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O.2 Multiplication facts for 6, 7, 8, 9, 10, 11, and 12

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Understanding multiplication facts

Multiplication facts are the basic number sentences we memorize to solve multiplication problems quickly and accurately. Knowing these facts for numbers 6 through 12 is essential for more advanced math.

Examples:
  • 6 × 4 = 24
  • 8 × 7 = 56
  • 12 × 5 = 60
Note

Multiplication is a faster way to add the same number multiple times. For example, 7 × 3 means three groups of seven, or 7 + 7 + 7.

Key facts for 6, 7, and 8

These numbers are often called the "middle facts." They build directly on the easier facts you already know for 0 through 5.

Patterns and strategies:
  • Sixes: A fact with 6 is the same as adding five groups and then one more group. (6 × 4 = (5 × 4) + 4 = 20 + 4 = 24)
  • Sevens: Think of a fact with 7 as a "five fact" plus a "two fact." (7 × 8 = (5 × 8) + (2 × 8) = 40 + 16 = 56)
  • Eights: The facts for 8 are double the facts for 4. (8 × 3 is double 4 × 3, so 8 × 3 = 24)
Note

If you know 5 × 9 = 45, then 6 × 9 is just one more group of 9, so 45 + 9 = 54. Use facts you know to solve ones you are learning.

Mastering facts for 9, 10, and 11

These numbers have helpful patterns that make their facts easier to remember and use.

Helpful patterns:
  • Nines: The digits in the product always add up to 9. For 9 × 7 = 63, check: 6 + 3 = 9. Also, the tens digit is one less than the other factor (7 - 1 = 6).
  • Tens: To multiply by 10, simply add a zero to the other number. (10 × 8 = 80)
  • Elevens: For 11 × 1 through 11 × 9, the product repeats the digit. (11 × 4 = 44). For 11 × 10 and above, use place value: 11 × 12 = 132.
Note

The pattern for nines works every time. Hold up ten fingers. For 9 × 4, put down your fourth finger. You have 3 fingers up on the left and 6 on the right: 36!

Working with twelves

Twelves are an extension of the tens facts. Think of them as "ten groups plus two more groups."

Strategy for twelves:
  • Break the problem into two simpler facts you know: 12 × n = (10 × n) + (2 × n).
  • Example: 12 × 7 = (10 × 7) + (2 × 7) = 70 + 14 = 84.
  • This strategy works for all multiplication with 12.
Note

You have already mastered 10s and 2s. Use them as your tools to conquer the 12s facts confidently.

Using facts to solve problems

Memorized facts help you solve real-world problems quickly, check your work, and prepare for division.

Application in sentences:
  • If one box holds 8 markers, how many markers are in 6 boxes? (6 × 8 = 48 markers)
  • A classroom has 9 rows with 11 desks in each row. How many desks total? (9 × 11 = 99 desks)
  • A gardener plants 12 tulip bulbs in each of 7 rows. How many bulbs are planted? (12 × 7 = 84 bulbs)
Note

When you see a word problem, look for phrases like "in each," "per," or "times as many." These often signal that multiplication is the correct operation.