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 · 22 questions

Problems

The complete solutions are available here after each question and on the printable answer-key page.

A1
Which is greater: 500−203 or 500−197? By how much?
Show answer and reasoning
Answer: 500−197 by 6
A smaller subtrahend leaves a larger difference. Since 203−197=6, the second expression is six larger.
A2
Add 1,963 + 435. Show a place-value breakdown.
Show answer and reasoning
Answer: 2398
1,963 is 1,900 + 63; add the two parts to 435. The sum is 2,398.
A3
A class starts with 214 pencils, adds 86, then gives away 125. Find the amount left.
Show answer and reasoning
Answer: 175
214+86=300; 300−125=175.
A4
Why is 607−299 the same as 608−300?
Show answer and reasoning
Answer: Equal adjustment
Adding one to both terms leaves their difference 308 unchanged.
A5
A school library has 520 books. 100 are on the front shelf. How many are elsewhere?
Show answer and reasoning
Answer: 420
The 520 books are the whole, 100 is a part. Subtract: 520 − 100 = 420.
A6
Find 99 + 383 using compensation.
Show answer and reasoning
Answer: 482
Increase 99 by 1 to get a multiple of 100; then subtract that same adjustment from the total. Result: 482.
A7
Two collections contain 70 items altogether. One has 10 more than the other. How many are in EACH collection?
Show answer and reasoning
Answer: 30 and 40
Remove the extra 10; 70 − 10 = 60. Two equal parts are 30 each. Larger part is 30 + 10 = 40.
A8
Invent an addition problem with answer 1,000 using 398 as one addend. State the other.
Show answer and reasoning
Answer: 602
1,000−398=602; 398+602=1,000.
A9
Nina has 54 tokens and loses 19, then receives 31. Explain why the result is greater than 54.
Show answer and reasoning
Answer: 66
The gain of 31 exceeds the loss of 19 by 12, so final amount is 66.
A10
Jules has 48 more cards than Ari. Jules has 132 cards. How many does Ari have?
Show answer and reasoning
Answer: 84
Ari’s bar is 48 shorter: 132−48=84.
A11
A student changes 498+147 to 500+147 but reports 647. Explain the needed correction.
Show answer and reasoning
Answer: 645
Replacing 498 by 500 adds two, so subtract two: 647−2=645.
A12
Two boxes hold 94 crayons together. One holds 16 more than the other. Find both.
Show answer and reasoning
Answer: 39 and 55
94−16=78; half is 39; other box 39+16=55.
A13
Use equal adjustment to find 389 − 99.
Show answer and reasoning
Answer: 290
Add 1 to BOTH numbers: 390 − 100 = 290. Their difference is unchanged.
A14
Why can a sum be solved by adding tens before hundreds, without changing the answer?
Show answer and reasoning
Answer: The parts are unchanged
Regrouping/reordering the same place-value contributions does not alter the total.
A15
Find 2,554 − 331 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 2223
Decompose 331 into tens and ones, subtract each part from 2,554, and check the difference 2,223.
A16
Leo collected 235 stamps. Mina collected 20 more than Leo. How many does Mina have?
Show answer and reasoning
Answer: 255
Draw Leo’s bar of 235; add the extra segment 20. Mina’s total is 235+20=255.
A17
A gardener bought 195 seedlings on Monday and 208 on Tuesday. Without column arithmetic, give an exact total.
Show answer and reasoning
Answer: 403
200−5 + 200+8 = 400+3=403.
A18
Two jars hold 120 marbles together. The larger jar has 80. How many more are in the larger jar?
Show answer and reasoning
Answer: 40
Smaller jar is 120−80=40; difference 80−40=40.
A19
A shop begins with 250 pencils, receives 80, then sells 10. How many pencils remain?
Show answer and reasoning
Answer: 320
First 250+80=330; then take away 10. Result: 320.
A20
Calculate 1,113 − 98 by using a nearby hundred.
Show answer and reasoning
Answer: 1015
Rewrite 98 as the nearby multiple of 100 with a small correction. Apply the correction to 1,113 and check the exact answer 1,015.
A21
What must be added to 58 to make 100?
Show answer and reasoning
Answer: 42
The missing part is 100 − 58 = 42; check 58 + 42 = 100.
A22
At a school 256 students arrive; 79 leave, then 46 arrive. How many are present?
Show answer and reasoning
Answer: 223
256−79=177; 177+46=223.

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