Multiplying by nine follows a clear pattern in the digits of the product. This pattern can help you learn and check your facts.
The digits in the product always add up to 9. Also, the tens digit is one less than the number you are multiplying by 9.
Use your fingers as a tool: Hold up all ten fingers. For 4 × 9, put down your fourth finger (from the left). You'll see 3 fingers up (tens digit) and 6 fingers up after it (ones digit): 36.
Start by building confidence with the smaller facts. These are the building blocks for the larger numbers.
Think of 9 × 5 as "ten groups of 5 minus one group of 5." (10 × 5 = 50, then 50 - 5 = 45). This strategy is called using a helper fact.
You can use facts you already know to solve new ones. If you know 9 × 5 = 45, you can find 9 × 6 by adding one more group of 9.
Repeated addition (9 + 9 + 9...) is a reliable way to check your answer. Multiplication is a faster way to add equal groups.
Multiplying nine by 10, 11, and 12 also follows rules. Knowing these completes your set of facts up to twelve.
For 9 × 12, the "break apart" strategy is very effective. Break 12 into 10 and 2, multiply each part by 9, and then add the products together.
Multiplication helps solve real-world problems involving equal groups or arrays. Identifying these situations is a key skill.
A teacher has 4 boxes of pencils. Each box holds 9 pencils. How many pencils are there in total?
Equation: 4 × 9 = 36
Solution: There are 36 pencils.
Look for phrases like "each has," "in each box," or "per row" to signal equal groups. The number of groups is one factor, and the number in each group is the other factor.