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Stage 16 of 20

Multiplication: 3, 4, and 6

Master the 3, 4, and 6 times tables through decomposition, double-double reasoning, ×5 anchors, skip-counting patterns, and carefully verified practice.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Recall products in the 3, 4, and 6 families through twelve
  • Build ×4 facts by doubling twice and ×6 facts by doubling ×3
  • Decompose unfamiliar products into established ×2, ×5, and ×10 facts
  • Explain and verify multiplication strategies using distributive reasoning

Understanding Multiplication: 3, 4, and 6

Stage 15 provided anchor facts rather than isolated answers. To multiply by 3, combine twice the number with one more copy: 8 × 3 = 8 × 2 + 8 = 16 + 8 = 24. This is the distributive property expressed in learner-friendly parts.

Multiplying by 4 means doubling twice. For 13 × 4, double 13 to make 26, then double 26 to make 52. The method works because multiplying by 2 and then by 2 has an overall scale factor of 4, and it reuses Stage 6 fluency.

A ×6 fact offers two useful constructions. Double the ×3 product—7 × 3 = 21, then 21 × 2 = 42—or use the Stage 15 anchor ×5 plus one more group—7 × 5 + 7 = 35 + 7 = 42. Choosing the easier intermediate number reduces mental load.

Skip-counting exposes regularity: multiples of 3 increase by 3, multiples of 4 by 4, and multiples of 6 by 6. It can help recover a neighboring fact, such as moving from 8 × 6 = 48 to 9 × 6 = 54, but decomposition is usually quicker for a distant fact.

Patterns are checks, not substitutes for meaning. Every multiple of 6 is even because it contains a factor of 2, and its products are also multiples of 3. If 7 × 6 were answered as 41, both checks would reject it. Division later reverses these same fact families.

Why This Skill Matters

The 3, 4, and 6 tables appear in arrays, perimeter, equal sharing, schedules, and measurements. Building them from known facts shows that multiplication is a connected system rather than a long list to memorize.

Decomposition also prepares multi-digit multiplication: 23 × 6 can become 20 × 6 + 3 × 6 using exactly the same distributive reasoning.

Worked Examples: Think It Through

Read the strategy, then prove you can use it: every example ends with a matching problem on new numbers that you answer and check right here. Answer it and press New numbers for as many fresh problems as you like.

Build times three

8 × 3

  1. 1 Use 3 as 2 + 1.
  2. 2 Calculate 8 × 2 = 16.
  3. 3 Add one more group of 8.

8 × 3 = 24

Your turn — try it on new numbers

4 × 4 = ?

Double twice

13 × 4

  1. 1 Double 13 to get 26.
  2. 2 Double 26 to get 52.
  3. 3 The two doublings multiply by four.

13 × 4 = 52

Your turn — try it on new numbers

10 × 4 = ?

Use times five plus one group

7 × 6

  1. 1 Calculate 7 × 5 = 35.
  2. 2 Add one additional group of 7.
  3. 3 Combine 35 + 7.

7 × 6 = 42

Your turn — try it on new numbers

4 × 3 = ?

Double a times-three fact

9 × 6

  1. 1 Find 9 × 3 = 27.
  2. 2 Double 27: 20 + 20 and 7 + 7.
  3. 3 Combine 40 + 14.

9 × 6 = 54

Your turn — try it on new numbers

7 × 6 = ?

Common Mistakes and How to Fix Them

Adding instead of scaling

Eight times three is three equal groups of eight, 24—not 8 + 3 = 11. Sketch three groups when the notation feels ambiguous.

Doubling only once for ×4

One doubling gives ×2. For 7 × 4, double 7 to 14 and double 14 again to reach 28.

Using ×5 plus one but forgetting the group size

For 9 × 6, add 9—not 1—to 9 × 5. Six groups contain one whole group more than five groups.

Multiplication: 3, 4, and 6 in Everyday Life

Four rows of 13 chairs hold 52 people. Double 13 for two rows, then double again for four rows; the array structure matches the double-double calculation.

At six bottles per crate, nine crates hold 54 bottles. Thinking five bottles per crate plus one more per crate gives 45 + 9, making the adjustment concrete.

Pro Tips

  • • For ×3, use ×2 plus one more group.
  • • For ×4, double the factor and double the result.
  • • For ×6, compare ×3 doubled with ×5 plus one group.
  • • Check every ×6 answer: it must be even and divisible by 3.

Practice Exercises

Work each problem mentally, then type the answer and check it. Nothing is marked correct until you enter a value that actually equals the result, and every problem keeps its mental-steps note in reach if you get stuck.

  1. 1. 8 × 3 = ?
  2. 2. 7 × 4 = ?
  3. 3. 11 × 6 = ?
  4. 4. 12 × 3 = ?
  5. 5. 9 × 4 = ?
  6. 6. 8 × 6 = ?
  7. 7. 11 × 4 = ?
  8. 8. 7 × 3 = ?
  9. 9. 12 × 6 = ?
  10. 10. 6 × 4 = ?
  11. 11. 10 × 3 = ?
  12. 12. 9 × 6 = ?
  13. 13. 13 × 4 = ?
  14. 14. 14 × 3 = ?
  15. 15. 7 × 6 = ?
  16. 16. 16 × 3 = ?
  17. 17. 15 × 4 = ?
  18. 18. 13 × 6 = ?

Drill Stage 16 with unlimited problems

Type your answer and press Enter. Every problem is generated on the spot and uses the 3, 4 and 6 multiplication tables. Get it wrong and the steps below show how that exact problem is solved mentally.

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Problem 1

12 × 4 = ?

Stage 16 Questions

Is ×6 always best solved as ×3 then double?

No. Use whichever intermediate fact is easier. For 12 × 6, ×5 plus one gives 60 + 12, while doubling 12 × 3 gives 36 × 2.

Why does double-double equal multiplication by four?

The first doubling makes two copies and the second doubles those two copies, producing four equal copies altogether.

How can I recover a forgotten ×3 fact?

Use a nearby fact and add or subtract one group of 3, or calculate ×2 plus one original factor. Then verify against the multiples-of-3 pattern.