Multi-Digit Multiplication

4.C.11 × multi-digit01/04

Multiply 1-digit by up to 4-digit numbers.

Step01of 04

Standard algorithm. Stack with the bigger number on top, single digit underneath. Multiply the single digit by EACH digit of the top number, going right to left, carrying when needed.

4.C.1 — Multiply 1-digit by up to 4-digit numbers.

Step 01 of 04

Standard algorithm. Stack with the bigger number on top, single digit underneath. Multiply the single digit by EACH digit of the top number, going right to left, carrying when needed.

Step 02 of 04

Worked example. 423 × 6.

Ones: 6 × 3 = 18. Write 8, carry 1. Tens: 6 × 2 = 12, plus carried 1 = 13. Write 3, carry 1. Hundreds: 6 × 4 = 24, plus carried 1 = 25. Write 25.

423 \times 6 = 2, 538

Step 03 of 04

Bigger numbers — same method. 5,247 × 8.

Ones: 8 × 7 = 56 → write 6, carry 5. Tens: 8 × 4 = 32, +5 = 37 → write 7, carry 3. Hundreds: 8 × 2 = 16, +3 = 19 → write 9, carry 1. Thousands: 8 × 5 = 40, +1 = 41 → write 41.

5, 247 \times 8 = 41, 976

Step 04 of 04

Mental shortcut for round numbers. Multiply the non-zero part, then append the zeros.

6 \times 4, 000 = 24, 000

9 \times 700 = 6, 300

Key insight

Stack, multiply right-to-left, carry when product exceeds 9 in a column. Memorize times tables (1×1 through 12×12) — it makes everything else faster.

4.C.2 — Multiply two 2-digit numbers.

Step 01 of 04

The standard algorithm has TWO partial products. Multiply the top number by the BOTTOM ONES digit, then by the BOTTOM TENS digit (with a placeholder zero). Add both partial products together.

Step 02 of 04

Worked example. 47 × 23.

Step 1 — multiply by the 3 (bottom ones).

47 \times 3 = 141

Step 2 — multiply by the 20 (bottom tens). Write a 0 in the ones position as placeholder.

47 \times 2 = 94 \to write 940

Step 03 of 04

Step 3 — add the partial products.

47 \times 23 141 + 940 1, 081

47 \times 23 = 1, 081

Step 04 of 04

Why the placeholder zero? Multiplying by the tens digit really multiplies by 20 (or 30, etc.), not by 2. The placeholder zero shows that the product belongs in the tens-and-up positions.

Estimate first. 47 × 23 ≈ 50 × 20 = 1,000. Our answer of 1,081 is close — sanity-check passed.

Key insight

Two partial products: ones-row first, tens-row with placeholder zero. Add them together. Always estimate first to catch big mistakes.

4.C.3 — Multiplicative comparisons.

Step 01 of 04

Multiplicative comparison says how many TIMES bigger one number is than another (rather than how much MORE).

Additive comparison	→"How much MORE?" → SUBTRACT
Multiplicative comparison	→"How many TIMES MORE?" → DIVIDE

Step 02 of 04

Worked example. Sara has 32 stickers, Jay has 8 stickers.

How many MORE does Sara have?	→32 − 8 = 24 more (additive)
How many TIMES as many?	→32 ÷ 8 = 4 times (multiplicative)

Step 03 of 04

Phrase recognition.

"3 times as many"	→multiply by 3
"5 more than"	→add 5
"twice as much"	→multiply by 2
"half of"	→divide by 2

Step 04 of 04

Word problem. Mike has 7 marbles. Lily has 4 times as many. How many does Lily have?

7 \times 4 = 28 marbles

"4 times as many" means MULTIPLY by 4. NOT add 4.

Key insight

"How many MORE" → subtract. "How many TIMES" → multiply or divide. Phrases like "twice," "triple," "half" all signal multiplicative comparison.

4.C.4 — Multiplication word problems — compare and equal groups.

Step 01 of 04

Equal-groups problem — multiplication is the natural choice when you have a number of EQUAL groups and want the total.

"Each crate holds 24 apples. How many apples in 7 crates?" → $24 \times 7 = 168$ .

Step 02 of 04

Comparison problem — multiplicative form.

"A pencil costs $2. A pen costs 3 times as much. How much does the pen cost?" → $$2 \times 3 = $6$ .

Step 03 of 04

Two-step multiplication problems.

"12 boxes hold 8 apples each. The apples sell for $3 each. Total revenue?" Multiply twice (or compute apples first, then revenue).

12 \times 8 = 96 apples

96 \times $3 = $288

Step 04 of 04

Mixed operations. Some problems combine multiplication with addition or subtraction.

"A bus holds 47 students. 6 buses are full, plus an extra group of 25 students walks. How many students total?"

6 \times 47 = 282; 282 + 25 = 307 students

Key insight

Equal groups → multiply. "Times as many" → multiply. Multi-step problems chain operations: solve one piece at a time. Always reread to check what the question is actually asking for.

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