Multiplying by a Multiple of 10
4A · Chapter 4 · Lesson 4 · MATH-4A-C04-L05
Learning goal. Use base-ten scaling and area models for tens multipliers.
Before you begin
Recall: Grade 3: multidigit × one digit, arrays; 4A Ch3: multiples; Multiplying by a 1-Digit Number — Part 2. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 122 × 3.
Show answer & reasoning
122 × 3 = (120 × 3) + (2 × 3) = 366. Each partial product uses its correct place value.
Calculate 118 × 8.
Show answer & reasoning
118 × 8 = (110 × 8) + (8 × 8) = 944. Each partial product uses its correct place value.
Calculate 165 × 4.
Show answer & reasoning
165 × 4 = (160 × 4) + (5 × 4) = 660. Each partial product uses its correct place value.
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
A multiplier such as 40 means four tens. Thus 23 × 40 = (23 × 4) × 10 = 920. The zero is not a decorative digit; it records scaling by ten. On an area diagram, one dimension can be split into tens to make the magnitude visible.
Model it: rectangle scaled by four groups of ten. 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 364 × 40.
40 represents 4 tens. Multiply by 4, then scale by 10 to obtain 14,560.
Check your understanding 1
Calculate 196 × 30.
Show answer & reasoning
30 represents 3 tens. Multiply by 3, then scale by 10 to obtain 5,880.
Worked example 2
Calculate 196 × 70.
70 represents 7 tens. Multiply by 7, then scale by 10 to obtain 13,720.
Check your understanding 2
Calculate 396 × 90.
Show answer & reasoning
90 represents 9 tens. Multiply by 9, then scale by 10 to obtain 35,640.
Worked example 3
Calculate 352 × 80.
80 represents 8 tens. Multiply by 8, then scale by 10 to obtain 28,160.
Check your understanding 3
Calculate 381 × 70.
Show answer & reasoning
70 represents 7 tens. Multiply by 7, then scale by 10 to obtain 26,670.
Guided practice
Calculate 162 × 50.
Show answer & reasoning
50 represents 5 tens. Multiply by 5, then scale by 10 to obtain 8,100.
Calculate 304 × 50.
Show answer & reasoning
50 represents 5 tens. Multiply by 5, then scale by 10 to obtain 15,200.
Calculate 266 × 90.
Show answer & reasoning
90 represents 9 tens. Multiply by 9, then scale by 10 to obtain 23,940.
Calculate 46 × 90.
Show answer & reasoning
90 represents 9 tens. Multiply by 9, then scale by 10 to obtain 4,140.
Calculate 162 × 60.
Show answer & reasoning
60 represents 6 tens. Multiply by 6, then scale by 10 to obtain 9,720.
Independent practice
Calculate 259 × 30.
Show answer & reasoning
30 represents 3 tens. Multiply by 3, then scale by 10 to obtain 7,770.
Calculate 102 × 40.
Show answer & reasoning
40 represents 4 tens. Multiply by 4, then scale by 10 to obtain 4,080.
Calculate 405 × 30.
Show answer & reasoning
30 represents 3 tens. Multiply by 3, then scale by 10 to obtain 12,150.
Calculate 300 × 80.
Show answer & reasoning
80 represents 8 tens. Multiply by 8, then scale by 10 to obtain 24,000.
Calculate 140 × 20.
Show answer & reasoning
20 represents 2 tens. Multiply by 2, then scale by 10 to obtain 2,800.
Calculate 386 × 50.
Show answer & reasoning
50 represents 5 tens. Multiply by 5, then scale by 10 to obtain 19,300.
Calculate 264 × 90.
Show answer & reasoning
90 represents 9 tens. Multiply by 9, then scale by 10 to obtain 23,760.
Calculate 198 × 90.
Show answer & reasoning
90 represents 9 tens. Multiply by 9, then scale by 10 to obtain 17,820.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student calculates 56 × 70 as 392. Explain why this is ten times too small and correct it.
Show answer & reasoning
70 is 7 tens. Multiply 56 by 7 and then by 10, giving 3920.
Calculate 96 × 80.
Show answer & reasoning
80 represents 8 tens. Multiply by 8, then scale by 10 to obtain 7,680.
Exit check
Calculate 203 × 60.
Show answer & reasoning
60 represents 6 tens. Multiply by 6, then scale by 10 to obtain 12,180.
Calculate 293 × 60.
Show answer & reasoning
60 represents 6 tens. Multiply by 6, then scale by 10 to obtain 17,580.
Calculate 69 × 30.
Show answer & reasoning
30 represents 3 tens. Multiply by 3, then scale by 10 to obtain 2,070.