Pencil and Paper
Pencil and paper multiplication (standard algorithm) is a Grade 4 skill in Saxon Math Intermediate 4 (Chapter 5). Write the larger number on top, smaller below, aligned right. Multiply the bottom digit by each top digit right to left. For 31 x 4: ones 4x1=4, tens 4x3(tens)=12(tens), giving 124. For 52 x 3: ones 3x2=6, tens 3x5(tens)=15(tens), giving 156. This systematic approach handles any multiplication with proper place value alignment.
Key Concepts
Property To multiply with pencil and paper, write the larger number on top and the smaller number below it, aligned to the right. First, multiply the bottom number by the ones digit of the top number. Then, multiply the bottom number by the tens digit of the top number. Combine the results to get the final product.
Example To multiply $31 \times 4$: First, multiply $4 \times 1 = 4$. Then, multiply $4 \times 3(\text{tens}) = 12(\text{tens})$. Combine them to get 124. Calculate $52 \times 3$: Start with the ones, $3 \times 2 = 6$. Then the tens, $3 \times 5(\text{tens}) = 15(\text{tens})$. The product is 156. For $63 \times 2$: Multiply the ones, $2 \times 3 = 6$. Then the tens, $2 \times 6(\text{tens}) = 12(\text{tens})$. Your final answer is 126.
Explanation This is the classic way to multiply, like a trusty recipe for success! Stack the numbers neatly, then multiply from right to left—first the ones, then the tens. This step by step method keeps your calculations organized and ensures you nail the correct answer every single time, especially when numbers get bigger and trickier.
Common Questions
How do you set up pencil-and-paper multiplication?
Write the larger number on top and the smaller below it, aligned to the right. Multiply the bottom digit by each digit of the top number from right to left, placing results correctly by place value.
How do you multiply 31 x 4?
Ones: 4 x 1 = 4. Tens: 4 x 3 = 12 (in the tens place). Combine: 124.
How do you multiply 52 x 3?
Ones: 3 x 2 = 6. Tens: 3 x 5 = 15 (in the tens place). Combine: 156.
How do you multiply 63 x 2?
Ones: 2 x 3 = 6. Tens: 2 x 6 = 12 (in the tens place). Combine: 126.
What is the key to keeping pencil-and-paper multiplication organized?
Align digits by place value — ones under ones, tens under tens. Multiply right to left so you handle ones before tens before hundreds. Neat column alignment prevents place value errors.