G.2 Multiplication facts to 12: fill in the missing numbers
What is multiplication?
Multiplication is a fast way to add the same number over and over again. When you multiply, you combine equal groups. The answer to a multiplication problem is called the product. The numbers being multiplied are called the factors.
- 4 + 4 + 4 = 12 is the same as 3 × 4 = 12
- 5 + 5 + 5 + 5 = 20 is the same as 4 × 5 = 20
- In 6 × 7 = 42, the factors are 6 and 7, and the product is 42.
The multiplication symbol (×) means "groups of." So 3 × 4 means "3 groups of 4."
The commutative property of multiplication
The commutative property tells us that you can multiply two factors in any order and the product will stay the same. The order of the factors does not change the answer.
- 5 × 3 = 15 and 3 × 5 = 15
- 7 × 4 = 28 and 4 × 7 = 28
- 9 × 6 = 54 and 6 × 9 = 54
This property means you only need to memorize half of the multiplication facts. If you know 8 × 3 = 24, you also know 3 × 8 = 24.
The identity property and zero property
The identity property of multiplication says that any number multiplied by 1 stays the same. The number 1 is called the multiplicative identity. The zero property of multiplication says that any number multiplied by 0 equals 0.
- 9 × 1 = 9 and 1 × 12 = 12 (identity property)
- 5 × 0 = 0 and 0 × 11 = 0 (zero property)
- 100 × 1 = 100 and 100 × 0 = 0
These are the easiest multiplication facts to remember. Any number multiplied by 1 is itself. Any number multiplied by 0 is always 0.
Multiplication facts for 0, 1, 2, and 5
Learning multiplication facts in groups makes them easier to remember. The facts for 0, 1, 2, and 5 are often the first ones to master because they have simple patterns.
- 0 times any number: 0×0=0, 0×1=0, 0×2=0, 0×3=0, 0×4=0, 0×5=0, 0×6=0, 0×7=0, 0×8=0, 0×9=0, 0×10=0, 0×11=0, 0×12=0
- 1 times any number: 1×0=0, 1×1=1, 1×2=2, 1×3=3, 1×4=4, 1×5=5, 1×6=6, 1×7=7, 1×8=8, 1×9=9, 1×10=10, 1×11=11, 1×12=12
- 2 times any number (doubles): 2×0=0, 2×1=2, 2×2=4, 2×3=6, 2×4=8, 2×5=10, 2×6=12, 2×7=14, 2×8=16, 2×9=18, 2×10=20, 2×11=22, 2×12=24
- 5 times any number (count by fives): 5×0=0, 5×1=5, 5×2=10, 5×3=15, 5×4=20, 5×5=25, 5×6=30, 5×7=35, 5×8=40, 5×9=45, 5×10=50, 5×11=55, 5×12=60
When multiplying by 2, think of "doubling" the number. When multiplying by 5, the products always end in 0 or 5.
Multiplication facts for 3 and 4
The multiplication facts for 3 and 4 build on the facts you already know. You can use counting patterns or skip-counting to help you remember them.
- 3 times any number (count by threes): 3×0=0, 3×1=3, 3×2=6, 3×3=9, 3×4=12, 3×5=15, 3×6=18, 3×7=21, 3×8=24, 3×9=27, 3×10=30, 3×11=33, 3×12=36
- 4 times any number (count by fours): 4×0=0, 4×1=4, 4×2=8, 4×3=12, 4×4=16, 4×5=20, 4×6=24, 4×7=28, 4×8=32, 4×9=36, 4×10=40, 4×11=44, 4×12=48
Notice that 3 × 4 = 12 and 4 × 3 = 12. You can also double a fact you know: 4 × 6 is the same as doubling 2 × 6 (12 + 12 = 24).
Multiplication facts for 6 and 7
The facts for 6 and 7 can be trickier, but you can use facts you already know to help you figure them out. For example, you can break apart one of the factors.
- 6 times any number: 6×0=0, 6×1=6, 6×2=12, 6×3=18, 6×4=24, 6×5=30, 6×6=36, 6×7=42, 6×8=48, 6×9=54, 6×10=60, 6×11=66, 6×12=72
- 7 times any number: 7×0=0, 7×1=7, 7×2=14, 7×3=21, 7×4=28, 7×5=35, 7×6=42, 7×7=49, 7×8=56, 7×9=63, 7×10=70, 7×11=77, 7×12=84
If you forget 6 × 8, think 5 × 8 = 40 and then add one more group of 8 (40 + 8 = 48). For 7 × 8, think 5 × 8 = 40 and 2 × 8 = 16, then add 40 + 16 = 56.
Multiplication facts for 8 and 9
The facts for 8 and 9 have helpful patterns. For 9, there is a famous finger trick, and the digits in the product always add up to 9 (until 9 × 10).
- 8 times any number: 8×0=0, 8×1=8, 8×2=16, 8×3=24, 8×4=32, 8×5=40, 8×6=48, 8×7=56, 8×8=64, 8×9=72, 8×10=80, 8×11=88, 8×12=96
- 9 times any number: 9×0=0, 9×1=9, 9×2=18, 9×3=27, 9×4=36, 9×5=45, 9×6=54, 9×7=63, 9×8=72, 9×9=81, 9×10=90, 9×11=99, 9×12=108
For 9 × 6, hold up both hands. Put down your sixth finger from the left. You have 5 fingers on the left and 4 on the right: 54. The digits 5 + 4 = 9.
Multiplication facts for 10, 11, and 12
Multiplying by 10, 11, and 12 follows simple patterns. By now, you have also seen many of these facts in other sections because of the commutative property.
- 10 times any number: 10×0=0, 10×1=10, 10×2=20, 10×3=30, 10×4=40, 10×5=50, 10×6=60, 10×7=70, 10×8=80, 10×9=90, 10×10=100, 10×11=110, 10×12=120
- 11 times any number (up to 9): 11×0=0, 11×1=11, 11×2=22, 11×3=33, 11×4=44, 11×5=55, 11×6=66, 11×7=77, 11×8=88, 11×9=99, 11×10=110, 11×11=121, 11×12=132
- 12 times any number: 12×0=0, 12×1=12, 12×2=24, 12×3=36, 12×4=48, 12×5=60, 12×6=72, 12×7=84, 12×8=96, 12×9=108, 12×10=120, 12×11=132, 12×12=144
To multiply by 10, just add a zero to the other factor. For 11 × 12, you can think 10 × 12 = 120 and then add one more 12 (120 + 12 = 132).
The distributive property
The distributive property says that you can break apart a factor into smaller parts, multiply each part separately, and then add the products together. This is a powerful strategy for figuring out facts you do not know yet.
- 7 × 6 = 7 × (3 + 3) = (7 × 3) + (7 × 3) = 21 + 21 = 42
- 8 × 9 = 8 × (5 + 4) = (8 × 5) + (8 × 4) = 40 + 32 = 72
- 6 × 12 = 6 × (10 + 2) = (6 × 10) + (6 × 2) = 60 + 12 = 72
This property works with subtraction too. For 9 × 7, think 10 × 7 = 70 and then subtract one group of 7 (70 − 7 = 63).
Using multiplication facts to solve word problems
Multiplication facts help you solve real-world problems. When you read a word problem, look for keywords that tell you to multiply, such as "in all," "total," "each," "per," or "every."
- Maria has 8 bags of apples. Each bag has 6 apples. How many apples does she have in all? 8 × 6 = 48 apples.
- A classroom has 9 rows of desks. Each row has 5 desks. What is the total number of desks? 9 × 5 = 45 desks.
- There are 7 days in one week. How many days are in 4 weeks? 7 × 4 = 28 days.
Always ask yourself: "Am I combining equal groups?" If yes, you probably need to multiply.
Strategies for memorizing multiplication facts
Memorizing all the facts up to 12 × 12 takes practice, but there are many strategies to make it easier. Use what works best for you.
- Skip-counting: Practice counting by 2s, 3s, 4s, and so on up to 12.
- Flashcards: Use cards with the fact on one side and the answer on the other. Practice a few minutes each day.
- Patterns: Look for patterns, like all multiples of 5 end in 0 or 5, or multiples of 9 have digits that add to 9.
- Rhymes and songs: There are many fun songs that help you remember facts like 6 × 8 = 48 or 7 × 7 = 49.
- Games: Play multiplication games online or with a partner to build speed.
Practice a little every day. In fourth grade, you should be able to recall any multiplication fact up to 12 in just a few seconds.
Multiplication fact families
A fact family in multiplication uses the same three numbers to create related multiplication and division facts. Understanding fact families helps you see the relationship between multiplication and division.
- For the numbers 3, 7, and 21: 3 × 7 = 21, 7 × 3 = 21, 21 ÷ 3 = 7, 21 ÷ 7 = 3
- For the numbers 6, 8, and 48: 6 × 8 = 48, 8 × 6 = 48, 48 ÷ 6 = 8, 48 ÷ 8 = 6
- For the numbers 9, 12, and 108: 9 × 12 = 108, 12 × 9 = 108, 108 ÷ 9 = 12, 108 ÷ 12 = 9
If you know a multiplication fact, you automatically know two division facts. This will help you in future math lessons.
Common Core alignment: CCSS.MATH.CONTENT.4.OA.A.1 – Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.OA.A.1 and supports fourth-grade mastery of multiplication facts up to 12 × 12 as a foundation for understanding multiplicative comparisons. All content is 100% free. Use it for whole-class instruction, independent study and practice, or homework. Encourage students to use the properties and strategies explained here to achieve automaticity with their facts, which is essential for success in fourth-grade math and beyond.