6 — Multi-Digit Multiplication

Multi-Digit Multiplication

Solution & Explanation · ID: 83649341

Question

284 × 135

Hint

Three partial products needed—don't forget placeholder zeros for tens and hundreds digits

Concept

Multi-digit multiplication uses the standard algorithm where we multiply each digit of one number by each digit of the other number, keeping track of place values.

Show Answer

38,340

Show Solution
1

Set up the multiplication vertically with 284 on top and 135 below it.

2

Multiply 284 by 5 (the ones digit): 284 × 5 = 1,420. Write 1420 as the first partial product.

3

Multiply 284 by 3 (the tens digit): 284 × 3 = 852. Since this is in the tens place, it represents 284 × 30 = 8,520. Write 8520 as the second partial product.

4

Multiply 284 by 1 (the hundreds digit): 284 × 1 = 284. Since this is in the hundreds place, it represents 284 × 100 = 28,400. Write 28400 as the third partial product.

5

Add all partial products: 1,420 + 8,520 + 28,400 = 38,340.

Long multiplication of 284 × 135 shown vertically. Top number 284, bottom number ×135. First partial product 1420 (from 284×5). Second partial product 8520 (from 284×30). Third partial product 28400 (from 284×100). Final sum 38340 with all digits aligned by place value.