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Stage 15 of 20

Multiplication: 1, 2, 5, and 10

Learn the 1, 2, 5, and 10 multiplication facts using identity, doubling, halving, place value, equal-group models, and practical mental shortcuts.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Interpret multiplication as equal groups and connect it to repeated addition
  • Recall products involving 1, 2, 5, and 10 accurately
  • Use doubling for ×2 and half-of-×10 reasoning for ×5
  • Apply commutativity and estimation to derive and check facts

Why This Matters

These four families are anchors for harder multiplication. Stage 16 builds ×4 by doubling twice and ×6 from ×5 plus one group. Fluent anchors reduce memorization and let unknown facts be reconstructed.

Multiples of 5 and 10 also dominate money, time, measurement, packaging, and percentage calculations.

The Reasoning Behind Multiplication: 1, 2, 5, and 10

Multiplication describes equal groups. Seven groups of two contain 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14. Earlier addition stages supply the meaning; multiplication gives a compact notation, 7 × 2, and a faster structure for repeated equal additions.

Multiplying by 1 preserves a quantity because one group of eight still contains eight. This identity pattern is conceptually different from adding 1, which increases a number. Keeping those operations distinct prevents the false answer 9 for 8 × 1.

Multiplying by 2 is doubling, returning directly to Stage 6. To find 17 × 2, partition 17 into 10 + 7, double each part to get 20 + 14, then combine them as 34. Place-value addition from Stages 11–12 supports larger doubles.

Ten equal groups reveal place value: 34 × 10 is 340 because three tens and four ones each become ten times as valuable. For whole numbers, the digits shift one place left and zero occupies the empty ones place; “attach a zero” is only a consequence of that value shift.

Five is half of ten, so n × 5 is half of n × 10. For 24 × 5, calculate 240 ÷ 2 = 120. With an odd factor such as 13, 130 can still be halved to 65. This method connects doubling, halving, and complements instead of relying only on chanting a table.

Where You Will Use Multiplication: 1, 2, 5, and 10

Five tickets at $18 each cost half of ten tickets: ten would cost $180, so five cost $90. This scales more reliably than adding eighteen five times.

Two trays of 27 seedlings contain 54 seedlings, while ten trays contain 270. The group interpretation makes the units in each calculation explicit.

See the Strategy in Action

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.

Double by partitioning

17 × 2

  1. 1 Split 17 into 10 + 7.
  2. 2 Double the parts: 20 and 14.
  3. 3 Add the partial products.

17 × 2 = 34

Your turn — try it on new numbers

7 × 5 = ?

Use half of times ten

24 × 5

  1. 1 Calculate 24 × 10 = 240.
  2. 2 Because 5 is half of 10, halve 240.
  3. 3 Half of 240 is 120.

24 × 5 = 120

Your turn — try it on new numbers

4 × 5 = ?

Halve an odd multiple of ten

13 × 5

  1. 1 Find 13 × 10 = 130.
  2. 2 Split 130 into 100 + 30.
  3. 3 Halve the parts: 50 + 15.

13 × 5 = 65

Your turn — try it on new numbers

8 × 10 = ?

Read the group meaning

9 × 1

  1. 1 Interpret this as nine groups of one.
  2. 2 Each group contributes one item.
  3. 3 Nine ones total nine.

9 × 1 = 9

Your turn — try it on new numbers

12 × 10 = ?

Self-Check: Errors to Avoid

Confusing ×1 with +1

Six times one means one copy of each of six units, so it remains 6; six plus one would be 7.

Shifting digits without place-value meaning

For whole-number ×10, 34 becomes 340 because every digit moves to a place worth ten times more. Do not apply “add zero” blindly to decimals.

Halving the factor but forgetting ×10

For 18 × 5, half of 18 is 9, but the product is 90. Use half of 180, not half of 18 alone.

Pro Tips

  • • Translate each fact into “number of groups × size of each group.”
  • • For ×5, compute ×10 first and then halve.
  • • Use known doubles rather than skip-counting one step at a time.
  • • Reverse factors when it reveals a friendlier interpretation.

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. 14 × 2 = ?
  2. 2. 17 × 5 = ?
  3. 3. 23 × 10 = ?
  4. 4. 36 × 1 = ?
  5. 5. 19 × 2 = ?
  6. 6. 26 × 5 = ?
  7. 7. 42 × 10 = ?
  8. 8. 31 × 2 = ?
  9. 9. 15 × 5 = ?
  10. 10. 48 × 1 = ?
  11. 11. 27 × 2 = ?
  12. 12. 32 × 5 = ?
  13. 13. 18 × 10 = ?
  14. 14. 45 × 2 = ?
  15. 15. 21 × 5 = ?
  16. 16. 64 × 10 = ?
  17. 17. 29 × 2 = ?
  18. 18. 35 × 5 = ?

Drill Stage 15 with unlimited problems

Type your answer and press Enter. Every problem is generated on the spot and uses the 1, 2, 5 and 10 multiplication tables. Get it wrong and the steps below show how that exact problem is solved mentally.

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Problem 1

7 × 10 = ?

Stage 15 Questions

Does order matter in these multiplication facts?

No. Commutativity means 5 × 8 and 8 × 5 both equal 40, though the group stories describe differently arranged groups.

Why does the ×5 shortcut work for odd numbers?

Any whole number times 10 is even, so that product can be halved exactly. For 13 × 5, half of 130 is 65.

Should I memorize or derive the facts?

Use patterns to derive them accurately, then repeated retrieval will build recall. Understanding provides a recovery route when memory fails.