Multiplication combines equal groups. When multiplying a two-digit number by a one-digit number, the two-digit number is the multiplicand (the number being multiplied), and the one-digit number is the multiplier (the number of times we multiply).
In the problem 24 × 3:
Think of 24 × 3 as 3 groups of 24. You can also think of it as 24 added together 3 times (24 + 24 + 24).
The standard algorithm is a reliable step-by-step method for multiplication. We multiply the one-digit number by each place value in the two-digit number, starting with the ones place, and then combine the results.
Step 1: Multiply the ones. 6 ones × 4 = 24 ones. Write the 4 in the ones place and regroup the 2 tens.
Step 2: Multiply the tens. 3 tens × 4 = 12 tens. Add the regrouped 2 tens: 12 + 2 = 14 tens. Write this in the answer.
Always start multiplying from the rightmost digit (ones place). The small number you write above is called "regrouping" or "carrying."
It is important to practice all combinations, including problems where the two-digit number has a zero in the ones or tens place, and problems that require multiple regrouping steps.
Multiply 50 × 3. Since 5 tens × 3 = 15 tens, which is 150.
Multiply 57 × 4. Multiply the ones (7 × 4 = 28, regroup 2). Then multiply the tens (5 × 4 = 20), add the regrouped 2 to get 22.
When you see a zero, remember: any number times zero is zero. In 50 × 3, you are multiplying 5 tens by 3, not 0 by 3, in the first step.
A good mathematician checks their work. You can verify a multiplication problem by using the inverse operation, division, or by estimating to see if your answer is reasonable.
Method 1: Use Division
If 84 ÷ 3 equals 28, then the multiplication is correct.
Method 2: Use Estimation
Round 28 to 30. 30 × 3 = 90. Since 84 is close to 90, the answer of 84 is reasonable.
Estimating is a quick and powerful tool. It helps you catch major errors by asking, "Does this answer make sense?"