Questions on Properties of Multiplication in Decimal Operations
Multiple choice questions on the Properties of Multiplication in Decimal Operations suitable for Grade 6, each with five answer choices (A–E). These problems are based on realistic scenarios and test understanding of commutative, associative, distributive, and identity properties of multiplication with decimals.
Properties of Multiplication in Decimal Operations – Questions
1. Which of the following demonstrates the commutative property of multiplication?
A) 0.4×(2×5)=(0.4×2)×50.4 \times (2 \times 5) = (0.4 \times 2) \times 50.4×(2×5)=(0.4×2)×5
B) 1×7.2=7.21 \times 7.2 = 7.21×7.2=7.2
C) 3.5×2=2×3.53.5 \times 2 = 2 \times 3.53.5×2=2×3.5
D) 4×0=04 \times 0 = 04×0=0
E) 0.75×4=30.75 \times 4 = 30.75×4=3
2. A worker is calculating (2.5×4)×3(2.5 \times 4) \times 3(2.5×4)×3. Using the associative property, which expression is equivalent?
A) 2.5×(4×3)2.5 \times (4 \times 3)2.5×(4×3)
B) (2.5×3)×4(2.5 \times 3) \times 4(2.5×3)×4
C) 2.5×4×32.5 \times 4 \times 32.5×4×3
D) All of the above
E) None of the above
3. Which of these examples shows the distributive property of multiplication over addition?
A) 5.1×0=05.1 \times 0 = 05.1×0=0
B) (3+2)×0.5=3×0.5+2×0.5(3 + 2) \times 0.5 = 3 \times 0.5 + 2 \times 0.5(3+2)×0.5=3×0.5+2×0.5
C) 1×7.8=7.81 \times 7.8 = 7.81×7.8=7.8
D) 4.2×5=5×4.24.2 \times 5 = 5 \times 4.24.2×5=5×4.2
E) 2.3×(4×1)=2.3×42.3 \times (4 \times 1) = 2.3 \times 42.3×(4×1)=2.3×4
4. Which of the following expressions uses the identity property?
A) 0.6×00.6 \times 00.6×0
B) 1×9.51 \times 9.51×9.5
C) 9.5×0.69.5 \times 0.69.5×0.6
D) 1×01 \times 01×0
E) 2.5×2.52.5 \times 2.52.5×2.5
5. A student writes:
4.8×(3+1)=4.8×3+4.8×14.8 \times (3 + 1) = 4.8 \times 3 + 4.8 \times 14.8×(3+1)=4.8×3+4.8×1
Which property is used?
A) Commutative
B) Associative
C) Identity
D) Distributive
E) Zero property
6. What is the result of using the zero property in 5.3×05.3 \times 05.3×0?
A) 5.3
B) 0
C) 1
D) 0.53
E) 53
7. Which equation demonstrates that order doesn't affect the product in decimal multiplication?
A) (0.2×3)×4=0.2×(3×4)(0.2 \times 3) \times 4 = 0.2 \times (3 \times 4)(0.2×3)×4=0.2×(3×4)
B) 7.1×1=7.17.1 \times 1 = 7.17.1×1=7.1
C) 2.6×5=5×2.62.6 \times 5 = 5 \times 2.62.6×5=5×2.6
D) 9.4×0=09.4 \times 0 = 09.4×0=0
E) 2.4×2.4=5.762.4 \times 2.4 = 5.762.4×2.4=5.76
8. Maya earns $1.5 per bracelet. She sells 6 to Peter and 4 to Anna. Using distributive property, how can we find total earnings?
A) 1.5×101.5 \times 101.5×10
B) 1.5×6+1.5×41.5 \times 6 + 1.5 \times 41.5×6+1.5×4
C) (6+4)×1.5(6 + 4) \times 1.5(6+4)×1.5
D) All of the above
E) Only A and B
9. Which of the following does NOT illustrate a property of multiplication?
A) 0.75×1=0.750.75 \times 1 = 0.750.75×1=0.75
B) 1×0.75=0.751 \times 0.75 = 0.751×0.75=0.75
C) (0.3+0.2)×4=0.3×4+0.2×4(0.3 + 0.2) \times 4 = 0.3 \times 4 + 0.2 \times 4(0.3+0.2)×4=0.3×4+0.2×4
D) 4×0.3+0.2×4=2.04 \times 0.3 + 0.2 \times 4 = 2.04×0.3+0.2×4=2.0
E) 2.5×(3×1)=7.52.5 \times (3 \times 1) = 7.52.5×(3×1)=7.5
10. Complete the identity:
9.6×___=9.69.6 \times \_\_\_ = 9.69.6×___=9.6
A) 0
B) 0.96
C) 1
D) 9.6
E) 10
11. Which of these uses the associative property with decimals?
A) (1.2×3)×2=1.2×(3×2)(1.2 \times 3) \times 2 = 1.2 \times (3 \times 2)(1.2×3)×2=1.2×(3×2)
B) 1.2×0=01.2 \times 0 = 01.2×0=0
C) 1.2×3=3×1.21.2 \times 3 = 3 \times 1.21.2×3=3×1.2
D) 1.2×1=1.21.2 \times 1 = 1.21.2×1=1.2
E) (1.2+3)×2=1.2×2+3×2(1.2 + 3) \times 2 = 1.2 \times 2 + 3 \times 2(1.2+3)×2=1.2×2+3×2
12. If a=0.9a = 0.9a=0.9, b=5b = 5b=5, and c=2c = 2c=2, use the associative property to rearrange (a×b)×c(a \times b) \times c(a×b)×c.
A) a×(b×c)a \times (b \times c)a×(b×c)
B) c×a×bc \times a \times bc×a×b
C) a+b+ca + b + ca+b+c
D) b×(a+c)b \times (a + c)b×(a+c)
E) (b×c)+a(b \times c) + a(b×c)+a
13. Why does 4.2×1=4.24.2 \times 1 = 4.24.2×1=4.2?
A) Identity property
B) Zero property
C) Distributive property
D) Commutative property
E) Associative property
14. Which equation shows that multiplying by zero always gives zero?
A) 0×9.1=00 \times 9.1 = 00×9.1=0
B) 9.1×0=09.1 \times 0 = 09.1×0=0
C) Both A and B
D) 1×9.1=9.11 \times 9.1 = 9.11×9.1=9.1
E) 9.1×9.1=82.819.1 \times 9.1 = 82.819.1×9.1=82.81
15. Choose the equation that illustrates the distributive property:
A) 6×(2.5+1.5)=6×2.5+6×1.56 \times (2.5 + 1.5) = 6 \times 2.5 + 6 \times 1.56×(2.5+1.5)=6×2.5+6×1.5
B) 1×4.8=4.81 \times 4.8 = 4.81×4.8=4.8
C) 5×0=05 \times 0 = 05×0=0
D) 4.8×1=4.84.8 \times 1 = 4.84.8×1=4.8
E) 2.4×5=5×2.42.4 \times 5 = 5 \times 2.42.4×5=5×2.4
16. What property justifies this equality:
2.4×3.1=3.1×2.42.4 \times 3.1 = 3.1 \times 2.42.4×3.1=3.1×2.4?
A) Identity
B) Distributive
C) Commutative
D) Associative
E) Zero
17. A baker calculates the total flour for cakes:
1.2×(3+2)1.2 \times (3 + 2)1.2×(3+2). What’s another way to write it using distributive property?
A) 1.2×3+1.2×21.2 \times 3 + 1.2 \times 21.2×3+1.2×2
B) 3+2×1.23 + 2 \times 1.23+2×1.2
C) (1.2+3)×2(1.2 + 3) \times 2(1.2+3)×2
D) 1.2×51.2 \times 51.2×5
E) Both A and D
18. A student solves 0.6×7×20.6 \times 7 \times 20.6×7×2. How can associative property help?
A) Multiply 0.6 and 7 first
B) Multiply 7 and 2 first
C) It doesn't matter
D) Group differently
E) All of the above
19. If (a×b)×c=a×(b×c)(a \times b) \times c = a \times (b \times c)(a×b)×c=a×(b×c), what property is being shown?
A) Commutative
B) Associative
C) Distributive
D) Identity
E) Zero
20. Using distributive property, what is another way to write 0.4×(6+9)0.4 \times (6 + 9)0.4×(6+9)?
A) 0.4×6+0.4×90.4 \times 6 + 0.4 \times 90.4×6+0.4×9
B) 0.4+6+90.4 + 6 + 90.4+6+9
C) 0.4×150.4 \times 150.4×15
D) A and C
E) B and C
- Questions on Decimal Subtraction
- Questions on Stem-and-Leaf Plots
- Questions on Multiplication of Decimals and Whole Numbers
Answer Key with Explanations
1. C – Order is reversed but product is the same (Commutative).
2. D – All express the associative property (grouping changes, order stays).
3. B – Shows multiplication distributed over addition.
4. B – Identity property: multiplying by 1 gives the same number.
5. D – Shows distributive property over addition.
6. B – Anything times 0 equals 0 (Zero property).
7. C – Order of factors doesn't affect the result (Commutative).
8. D – All options represent distributive property.
9. D – While correct numerically, not a demonstration of a property.
10. C – Identity number in multiplication is 1.
11. A – Change in grouping, not order, is associative.
12. A – Associative property allows regrouping: a×(b×c)a \times (b \times c)a×(b×c).
13. A – Multiplying by 1 does not change the number.
14. C – Both demonstrate zero property.
15. A – Demonstrates the distributive property.
16. C – Order of numbers changes (Commutative).
17. E – Both A and D are correct.
18. E – Associative property lets us group any way.
19. B – Changing grouping: Associative property.
20. D – Both A (distributed form) and C (simplified form) are correct.
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