Question

1. which property shows that $3 \times 5 = 5 \times 3$?

a. identity property \qquad \qquad \quad c. order property
b. zero property \qquad \qquad \quad \\ \\ d. grouping property

1. what property is shown in $(2 \times 3) \times 4 = 2 \times (3 \times 4)$?

a. distributive \qquad \qquad \quad \\ \\ c. identity
b. zero \qquad \qquad \qquad \quad \\ \\ \\ d. grouping

1. what property is shown in $7 \times 1 = 7$?

a. zero property \qquad \qquad \quad c. distributive property
b. identity property \qquad \qquad d. grouping property

1. what is the answer when any number is multiplied by 0?

a. product \qquad b. 1 \qquad c. 0 \qquad d. 10

1. $6 \times 0 = 0$ shows which property?

a. identity property \qquad \qquad c. distributive property
b. zero property \qquad \qquad \\ \\ d. grouping property

1. which makes it easier to solve $4 \times 9$ by changing the order?

a. zero property \qquad \qquad \quad c. distributive property
b. identity property \qquad \qquad d. grouping property

1. which multiplication sentence shows the identity property?

a. $5 \times 0 = 0$ \qquad \qquad \quad c. $2 \times 3 = 3 \times 2$
b. $6 \times 1 = 6$ \qquad \qquad \\ \\ d. $(1 \times 4) \times 5$

1. which is true?

a. $8 \times 0 = 8$ \qquad \qquad \quad c. $3 \times 4 = 12$
b. $9 \times 1 = 1$ \qquad \qquad \\ \\ d. $5 \times 1 = 0$

1. which property helps group numbers to make multiplication easier?

a. zero \qquad \qquad \qquad \quad \\ \\ c. distributive
b. identity \qquad \qquad \qquad \\ \\ d. grouping property

1. why do we use multiplication properties?

a. to make numbers bigger \qquad c. to subtract faster
b. to make solving easier and faster \\ \\ d. to divide numbers

Explanation:

1. Swapping factors doesn’t change the product (Order Property).
2. Changing grouping of factors doesn’t change the product (Grouping Property).
3. Multiplying by 1 leaves the number unchanged (Identity Property).
4. Any number times 0 equals 0 (Zero Property result).
5. Multiplying by 0 gives 0 (Zero Property).
6. Distributive Property allows rewriting \(4×9\) as \(4×(10-1)\) for easier calculation.
7. Multiplying by 1 preserves the number (Identity Property).
8. \(3×4=12\) is a correct multiplication fact.
9. Grouping Property rearranges factor groups for easier multiplication.
10. Multiplication properties simplify and speed up calculations.

Answer:

1. c. Order Property
2. d. Grouping
3. b. Identity Property
4. c. 0
5. b. Zero Property
6. c. Distributive Property
7. b. 6 × 1 = 6
8. c. 3 × 4 = 12
9. d. Grouping Property
10. b. To make solving easier and faster