The distributive property of multiplication allows us to break down the highest term of the exercise into a smaller number. This simplifies the multiplication operation and we can solve the exercise without the need to use a calculator.
Distributive Property Practice Problems for 7th Grade Math
Master the distributive property with step-by-step practice problems. Learn to multiply and divide using distribution for easier calculations in 7th grade math.
📚What You'll Practice and Master
- Apply distributive property to simplify multiplication problems with large numbers
- Break down complex numbers into smaller, easier-to-calculate components
- Use distributive property with addition and subtraction in parentheses
- Solve division problems using distributive property techniques
- Calculate expressions like (40+70+35-7)×9 step by step
- Master both a×(b+c) and (a+b)÷c distributive forms
Understanding The Distributive Property in the Case of Multiplication
Complete explanation with examples
Example of an exercise where the distributive property is applied with multiplications
Let's assume we have an exercise with a multiplication that is simple, but with large numbers, for example:
Thanks to the distributive property, we can break it down into simpler exercises:
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Practice The Distributive Property in the Case of Multiplication
Test your knowledge with 25 quizzes
Which equation is the same as the following?
\( 160\times6 \)
Examples with solutions for The Distributive Property in the Case of Multiplication
Step-by-step solutions included
Exercise #1
Step-by-Step Solution
In order to simplify the calculation , we first break down 94 and 72 into smaller and preferably round numbers.
We obtain the following exercise:
Using the associative property, we then rearrange the exercise to be more functional.
We solve the exercise in the following way, first the round numbers and then the small numbers.
Which results in the following exercise:
Answer:
166
Video Solution
Exercise #2
Step-by-Step Solution
To solve the problem, first we will use the distributive property on the two numbers:
(60+3)-(30+6)
Now, we will use the substitution property to arrange the exercise in the way that is most convenient for us to solve:
60-30+3-6
It is important to pay attention that when we open the second parentheses, the minus sign moved to the two numbers inside.
30-3 =Â
27
Answer:
27
Video Solution
Exercise #3
Step-by-Step Solution
We will use the distributive law and split the number 143 into a sum of 100 and 43.
The distributive law allows us to distribute, meaning, to split a number into two or more numbers. This actually allows us to work with smaller numbers and simplify the operation.
We will operate according to the order of operations
We can remove parentheses and perform addition and subtraction operations in any order since there are only addition and subtraction operations in the equation
Therefore, the answer is option C - 100.
And now let's see the solution to the exercise in a centered format:
Answer:
100
Video Solution
Exercise #4
Step-by-Step Solution
In order to solve the question, we first use the distributive property for 133:
We then use the distributive property for 33:
We rearrange the exercise into a more practical form:
We solve the middle exercise:
Which results in the final exercise as seen below:
Answer:
163
Video Solution
Exercise #5
Step-by-Step Solution
In order to simplify the resolution process, we begin by using the distributive property for 140:
We then rearrange the exercise using the substitution property into a more practical form:
Lastly we solve the exercise from left to right:
Answer:
70
Video Solution
Frequently Asked Questions
What is the distributive property in 7th grade math?
+The distributive property allows you to multiply a number by a sum or difference by distributing the multiplication to each term inside parentheses. For example, 8×(500+30+2) = 8×500 + 8×30 + 8×2 = 4000+240+16 = 4256.
How do you use distributive property to make multiplication easier?
+Break large numbers into smaller, friendlier numbers. Instead of calculating 74×8 directly, rewrite it as (70+4)×8 = 70×8 + 4×8 = 560+32 = 592. This eliminates the need for complex mental math or calculators.
What's the difference between distributive property with addition and subtraction?
+With addition: a×(b+c) = a×b + a×c. With subtraction: a×(b-c) = a×b - a×c. For example, 48×6 = (50-2)×6 = 50×6 - 2×6 = 300-12 = 288.
Can you use distributive property with division problems?
+Yes! The distributive property works with division too: (a+b)÷c = a÷c + b÷c. For example, (22+14)÷2 = 22÷2 + 14÷2 = 11+7 = 18.
What are common mistakes students make with distributive property?
+Common errors include: 1) Forgetting to distribute to all terms inside parentheses, 2) Mixing up signs when distributing with subtraction, 3) Not simplifying completely after distributing. Always double-check that every term gets multiplied.
How do you solve complex expressions like (40+70+35-7)×9?
+Distribute the 9 to each term: 40×9 + 70×9 + 35×9 - 7×9 = 360 + 630 + 315 - 63. Then add and subtract from left to right: 990 + 315 - 63 = 1305 - 63 = 1242.
When should 7th graders use the distributive property?
+Use it when multiplying by large numbers, when numbers inside parentheses are easier to work with separately, or when calculators aren't allowed. It's especially helpful for mental math and building number sense.
How does distributive property help with algebraic expressions?
+The distributive property is foundational for algebra. It teaches students how to expand expressions like 3(x+4) = 3x+12, which is essential for solving equations and simplifying algebraic expressions in advanced math courses.