I.1 Multiplication patterns with place value
What does it mean to multiply by a one-digit number?
Multiplying by a one-digit number means taking a number and adding it to itself repeatedly, based on the one-digit number. It is a quick way to add the same number many times.
- 4 × 3 means 4 + 4 + 4 = 12
- 7 × 5 means 7 + 7 + 7 + 7 + 7 = 35
Think of multiplication as repeated addition. The first number tells you what to add, and the second number tells you how many times to add it.
How do you identify multiplication by a one-digit number?
You can identify these problems because one of the numbers being multiplied is a single digit (0–9), and the other number may be one digit, two digits, or larger.
- 6 × 8 → both numbers are one-digit
- 23 × 4 → one number is two-digit, the other is one-digit
- 325 × 7 → a larger number multiplied by a one-digit number
Always check: is one number a single digit? If so, it is multiplication by a one-digit number.
Multiplication patterns with place value
When multiplying by a one-digit number, patterns with place value help you solve quickly. Each digit of the larger number is multiplied separately, starting with the ones place, then tens, hundreds, and so on.
- 23 × 4
- Break apart 23 → (20 + 3)
- (20 × 4) + (3 × 4) = 80 + 12 = 92
- 8 × 9 = 72
- 80 × 9 = 720
- 800 × 9 = 7,200
- 8,000 × 9 = 72,000
Complete the blanks to see the pattern:
8 × [] = 72
80 × [] = 720
800 × [] = 7,200
8,000 × [] = 72,000
The missing factors are 9, 90, 900, and 9,000. Notice how each time you add a zero to 8 (80, 800, 8,000), the factor also grows by a zero (9 → 90 → 900 → 9,000). This shows the multiplication pattern with place value.
Using multiplication in word problems
Word problems often use multiplication with a one-digit number. These problems connect multiplication to real-life situations.
- “There are 8 baskets, and each basket has 6 apples. How many apples are there in total?” → 8 × 6 = 48
- “A classroom has 24 students, and each student gets 3 pencils. How many pencils are needed?” → 24 × 3 = 72
Look for words like “each,” “groups of,” or “times” in problems. These usually mean multiplication is needed.