ArithMind Mental Arithmetic Lessons
Stage 4 · Phase 1: Foundations beginner children

Simple Mental Division

Learn to divide mentally by numbers 1 through 10 using inverse multiplication.

Turning Times Tables Around

Simple mental division is finding equal groups without written calculation. In 24 ÷ 6 = 4, 24 is the total, 6 is the size of each group, and 4 is the number of groups. The same expression can also describe sharing 24 objects equally among 6 people, giving 4 each.

This stage follows multiplication tables because division reverses multiplication. The known fact 6 × 4 = 24 gives both 24 ÷ 6 = 4 and 24 ÷ 4 = 6. Instead of treating division as a completely new collection of facts, you can turn familiar table facts around.

When Division Solves a Real Problem

Suppose 36 strawberries must be placed equally into 6 bowls for a picnic. 36 ÷ 6 = 6 tells you to put 6 strawberries in each bowl. You can distribute them one at a time, but a multiplication fact reaches the result before the fruit needs to be moved. Division also helps with equal team sizes, portions, unit prices, and deciding how many full packs can be made.

Route One: Find the Missing Factor

The inverse multiplication method changes a division into a missing-factor question. For 56 ÷ 8, ask 8 × ? = 56. Since 8 × 7 = 56, the quotient is 7. If recall is not immediate, list multiples of 8 until you reach 56: 8, 16, 24, 32, 40, 48, 56. Seven equal jumps were needed.

This method also gives a clean check. Multiply the quotient by the divisor; the product should return to the dividend. For an exact division question, 7 × 8 = 56 confirms the result.

Route Two: Split into Friendly Chunks

When the answer extends beyond the most familiar table facts, use quotient chunking. Split the dividend into parts that are both divisible by the divisor. For 72 ÷ 6, choose 60 and 12:

60 ÷ 6 = 10 and 12 ÷ 6 = 2, so 72 ÷ 6 = 10 + 2 = 12.

The chunks total 72, and each was divided by the same number. Other valid splits are possible. For 84 ÷ 7, 70 + 14 is convenient, producing 10 + 2 = 12. Choose chunks you trust rather than copying a split that feels awkward.

Four Complete Walkthroughs

For 56 ÷ 8, turn the question around to 8 × ? = 56; the missing factor is 7.

For 45 ÷ 9, count five multiples of 9 to reach 45. Therefore, five groups fit exactly.

For 72 ÷ 6, divide 60 and 12 separately to get 10 and 2, then combine them for 12.

For 84 ÷ 7, use 70 ÷ 7 = 10 and 14 ÷ 7 = 2. Together, the quotient is 12.

Errors That Give Useful Clues

It is easy to reverse the divisor and quotient. In 35 ÷ 5, ask whether you need groups of 5 or five groups; either interpretation still leads to 7, but naming the roles keeps harder questions clear. Do not divide only one chunk: after splitting 72 into 60 and 12, both pieces must be divided by 6.

Another warning sign is an answer larger than the dividend when dividing a positive whole number by 2 or more. For example, 40 ÷ 5 cannot be 200; that is the product 40 × 5. Use multiplication to check and calmly revise.

Practice: Equal Groups

These questions divide exactly. Suggested breakdowns appear beside four.

  1. 24 ÷ 6
  2. 35 ÷ 5
  3. 63 ÷ 9
  4. 48 ÷ 8
  5. 54 ÷ 6
  6. 42 ÷ 7
  7. 81 ÷ 9
  8. 32 ÷ 4
  9. 66 ÷ 6 → (60 ÷ 6) + (6 ÷ 6)
  10. 96 ÷ 8 → (80 ÷ 8) + (16 ÷ 8)
  11. 75 ÷ 5
  12. 36 ÷ 3
  13. 91 ÷ 7 → (70 ÷ 7) + (21 ÷ 7)
  14. 64 ÷ 8
  15. 90 ÷ 10
  16. 44 ÷ 4
  17. 108 ÷ 9 → (90 ÷ 9) + (18 ÷ 9)
  18. 56 ÷ 7

Answer key: 1) 4, 2) 7, 3) 7, 4) 6, 5) 9, 6) 6, 7) 9, 8) 8, 9) 11, 10) 12, 11) 15, 12) 12, 13) 13, 14) 8, 15) 9, 16) 11, 17) 12, 18) 8.

Practice Without Pressure

Make fact-family triangles using three numbers, such as 7, 8, and 56, then say the two multiplication and two division facts. Use counters when “equal groups” feels abstract, and stop before practice becomes tiring. At this stage, focus on exact quotients; remainders can come later. Explaining why a split works is as valuable as answering quickly.

Division FAQs

Why can I not divide by zero?

There is no whole number of zero-sized groups that reconstructs a nonzero total. Division by zero is therefore undefined.

Must I use the chunks shown here?

No. For 96 ÷ 8, both 80 + 16 and 48 + 48 work because every chosen chunk divides by 8.

What if a number does not divide exactly?

It may have a remainder, but this stage uses exact divisions first. You can identify the greatest whole multiple below the dividend and note what remains when you reach that later topic.

Practice Examples

Example 1: 56 ÷ 8 = ?

  1. Rewrite the question as 8 × ? = 56
  2. Recall or build the fact 8 × 7 = 56
  3. The missing factor is 7, so 56 ÷ 8 = 7
  4. Check by multiplying the answer: 7 × 8 = 56

Answer: 7

Example 2: 45 ÷ 9 = ?

  1. Ask how many equal groups of 9 make 45
  2. Count multiples if needed: 9, 18, 27, 36, 45
  3. Five multiples reach 45, so the quotient is 5
  4. Confirm with 5 × 9 = 45

Answer: 5

Example 3: 72 ÷ 6 = ?

  1. Split 72 into 60 + 12; both parts divide exactly by 6
  2. Calculate 60 ÷ 6 = 10
  3. Calculate 12 ÷ 6 = 2
  4. Combine the quotients: 10 + 2 = 12

Answer: 12

Example 4: 84 ÷ 7 = ?

  1. Break 84 into 70 + 14
  2. Find 70 ÷ 7 = 10
  3. Find 14 ÷ 7 = 2
  4. Add the two equal-group counts: 10 + 2 = 12

Answer: 12