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
A student claims 864÷4=26. Is the quotient reasonable? Find it.
Show answer and reasoning
Answer: 216
Since 4×200=800, quotient is above 200. Exact 864÷4=216.
A2
Why does 360÷3 equal 120 rather than 12?
Show answer and reasoning
Answer: 120
360 is 36 tens. Divide 36 tens by 3 = 12 tens = 120.
A3
Why can 168÷4 have a two-digit quotient?
Show answer and reasoning
Answer: Because 168 < 4×100
Four hundreds would require at least 400. The quotient must be smaller than 100; 168÷4=42.
A4
Calculate 390 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 195
Group 390 into 2 equal parts using place-value exchanges. Each group has 195. Verify 195×2=390.
A5
Calculate 74 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 37
Group 74 into 2 equal parts using place-value exchanges. Each group has 37. Verify 37×2=74.
A6
Compute 408÷2 with a place-value explanation.
Show answer and reasoning
Answer: 204
4 hundreds÷2=2 hundreds; 0 tens÷2=0 tens; 8 ones÷2=4 ones.
A7
Calculate 464 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 232
Group 464 into 2 equal parts using place-value exchanges. Each group has 232. Verify 232×2=464.
A8
Divide 504 by 3 and explain both place-value exchanges.
Show answer and reasoning
Answer: 168
Share 5 hundreds among three groups: 1 hundred each, 2 hundreds remain. Exchange 2 hundreds for 20 tens, share 6 tens per group with 2 tens left, then exchange the remaining 2 tens for 20 ones. Add 4 more ones and share 24 ones as 8 each. Each share is 1 hundred + 6 tens + 8 ones = 168.
A9
Seventy-four markers are split equally into 2 classrooms. Explain the exchange.
Show answer and reasoning
Answer: 37
Seven tens: give three to each class, exchange the remaining one ten for ten ones, making 14 ones; give seven ones each.
A10
A student gets 306÷3=12 after omitting the tens zero. Explain the correct quotient.
Show answer and reasoning
Answer: 102
3 hundreds÷3=1 hundred; 0 tens÷3=0 tens; 6 ones÷3=2 ones. Answer 102.
A11
Calculate 200 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 40
Group 200 into 5 equal parts using place-value exchanges. Each group has 40. Verify 40×5=200.
A12
There are 282 cards divided among three tables. The first table gets the same as the others. How many per table?
Show answer and reasoning
Answer: 94
282÷3=94, checked 94×3=282.
A13
Calculate 48 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 24
Group 48 into 2 equal parts using place-value exchanges. Each group has 24. Verify 24×2=48.
A14
Calculate 270 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 54
Group 270 into 5 equal parts using place-value exchanges. Each group has 54. Verify 54×5=270.
A15
Calculate 3,600 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 900
Group 3,600 into 4 equal parts using place-value exchanges. Each group has 900. Verify 900×4=3,600.
A16
A factory packs 624 bolts equally into 4 crates. How many bolts per crate?
Show answer and reasoning
Answer: 156
624÷4=156; 156×4=624.
A17
Calculate 52 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 13
Group 52 into 4 equal parts using place-value exchanges. Each group has 13. Verify 13×4=52.
A18
Calculate 500 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 125
Group 500 into 4 equal parts using place-value exchanges. Each group has 125. Verify 125×4=500.
A19
Calculate 28 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 14
Group 28 into 2 equal parts using place-value exchanges. Each group has 14. Verify 14×2=28.
A20
Calculate 85 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 17
Group 85 into 5 equal parts using place-value exchanges. Each group has 17. Verify 17×5=85.
A21
Calculate 180 ÷ 4. Explain how you check your quotient.
Show answer and reasoning
Answer: 45
Group 180 into 4 equal parts using place-value exchanges. Each group has 45. Verify 45×4=180.
A22
Calculate 94 ÷ 2. Explain how you check your quotient.
Show answer and reasoning
Answer: 47
Group 94 into 2 equal parts using place-value exchanges. Each group has 47. Verify 47×2=94.
A23
Calculate 680 ÷ 5. Explain how you check your quotient.
Show answer and reasoning
Answer: 136
Group 680 into 5 equal parts using place-value exchanges. Each group has 136. Verify 136×5=680.
A24
A coach has 95 shirts and packs them in sets of 5. How many sets?
Show answer and reasoning
Answer: 19
95÷5=19; 19×5=95.

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