3A · Chapter 5 · Practice
Chapter practice examination
This original untimed public practice examination is not a secure school or placement test.
This original untimed public practice examination is not a secure school or placement test. No name, account, or answer is transmitted to any server.
Assessment · 24 questions
Problems
The complete solutions are available here after each question and on the printable answer-key page.
- A1
Explain why 26×4 = 20×4 + 6×4.
Show answer and reasoning
Answer: Distributive property
26 is 20+6. Four copies of the whole contain four copies of both parts.
- A2
Calculate 112 × 3 using partial products.
Show answer and reasoning
Answer: 336
Split 112 by place value; multiply each part by 3 and add. Total is 336.
- A3
Which product is larger: 59×2 or 31×4? By how much?
Show answer and reasoning
Answer: 31×4 by 6
59×2=118 and 31×4=124, difference 6.
- A4
An incorrect answer to 38×3 is 924: the student wrote 9 and 24 next to each other. Diagnose and correct.
Show answer and reasoning
Answer: 114
30×3=90, 8×3=24. Add 90+24=114; partial products must be added using place values.
- A5
Six shelves each hold 135 books. Twenty books are borrowed. How many remain?
Show answer and reasoning
Answer: 790
6×135=810; 810−20=790.
- A6
Find 74×3 using place value, and describe the exchanges.
Show answer and reasoning
Answer: 222
4×3=12 ones=1 ten+2 ones; 7 tens×3+1=22 tens=2 hundreds+2 tens.
- A7
Calculate 475 × 3 and show the exchanges.
Show answer and reasoning
Answer: 1425
475×3 = 1200 + 210 + 15 = 1425; combine partial products and exchange groups of ten.
- A8
Calculate 15 × 2 and show the exchanges.
Show answer and reasoning
Answer: 30
15×2 = 0 + 20 + 10 = 30; combine partial products and exchange groups of ten.
- A9
Find 2 × 200; explain the units of the product.
Show answer and reasoning
Answer: 400
200 is 2 groups of 100; 2×2=4 groups of 100 equals 400.
- A10
Find 207×3; why must you keep a zero place?
Show answer and reasoning
Answer: 621
200×3=600 and 7×3=21. Zero tens is a placeholder, product 621.
- A11
Why is 6×40 equal to 240, not 24?
Show answer and reasoning
Answer: Forty is four tens
6×4 tens =24 tens=240 ones.
- A12
Calculate 25 × 2 and show the exchanges.
Show answer and reasoning
Answer: 50
25×2 = 0 + 40 + 10 = 50; combine partial products and exchange groups of ten.
- A13
Calculate 236 × 2 and show the exchanges.
Show answer and reasoning
Answer: 472
236×2 = 400 + 60 + 12 = 472; combine partial products and exchange groups of ten.
- A14
Calculate 61 × 2 and show the exchanges.
Show answer and reasoning
Answer: 122
61×2 = 0 + 120 + 2 = 122; combine partial products and exchange groups of ten.
- A15
A child writes 68×3=184. Which carry was lost and what is correct?
Show answer and reasoning
Answer: 204
8×3=24 ones gives 2 extra tens; 6 tens×3+2 tens=20 tens. So product is 204.
- A16
Three buses hold 184 passengers each. If all are full, what is their combined capacity?
Show answer and reasoning
Answer: 552
184×3=552.
- A17
Calculate 65 × 3 and show the exchanges.
Show answer and reasoning
Answer: 195
65×3 = 0 + 180 + 15 = 195; combine partial products and exchange groups of ten.
- A18
Calculate 51 × 2 and show the exchanges.
Show answer and reasoning
Answer: 102
51×2 = 0 + 100 + 2 = 102; combine partial products and exchange groups of ten.
- A19
Calculate 55 × 3 and show the exchanges.
Show answer and reasoning
Answer: 165
55×3 = 0 + 150 + 15 = 165; combine partial products and exchange groups of ten.
- A20
Calculate 112 × 2 using partial products.
Show answer and reasoning
Answer: 224
Split 112 by place value; multiply each part by 2 and add. Total is 224.
- A21
Calculate 375 × 3 and show the exchanges.
Show answer and reasoning
Answer: 1125
375×3 = 900 + 210 + 15 = 1125; combine partial products and exchange groups of ten.
- A22
Calculate 136 × 2 and show the exchanges.
Show answer and reasoning
Answer: 272
136×2 = 200 + 60 + 12 = 272; combine partial products and exchange groups of ten.
- A23
Find 3 × 50; explain the units of the product.
Show answer and reasoning
Answer: 150
50 is 5 groups of 10; 3×5=15 groups of 10 equals 150.
- A24
A market stocks 4 cases of 126 oranges. How many oranges is that?
Show answer and reasoning
Answer: 504
4×(100+20+6)=400+80+24=504.