Partial Products
Solve: 23 × 4 using partial products.
23 × 4 = (20 × 4) + (3 × 4) = 80 + 12 = 92
Find 5 × 10.
5 × 10 = 50
Each box has 10 pencils. How many pencils in 3 boxes?
10 × 3 = 30 pencils
Show an area model for 12 × 3.
12 × 3 = (10 × 3) + (2 × 3) = 30 + 6 = 36
Estimate: 49 × 2 ≈ ?
49 × 2 ≈ 50 × 2 = 100
Show the partial products for 327 × 6.
327 × 6 = (300 × 6) + (20 × 6) + (7 × 6) = 1,800 + 120 + 42 = 1,962
Use mental math: 25 × 4.
25 × 4 = (25 × 2) × 2 = 50 × 2 = 100
Mrs. Wallingford sells 5 boxes of 60 cards. How many cards?
5 × 60 = 300 cards
Use an area model: 24 × 5.
24 × 5 = (20 × 5) + (4 × 5) = 100 + 20 = 120
Estimate: 198 × 5 ≈ ?
198 × 5 ≈ 200 × 5 = 1,000
What are the partial products for 2,361 × 4?
2,361 × 4 = (2,000 × 4) + (300 × 4) + (60 × 4) + (1 × 4) = 8,000 + 1,200 + 240 + 4 = 9,444
Solve 195 × 3 using mental math.
195 × 3 = (200 × 3) – (5 × 3) = 600 – 15 = 585
A deli sells 267 turkey sandwiches each month. How many in 4 months?
267 × 4 = 1,068 sandwiches
Draw an area model: 224 × 4.
224 × 4 = (200 × 4) + (20 × 4) + (4 × 4) = 800 + 80 + 16 = 896
Mr. Brouard buys 3 laptops at $387 each. About how much total?
3 × 387 ≈ 3 × 400 = 1,200
Solve 532 × 7 using partial products.
532 × 7 = (500 × 7) + (30 × 7) + (2 × 7) = 3,500 + 210 + 14 = 3,724
Use mental math: 5 × 790.
5 × 790 = (5 × 800) – (5 × 10) = 4,000 – 50 = 3,950
Rudy’s Pizza makes 317 pizzas a day. How many in 3 days?
317 × 3 = 951 items (only pizzas, if subs included: 317 + 54 = 371; 371 × 3 = 1,113)
Use an area model: 256 × 4.
256 × 4 = (200 × 4) + (50 × 4) + (6 × 4) = 800 + 200 + 24 = 1,024
Estimate: 3 × 1,149 TVs + 3 × 487 TVs ≈ ?
(3 × 1,149) + (3 × 487) ≈ (3 × 1,150) + (3 × 500) = 3,450 + 1,500 = 4,950
Multiply 145 × 12 using partial products.
145 × 12 = (145 × 10) + (145 × 2) = 1,450 + 290 = 1,740
Use mental math to solve 99 × 5. Show your steps.
99 × 5 = (100 × 5) – (1 × 5) = 500 – 5 = 495
A store sells 3 TVs at $1,149 each and 3 at $487 each. What’s the total?
128 × 25 = (128 × 100) ÷ 4 = 12,800 ÷ 4 = 3,200 toys
Use an area model to solve 312 × 6.
312 × 6 = (300 × 6) + (10 × 6) + (2 × 6) = 1,800 + 60 + 12 = 1,872
Estimate 486 × 29. Explain your reasoning.
486 × 29 ≈ 500 × 30 = 15,000