The worksheet focuses on applying the
distributive property to simplify and solve mathematical expressions. The distributive property states:
\[
a \times (b + c) = a \times b + a \times c
\]
We will solve each problem step by step using this property.
---
Problem 1: \( 44 \times 8 + 44 \times 92 \)
Using the distributive property:
\[
44 \times 8 + 44 \times 92 = 44 \times (8 + 92)
\]
Simplify inside the parentheses:
\[
8 + 92 = 100
\]
So:
\[
44 \times (8 + 92) = 44 \times 100 = 4400
\]
Answer:
\[
\boxed{4400}
\]
---
Problem 2: \( 4 \times 3 \times 12 \times 966 + 144 \times 34 \)
First, simplify the left part of the expression:
\[
4 \times 3 \times 12 \times 966 = 144 \times 966
\]
So the expression becomes:
\[
144 \times 966 + 144 \times 34
\]
Now apply the distributive property:
\[
144 \times 966 + 144 \times 34 = 144 \times (966 + 34)
\]
Simplify inside the parentheses:
\[
966 + 34 = 1000
\]
So:
\[
144 \times (966 + 34) = 144 \times 1000 = 144000
\]
Answer:
\[
\boxed{144000}
\]
---
Problem 3: \( 127834 \times 1001 - 127834 \)
Factor out \( 127834 \):
\[
127834 \times 1001 - 127834 = 127834 \times (1001 - 1)
\]
Simplify inside the parentheses:
\[
1001 - 1 = 1000
\]
So:
\[
127834 \times (1001 - 1) = 127834 \times 1000 = 127834000
\]
Answer:
\[
\boxed{127834000}
\]
---
Problem 4: \( 9999 \times 7 + 3 \times 9999 \)
Factor out \( 9999 \):
\[
9999 \times 7 + 3 \times 9999 = 9999 \times (7 + 3)
\]
Simplify inside the parentheses:
\[
7 + 3 = 10
\]
So:
\[
9999 \times (7 + 3) = 9999 \times 10 = 99990
\]
Answer:
\[
\boxed{99990}
\]
---
Problem 5: \( 16 \times 16 + 2 \times 8 \times 4 \)
First, simplify the right part of the expression:
\[
2 \times 8 \times 4 = 64
\]
So the expression becomes:
\[
16 \times 16 + 64
\]
Calculate \( 16 \times 16 \):
\[
16 \times 16 = 256
\]
Add the results:
\[
256 + 64 = 320
\]
Answer:
\[
\boxed{320}
\]
---
Problem 6: \( 3 \times 15 \times 6 + 4 \times 45 \)
First, simplify the left part of the expression:
\[
3 \times 15 \times 6 = 270
\]
So the expression becomes:
\[
270 + 4 \times 45
\]
Simplify the right part:
\[
4 \times 45 = 180
\]
Add the results:
\[
270 + 180 = 450
\]
Answer:
\[
\boxed{450}
\]
---
Problem 7: \( 49 \times 1444 - 444 \times 7 \times 7 \)
First, simplify the right part of the expression:
\[
7 \times 7 = 49
\]
\[
444 \times 49 = 21756
\]
So the expression becomes:
\[
49 \times 1444 - 21756
\]
Simplify the left part:
\[
49 \times 1444 = 70756
\]
Subtract:
\[
70756 - 21756 = 49000
\]
Answer:
\[
\boxed{49000}
\]
---
Problem 8: \( 2 \times 78361 - 836198 \times 0 \)
Simplify the right part of the expression:
\[
836198 \times 0 = 0
\]
So the expression becomes:
\[
2 \times 78361 - 0 = 2 \times 78361
\]
Calculate:
\[
2 \times 78361 = 156722
\]
Answer:
\[
\boxed{156722}
\]
---
Final Answers:
\[
\boxed{4400, 144000, 127834000, 99990, 320, 450, 49000, 156722}
\]
Parent Tip: Review the logic above to help your child master the concept of distributive property practice 6 4 worksheet.
