Two-Digit by Single-Digit Multiplication

Lesson overview

What you will learn

Multiplying a two-digit number by a single digit is an application of the distributive property: 47 × 6 equals (40 × 6) plus (7 × 6). Splitting the two-digit number into tens and ones turns one hard multiplication into two easy ones plus an addition.

Working from the larger partial product first (40 × 6 = 240) gives you a meaningful running total before you add the smaller piece (42), landing at 282. This left-to-right partial-product approach mirrors the addition strategy from earlier stages.

The method scales to any two-digit factor regardless of whether ones or tens are larger. It also prepares you for multiplying by 11, 12, or other small multi-digit numbers by the same decomposition logic.

Because each partial product uses a single-digit multiplier, your times-table fluency directly determines your speed here. Weak table facts become bottlenecks at this stage.

Why it matters

Build the idea before the speed

The distributive method is reliable, scalable, and easier to check than memorizing isolated tricks.

In adult life

Where this skill shows up

Calculating weekly earnings at an hourly rate is a natural two-digit-by-single-digit problem: $47 per hour for 6 hours is 47 × 6, decomposed as 40 × 6 + 7 × 6 = $282.

Bulk pricing uses the same structure: if one case holds 83 items and you need 7 cases, compute 80 × 7 + 3 × 7 = 560 + 21 = 581 items total.

The method

Step by step

1. 1Split the two-digit number into tens and ones.
2. 2Multiply each part by the single digit.
3. 3Add the partial products.

Worked examples

See the structure

Avoid these traps

Common mistakes

• Multiplying only the tens digit and forgetting the ones digit entirely — computing 40 × 6 = 240 and stopping.
• Adding the partial products incorrectly, especially when the ones product exceeds 50 and creates a carry-like jump.
• Splitting at the wrong boundary — treating 29 as 2 + 9 instead of 20 + 9.
• Attempting to recall the full product from memory for unfamiliar combinations instead of decomposing.

Practice tips

• Always write or speak the split first: "forty and seven, times six."
• Compute the tens partial product, pause to register its size, then add the ones partial product.
• Estimate before decomposing: 47 × 6 should be near 50 × 6 = 300; if your answer is far from that, recheck.
• Drill the hardest single-digit multipliers (×7, ×8, ×9) as isolated facts to remove bottlenecks.

Check your understanding

1. Why does 83 × 7 equal (80 × 7) + (3 × 7) rather than (8 × 7) + (3 × 7)?
2. What estimate would confirm that 29 × 4 = 116 is reasonable?
3. How does this method prepare you for multiplying a two-digit number by 11?

Your turn

Interactive practice

Answer one problem at a time. Each problem has a fresh 60-second timer, immediate correction, and a final accuracy score. Aim for understanding first; speed comes after accuracy.