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
Estimate 5,143 + 1,731 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 6,870
Round 5,143 to 5,140 and 1,731 to 1,730. Estimate 5,140 + 1,730 = 6,870; it need not equal the exact answer.
A2
Estimate 1,273 − 661 by rounding BOTH numbers to the nearest 10.
Show answer and reasoning
Answer: 610
Round 1,273 to 1,270 and 661 to 660. Estimate 1,270 − 660 = 610; it need not equal the exact answer.
A3
Calculate 3,040 − 587; explain how you cross the zero places.
Show answer and reasoning
Answer: 2453
Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 3,040 − 587 = 2,453.
A4
Add 2,198 and 1,317. Explain one exchange of ten units.
Show answer and reasoning
Answer: 3515
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,198 + 1,317 = 3,515.
A5
Why must 7+8 in a ones column produce a tens exchange?
Show answer and reasoning
Answer: 15 ones = 1 ten + 5 ones
Ten ones have the same value as one ten, leaving five ones.
A6
Round 5,749 and 2,151 to the nearest hundred and estimate their difference.
Show answer and reasoning
Answer: 3,500
5,749 rounds to 5,700; 2,151 rounds to 2,200; difference 5,700−2,200=3,500.
A7
Explain how 5,000−998 can be done without complicated written borrowing.
Show answer and reasoning
Answer: 4,002
Subtract 1,000 then add 2 back: 5,000−1,000+2=4,002.
A8
An exhibit recorded 5,587 visitors in the morning and 966 more in the afternoon. How many altogether?
Show answer and reasoning
Answer: 6553
Identify the whole and its parts, then compute 5,587 + 966 = 6,553. Estimate to hundreds to check size.
A9
Calculate 4,005 − 660; explain how you cross the zero places.
Show answer and reasoning
Answer: 3345
Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 4,005 − 660 = 3,345.
A10
Estimate 1,489+2,515 by rounding to hundreds, then find the exact sum.
Show answer and reasoning
Answer: Estimate 4,000; exact 4,004
1,489≈1,500 and 2,515≈2,500; exact sum 4,004.
A11
Add 2,368 and 1,447. Explain one exchange of ten units.
Show answer and reasoning
Answer: 3815
Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,368 + 1,447 = 3,815.
A12
Estimate 1,604 − 852 by rounding BOTH numbers to the nearest 100.
Show answer and reasoning
Answer: 700
Round 1,604 to 1,600 and 852 to 900. Estimate 1,600 − 900 = 700; it need not equal the exact answer.
A13
A museum had 5,364 tickets and sold 895. How many tickets remain?
Show answer and reasoning
Answer: 4469
Identify the whole and its parts, then compute 5,364 − 895 = 4,469. Estimate to hundreds to check size.
A14
A student subtracts 2,034−586 by doing larger digit minus smaller digit in each column. Why is that invalid?
Show answer and reasoning
Answer: It ignores place value and exchanges
A minuend column with too few units must exchange from a higher place; digit-by-digit absolute differences do not preserve the whole.
A15
A warehouse has 2,005 packages, then ships 968. It receives another 225. How many now?
Show answer and reasoning
Answer: 1,262
2,005−968=1,037; plus 225 gives 1,262.
A16
A school purchased 3,240 books and donated 1,475. How many remain? Check by addition.
Show answer and reasoning
Answer: 1,765
3,240−1,475=1,765; 1,765+1,475=3,240.
A17
The difference of two whole numbers is 603. The smaller is 798. What is the larger?
Show answer and reasoning
Answer: 1,401
798+603=1,401.
A18
Find an addition problem with two four-digit addends whose sum ends in 00. Give one example.
Show answer and reasoning
Answer: 1,250 + 1,750 = 3,000
50+50 creates 100 and the other digits combine to a whole hundred/thousand.
A19
Subtract 2,042 − 498; show any place-value exchange.
Show answer and reasoning
Answer: 1544
Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,544; add 498 to check.
A20
Estimate 5,474 + 222 by rounding BOTH numbers to the nearest 100.
Show answer and reasoning
Answer: 5,700
Round 5,474 to 5,500 and 222 to 200. Estimate 5,500 + 200 = 5,700; it need not equal the exact answer.
A21
Two methods give 702−496=206 and 702−496=214. Which is reasonable and why?
Show answer and reasoning
Answer: 206
702−500=202, plus 4 back =206; 214 differs from the correct compensation.
A22
Compute 4,002−185 and show every necessary exchange.
Show answer and reasoning
Answer: 3,817
Rename 4,002 as 3 thousands, 9 hundreds, 9 tens, 12 ones. Subtract 185 to get 3,817.
A23
Subtract 2,192 − 558; show any place-value exchange.
Show answer and reasoning
Answer: 1634
Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,634; add 558 to check.
A24
Museum A had 1,876 guests and Museum B had 945. About how many more visited A? Round both to hundreds.
Show answer and reasoning
Answer: About 1,000
1,876≈1,900 and 945≈900; difference ≈1,000.

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