3A · Chapter 4 · 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 · 21 questions
Problems
The complete solutions are available here after each question and on the printable answer-key page.
- A1
There are 7 equal rows with 8 counters each. How many counters?
Show answer and reasoning
Answer: 56
There are 7 groups of 8; multiply 7×8=56. Turning the array does not change the total.
- A2
Thirty-six children must form teams of 4. After two teams leave, how many children remain?
Show answer and reasoning
Answer: 28
9 teams total; two contain 8 children, leaving 28.
- A3
Three times as many as 12 is different from 12 more than 3. Find both amounts.
Show answer and reasoning
Answer: 36 and 15
3×12=36 whereas 12+3=15; the relationships are distinct.
- A4
For 6×(10+4), a child computes 60+4. Identify and correct the error.
Show answer and reasoning
Answer: 84
Multiply both parts by 6: 6×10+6×4=60+24=84.
- A5
A store has 9 packs of 6 markers, then sells 14 markers. How many remain?
Show answer and reasoning
Answer: 40
First find total 9×6=54, then subtract 14 to get 40.
- A6
An array has area 6×9. Show a decomposition using 6×(10−1).
Show answer and reasoning
Answer: 54
6×10−6×1=60−6=54.
- A7
Sam has 26 beads. Nora has 2 times as many. How many beads does Nora have?
Show answer and reasoning
Answer: 52
Draw one unit 26 for Sam and 2 matching units for Nora: 26 × 2 = 52.
- A8
Why does 0÷5 equal 0, but 5÷0 is undefined?
Show answer and reasoning
Answer: Zero shares versus zero divisor
Zero items can be divided into 5 empty groups; division by 0 cannot satisfy inverse multiplication for nonzero 5.
- A9
Two groups contain 17 and 19 counters. Can they form 9 equal groups of 4?
Show answer and reasoning
Answer: Yes
17+19=36, and 36÷4=9 equal groups.
- A10
Is 119 + 35 odd or even? Explain using pairs.
Show answer and reasoning
Answer: even
119 is odd, 35 is odd; their sum 154 is even because 154 leaves 0 unpaired item.
- A11
Without multiplying, decide whether 8×7 is odd or even. Explain.
Show answer and reasoning
Answer: Even
Eight equal groups of seven can be paired by joining two groups at a time; 8 is even.
- A12
A child has 43 counters. How many groups of 6 can be made, with how many left over?
Show answer and reasoning
Answer: 7 groups, 1 left
6×7=42 and 43−42=1, which is smaller than 6.
- A13
Each of 8 shelves holds 22 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 176
The total is 8 equal groups of 22: 8 × 22 = 176.
- A14
A teacher buys 7 packs of 6 pencils, then distributes 30. How many remain?
Show answer and reasoning
Answer: 12
7×6=42; 42−30=12.
- A15
52 counters are shared equally among 4 children. How many does each receive?
Show answer and reasoning
Answer: 13
4 equal groups contain 52 counters: 52÷4=13; verify 13×4=52.
- A16
A library displays 45 books in 5 equal rows. It removes one complete row. How many remain?
Show answer and reasoning
Answer: 36
Each row has 45÷5=9; four rows remain, 4×9=36.
- A17
Calculate 32 × 2 by splitting 32 into tens and ones.
Show answer and reasoning
Answer: 64
(30+2)×2=(30×2)+(2×2)=64.
- A18
Calculate 27 × 1, and explain why.
Show answer and reasoning
Answer: 27
The meaning of equal groups gives 27. One group preserves a quantity; zero groups give zero; zero split among nonzero groups is zero.
- A19
241 oranges are packed into bags holding 8 each. How many FULL bags and how many oranges left?
Show answer and reasoning
Answer: 30 bags, 1 left
241=8×30+1; since 1<8, 30 bags are full and 1 oranges remain.
- A20
Five vans carry 7 students each and three more students travel by car. Total students?
Show answer and reasoning
Answer: 38
5×7+3=35+3=38.
- A21
A gardener has 58 plants and places 8 in each tray. How many trays are needed to contain them all?
Show answer and reasoning
Answer: 8 trays
Seven trays hold 56, leaving two plants for an eighth tray.