Multiplying by a 1-Digit Number — Part 1
4A · Chapter 4 · Lesson 2 · MATH-4A-C04-L02
Learning goal. Explain multi-place one-digit multiplication using partial products before regrouping.
Before you begin
Recall: Grade 3: multidigit × one digit, arrays; 4A Ch3: multiples; Mental Math for Multiplication. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 26 × 7 using a split or friendly number.
Show answer & reasoning
Split 26 into 20 + 6. Then multiply each part by 7 and add the partial products.
Calculate 25 × 7 using a split or friendly number.
Show answer & reasoning
Split 25 into 20 + 5. Then multiply each part by 7 and add the partial products.
Calculate 87 × 2 using a split or friendly number.
Show answer & reasoning
Split 87 into 80 + 7. Then multiply each part by 2 and add the partial products.
Key vocabulary
- partial product
- product of one part of each decomposed factor
- distributive property
- multiplication distributed across a sum
- area model
- rectangular representation of a product
- regroup
- exchange ten small units for one larger unit
Understand the concept
Multiplying a two- or three-digit number by one digit means multiplying each place-value part. For 213 × 4, calculate 200×4, 10×4 and 3×4, then combine 800+40+12. A written algorithm compresses the same reasoning, but the place values remain the foundation.
Model it: partial-products area partition. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Calculate 78 × 2.
78 × 2 = (70 × 2) + (8 × 2) = 156. Each partial product uses its correct place value.
Check your understanding 1
Calculate 85 × 4.
Show answer & reasoning
85 × 4 = (80 × 4) + (5 × 4) = 340. Each partial product uses its correct place value.
Worked example 2
Calculate 41 × 6.
41 × 6 = (40 × 6) + (1 × 6) = 246. Each partial product uses its correct place value.
Check your understanding 2
Calculate 76 × 4.
Show answer & reasoning
76 × 4 = (70 × 4) + (6 × 4) = 304. Each partial product uses its correct place value.
Worked example 3
Calculate 66 × 9.
66 × 9 = (60 × 9) + (6 × 9) = 594. Each partial product uses its correct place value.
Check your understanding 3
Calculate 34 × 3.
Show answer & reasoning
34 × 3 = (30 × 3) + (4 × 3) = 102. Each partial product uses its correct place value.
Guided practice
Calculate 27 × 7.
Show answer & reasoning
27 × 7 = (20 × 7) + (7 × 7) = 189. Each partial product uses its correct place value.
Calculate 84 × 2.
Show answer & reasoning
84 × 2 = (80 × 2) + (4 × 2) = 168. Each partial product uses its correct place value.
Calculate 95 × 9.
Show answer & reasoning
95 × 9 = (90 × 9) + (5 × 9) = 855. Each partial product uses its correct place value.
Calculate 92 × 6.
Show answer & reasoning
92 × 6 = (90 × 6) + (2 × 6) = 552. Each partial product uses its correct place value.
Calculate 42 × 9.
Show answer & reasoning
42 × 9 = (40 × 9) + (2 × 9) = 378. Each partial product uses its correct place value.
Independent practice
Calculate 98 × 9.
Show answer & reasoning
98 × 9 = (90 × 9) + (8 × 9) = 882. Each partial product uses its correct place value.
Calculate 48 × 3.
Show answer & reasoning
48 × 3 = (40 × 3) + (8 × 3) = 144. Each partial product uses its correct place value.
Calculate 86 × 6.
Show answer & reasoning
86 × 6 = (80 × 6) + (6 × 6) = 516. Each partial product uses its correct place value.
Calculate 88 × 8.
Show answer & reasoning
88 × 8 = (80 × 8) + (8 × 8) = 704. Each partial product uses its correct place value.
Calculate 20 × 4.
Show answer & reasoning
20 × 4 = (20 × 4) + (0 × 4) = 80. Each partial product uses its correct place value.
Calculate 63 × 2.
Show answer & reasoning
63 × 2 = (60 × 2) + (3 × 2) = 126. Each partial product uses its correct place value.
Calculate 41 × 7.
Show answer & reasoning
41 × 7 = (40 × 7) + (1 × 7) = 287. Each partial product uses its correct place value.
Calculate 32 × 5.
Show answer & reasoning
32 × 5 = (30 × 5) + (2 × 5) = 160. Each partial product uses its correct place value.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student calculates 44 × 6 using only its tens: 40 × 6. What partial product is missing and what is the correct total?
Show answer & reasoning
The ones part 4 × 6 = 24 must also be included. The complete product is 264.
Calculate 59 × 6.
Show answer & reasoning
59 × 6 = (50 × 6) + (9 × 6) = 354. Each partial product uses its correct place value.
Exit check
Calculate 80 × 8.
Show answer & reasoning
80 × 8 = (80 × 8) + (0 × 8) = 640. Each partial product uses its correct place value.
Calculate 69 × 4.
Show answer & reasoning
69 × 4 = (60 × 4) + (9 × 4) = 276. Each partial product uses its correct place value.
Calculate 90 × 2.
Show answer & reasoning
90 × 2 = (90 × 2) + (0 × 2) = 180. Each partial product uses its correct place value.