Multi-digit Multiplication

Welcome to the Multi-digit Multiplication page at STEM Scholars Hub. Here, we focus on helping learners master the skill of multiplying numbers with multiple digits. Our hands-on approach and personalized guidance make learning this essential math concept engaging and effective for students of all ages.

What is Multi-Digit Multiplication?

Multi-digit multiplication helps calculate the total when there are many groups with large numbers. For example, if you have 34 groups with 12 items each, you multiply 34 × 12 to find the total.

Key Terms to Know

1.     Multiplication: A quick way of adding the same number multiple times.

Example: 3×4=12

This means you add 3 four times:

3+3+3+3=12

2.     Multiplier and Multiplicand:

The multiplicand is the number being multiplied (the "input" being scaled).

The multiplier is the number by which the multiplicand is multiplied (the "repeated count"). Example:

In 3×4, 3 is the multiplicand (what you’re scaling), and 4 is the multiplier (how many times you scale it).

 

3.     Factors: The numbers involved in multiplication (both the multiplicand and the multiplier are factors).

Example: In 34×12, 34 and 12 are the factors.

 

4.     Product: The result of multiplying two numbers.

Example:

How to Multiply Multi-Digit Numbers

1.     Write the numbers vertically:

     34  

×    12  

    --------  

2.     Multiply the ones place. Multiply 2 by 34:

     34  

×     2  

  --------  

     68  

3.     Multiply the tens place. Multiply 1 (representing 10) by 34. Write the result one place to the left:

     34  

×    10  

--------  

    340  

4.     Add the results together:

     68  

+   340  

--------  

     408  

Key Takeaways

•        Partial products are the results from multiplying each digit separately.

•        Always align numbers properly by place value.

•        Add the partial products to get the final product.

References

•        National Council of Teachers of Mathematics. (n.d.). Principles and Standards for School Mathematics. Retrieved from www.nctm.org

•        U.S. Department of Education. (n.d.). Helping Your Child Learn Mathematics. Retrieved from www.ed.gov