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D.7 Multiply whole numbers by 1-digit numbers

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What does it mean to multiply whole numbers?

Multiplication is a way to find the total when you have equal groups of the same size. It tells how many items there are in all.

Examples:
  • 3 groups of 4 apples = 3 × 4 = 12 apples
  • 5 boxes with 6 pencils each = 5 × 6 = 30 pencils
  • 7 rows of 8 chairs = 7 × 8 = 56 chairs
Note

Think of multiplication as repeated addition. For example, 4 × 3 means 4 + 4 + 4.

Multiplying whole numbers by 1-digit numbers

When you multiply a whole number by a 1-digit number, you are finding how many equal groups there are in total. Each digit of the larger number is multiplied by the 1-digit number, starting from the ones place.

Example:
  • Multiply 243 × 3
  • 3 × 3 = 9 (ones place)
  • 3 × 4 = 12 (write 2 in the tens place, carry 1)
  • 3 × 2 = 6, plus the 1 carried = 7
  • Answer: 243 × 3 = 729
Note

Always multiply from right to left, and remember to carry any extra value to the next place value column.

Understanding place value in multiplication

Place value helps you understand the value of each digit in a number. When you multiply, each digit’s value matters because it shows how many ones, tens, or hundreds you are multiplying.

Example:
  • 456 × 2
  • 6 × 2 = 12 (write 2, carry 1)
  • 5 × 2 = 10, plus 1 carried = 11 (write 1, carry 1)
  • 4 × 2 = 8, plus 1 carried = 9
  • Answer: 456 × 2 = 912
Note

Carrying over means moving extra value to the next place. This keeps the digits in the correct place value order.

Using estimation to check your work

Estimation helps you check if your answer makes sense. Round one or both numbers to the nearest ten or hundred before multiplying.

Example:
  • Estimate 247 × 4
  • Round 247 to 250
  • 250 × 4 = 1,000 (this is an estimate)
  • Exact answer: 247 × 4 = 988
Note

If your exact answer is close to your estimate, your multiplication is probably correct.

Word problems with multiplication

Multiplication helps solve real-world problems that involve equal groups, arrays, or repeated addition. Read carefully to understand what the question is asking.

Example:
  • There are 8 baskets with 6 oranges in each. How many oranges are there in total?
  • 8 × 6 = 48
  • Answer: There are 48 oranges in all.
Note

When solving word problems, look for clues like “each,” “every,” or “in all.” These words often mean multiplication is needed.