as in the example.

Example: When you add two division facts, the dividends add together and the quotients add together.

8÷4=28 \div 4 = 2
12÷4=312 \div 4 = 3
20÷4=5‾\overline{20 \div 4 = 5}

Using the same method, find the number for each box below.

20÷4=□20 \div 4 = \square
□÷4=□\square \div 4 = \square
36÷4=□‾\overline{36 \div 4 = \square}

Show solution

Understand

The example shows that when two division facts share the same divisor, the dividends add and the quotients add. Using that adding rule, fill the boxes so that 20 div 4 plus another fact equals 36 div 4.

Givens
  • The rule: with the same divisor, add the dividends and add the quotients.
  • The stack is 20 div 4 = box, then box div 4 = box, summing to 36 div 4 = box.
  • All three facts use divisor 4.
Unknowns
  • The quotient of 20 div 4.
  • The middle dividend and its quotient.
  • The quotient of 36 div 4.
Constraints
  • All three facts use divisor 4.
  • The first two dividends must add to 36, and the first two quotients must add to the bottom quotient.

Plan

#5 Look for a Pattern · also uses: #11 Work Backwards

The example reveals a pattern: dividends add and quotients add. We follow that pattern, and work backwards from the known total 36 to find the missing middle dividend.

Execute

#5 Look for a Pattern 3.OA.A.2
Divide 20 by 4. Since 4 times 5 is 20, the quotient is 5.
20÷4=520 \div 4 = 5
Grade 3 division: 20 split into groups of 4 makes 5 groups.
#11 Work Backwards 3.NBT.A.2
The pattern says the top two dividends add to the bottom dividend: 20 plus the middle dividend equals 36. So the middle dividend is 36 minus 20 = 16.
36−20=1636 - 20 = 16
Grade 3 subtraction: since the dividends must add to 36, the missing one is 36 take away 20.
#5 Look for a Pattern 3.OA.A.2
Divide 16 by 4: 4 times 4 is 16, so 16 div 4 = 4.
16÷4=416 \div 4 = 4
Grade 3 division: 16 split into groups of 4 makes 4 groups.
#5 Look for a Pattern 3.OA.A.3
Divide 36 by 4 to get 9. This matches the pattern because the top two quotients add: 5 plus 4 equals 9.
36÷4=9,5+4=936 \div 4 = 9, \quad 5 + 4 = 9
Grade 3: the quotients add the same way the dividends do, confirming 9 is right.
Answer: 20 div 4 = 5; 16 div 4 = 4; 36 div 4 = 9

Review

Dividends: 20 + 16 = 36 (correct total). Quotients: 5 + 4 = 9, and 36 div 4 is indeed 9. Both sums line up with the example's rule.

Skip-count by 4 to fill the boxes: reach 20 in 5 steps, continue to 16 in 4 steps, and 36 in 9 steps, giving the same quotients.

Standards · min grade 3

  • 3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing 20 and 16 by 4 to get the quotients.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Finding the missing middle dividend as 36 minus 20.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Confirming the quotients add to the bottom quotient.
💡 When the divisor stays the same, dividends add and quotients add, so the boxes are 5, 16, 4, and 9!