4th Grade Common Core Math Worksheets - Free Printable

Here are the solutions to the problems on the worksheet, broken down step-by-step.

1. Name the property shown by each model.

* Left Model: The equation shows $4 \times 6$ being split into $(4 \times 5) + (4 \times 1)$. This breaks a number apart to make multiplication easier.
* Solution: Distributive Property
* Right Model: The equation shows $(3 \times 2) \times 5 = 3 \times (2 \times 5)$. The grouping symbols (parentheses) moved, but the order of numbers stayed the same.
* Solution: Associative Property

2. Name the property used in the following equations.

* a. $0 \times 50 = 0$: Anything multiplied by zero is zero.
* Solution: Zero Property of Multiplication
* b. $8 \times 16 = 8 \times 10 + 8 \times 6$: The 16 was broken into $10 + 6$ and distributed to the 8.
* Solution: Distributive Property
* c. $12 \times 5 = 5 \times 12$: The numbers switched places.
* Solution: Commutative Property
* d. $(3 \times 7) \times 6 = 3 \times (7 \times 6)$: The parentheses moved to group different numbers.
* Solution: Associative Property

3. Use the distributive property to find the product.
*(Break the larger number into tens and ones)*

* a. $6 \times 16$
* Think: $6 \times (10 + 6)$
* $(6 \times 10) + (6 \times 6) = 60 + 36 = 96$
* Solution: 96
* b. $5 \times 13$
* Think: $5 \times (10 + 3)$
* $(5 \times 10) + (5 \times 3) = 50 + 15 = 65$
* Solution: 65
* c. $8 \times 12$
* Think: $8 \times (10 + 2)$
* $(8 \times 10) + (8 \times 2) = 80 + 16 = 96$
* Solution: 96
* d. $2 \times 75$
* Think: $2 \times (70 + 5)$
* $(2 \times 70) + (2 \times 5) = 140 + 10 = 150$
* Solution: 150

4. Show two ways to group by using the associative property.
*(You can move the parentheses to the first two numbers or the last two numbers)*

* a. $1 \times 9 \times 5$
* Solution: $(1 \times 9) \times 5$ OR $1 \times (9 \times 5)$
* b. $7 \times 4 \times 4$
* Solution: $(7 \times 4) \times 4$ OR $7 \times (4 \times 4)$
* c. $5 \times 8 \times 2$
* Solution: $(5 \times 8) \times 2$ OR $5 \times (8 \times 2)$
* d. $3 \times 3 \times 6$
* Solution: $(3 \times 3) \times 6$ OR $3 \times (3 \times 6)$

5. Write a word problem that can be solved by using the following numbers: $(3 \times 5) \times 2$

* Solution: Sarah buys 3 packs of markers. Each pack has 5 markers. She buys 2 sets of these packs for her art class. How many markers does she have in total?

6. Which is the missing number?
Equation: $4 \times 25 = (4 \times \_\_\_\_\_) + (4 \times 5)$

* We know that $25$ is the number being broken apart.
* The second part shows $(4 \times 5)$, which means 5 is one part of the 25.
* To get from 25 to 5, we subtract: $25 - 5 = 20$.
* So, the missing part must be 20.
* Check: Does $4 \times 20 + 4 \times 5$ equal $4 \times 25$?
* $80 + 20 = 100$.
* $4 \times 25 = 100$.
* It matches.

* Solution: D. 20

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Final Answer:
1. Distributive Property; Associative Property
2. a. Zero Property; b. Distributive Property; c. Commutative Property; d. Associative Property
3. a. 96; b. 65; c. 96; d. 150
4. a. $(1 \times 9) \times 5$ or $1 \times (9 \times 5)$; b. $(7 \times 4) \times 4$ or $7 \times (4 \times 4)$; c. $(5 \times 8) \times 2$ or $5 \times (8 \times 2)$; d. $(3 \times 3) \times 6$ or $3 \times (3 \times 6)$
5. Example: There are 3 rows of chairs with 5 chairs in each row. If there are 2 sections like this, how many chairs are there? $(3 \times 5) \times 2$
6. D. 20