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Factors and multiplesMultiplying multi digit numbers
Place valueHere you will learn about the distributive property, including what it is, and how to use it to solve problems.
Students will first learn about the distributive property as part of operations and algebraic thinking in 3rd grade.
The distributive property states that multiplying the sum of two or more numbers is the same as multiplying the addends separately.
For example,
When multiplying 2 \times 8, you can break 8 up into 2 + 6.
The distributive property says that you can multiply the parts separately and then add the products together.
Any way you solve the equivalent expressions, the product is the same.
For most expressions, there is more than one way to use the distributive property.
For example,
When multiplying 2 \times 8, you can break 8 up into 5 + 3.
The distributive property says that you can multiply the parts separately and then add the products together.
Any way you solve the equivalent expressions, the product is the same.
How does this relate to 3rd grade math?
Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents. 40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!
DOWNLOAD FREEPrepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents. 40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!
DOWNLOAD FREEIn order to use the distributive property:
Show how to solve 3 \times 5 using the distributive property.
You can use the distributive property with 3 \times 5, since it is multiplication.
2Show one of the numbers being multiplied as a sum of numbers.
Either number can be used, but for this example let’s break up 5 into 4 + 1.
3 \times 5=3 \times(4+1)
3Multiply each number in the sum.
\begin{aligned} & 3 \times(4+1) \\\\ & =(3 \times 4)+(3 \times 1) \\\\ & =12+3 \end{aligned}
4Add the partial products together to find the final product.
12 + 3 = 15
3 \times 5=15 can be solved using the distributive property.
Show how to solve 12 \times 9 using the distributive property.
Identify an equation multiplying two numbers.
You can use the distributive property with 12 \times 9, since it is multiplication.
Show one of the numbers being multiplied as a sum of numbers.
Either number can be used, but for this example let’s break up 9 into 3 + 3 + 3.
12 \times 9=12 \times(3+3+3)
Multiply each number in the sum.
\begin{aligned} & 12 \times(3+3+3) \\\\ & =(12 \times 3)+(12 \times 3)+(12 \times 3) \\\\ & =36+36+36 \end{aligned}
Add the partial products together to find the final product.
36 + 36 + 36 = 108
12 \times 9=108 can be solved using the distributive property.
Show how to solve 7 \times 6 using the distributive property.
Identify an equation multiplying two numbers.
You can use the distributive property with 7 \times 6, since it is multiplication.
Show one of the numbers being multiplied as a sum of numbers.
Either number can be used, but for this example let’s break up 7 into 4 + 3.
7 \times 6=(4+3) \times 6
Multiply each number in the sum.
\begin{aligned} & (4+3) \times 6 \\\\ & =(4 \times 6)+(3 \times 6) \\\\ & =24+18 \end{aligned}
Add the partial products together to find the final product.
24 + 18 = 42
7 \times 6=42 can be solved using the distributive property.
Show how to solve 4 \times 11 using the distributive property.
Identify an equation multiplying two numbers.
You can use the distributive property with 4 \times 11, since it is multiplication.
Show one of the numbers being multiplied as a sum of numbers.
Either number can be used, but for this example let’s break up 11 into 10 + 1.
4 \times 11=4 \times(10+1)
Multiply each number in the sum.
\begin{aligned} & 4 \times(10+1) \\\\ & =(4 \times 10)+(4 \times 1) \\\\ & =40+4 \end{aligned}
Add the partial products together to find the final product.
40 + 4 = 44
4 \times 11=44 can be solved using the distributive property.
Show how to solve 8 \times 5 using the distributive property.
Identify an equation multiplying two numbers.
You can use the distributive property with 8 \times 5, since it is multiplication.
Show one of the numbers being multiplied as a sum of numbers.
Either number can be used, but for this example let’s break up 8 into 2 + 6.
8 \times 5=(2+6) \times 5
Multiply each number in the sum.
\begin{aligned} & (2+6) \times 5 \\\\ & =(2 \times 5)+(6 \times 5) \\\\ & =10+30 \end{aligned}
Add the partial products together to find the final product.
10 + 30 = 40
8 \times 5=40 can be solved using the distributive property.
Show how to solve 3 \times 12 using the distributive property.
Identify an equation multiplying two numbers.
You can use the distributive property with 3 \times 12, since it is multiplication.
Show one of the numbers being multiplied as a sum of numbers.
Either number can be used, but for this example let’s break up 12 into 1 + 1 + 10.
3 \times 12=3 \times(1+1+10)
Multiply each number in the sum.
\begin{aligned} & 3 \times(1+1+10) \\\\ & =(3 \times 1)+(3 \times 1)+(3 \times 10) \\\\ & =3+3+30 \end{aligned}
Add the partial products together to find the final product.
3 + 3 + 30 = 36
3 \times 12=36 can be solved using the distributive property.
1. Which of the following equations shows 12 \times 6 using the distributive property?
The numbers are being multiplied, so the distributive property can be used.
\begin{aligned} & 12 \times 6 \\\\ & =12 \times(3+3) \hspace{1.2cm} \text{ *Break 6 up into 3 + 3}\\\\ & =(12 \times 3)+(12 \times 3) \hspace{0.3cm} \text{ *Multiply each 3 by 12} \\\\ & =36+36 \hspace{1.8cm} \text{ *Add the partial products back together} \\\\ & =72 \end{aligned}
2. Which of the following equations shows 7 \times 9 using the distributive property?
The numbers are being multiplied, so the distributive property can be used.
\begin{aligned} & 7 \times 9 \\\\ & =(4+3) \times 9 \hspace{1.2cm} \text{ *Break 7 up into 4 + 3}\\\\ & =(4 \times 9)+(3 \times 9) \hspace{0.4cm} \text{ *Multiply both 4 and 3 by 9} \\\\ & =36+27 \hspace{1.6cm} \text{ *Add the partial products back together} \\\\ & =63 \end{aligned}
3. Which of the following equations shows 11 \times 8 using the distributive property?
The numbers are being multiplied, so the distributive property can be used.
\begin{aligned} & 11 \times 8 \\\\ & =(1+10) \times 8 \hspace{1.1cm} \text{ *Break 11 up into 1 + 10}\\\\ & =(1 \times 8)+(10 \times 8) \hspace{0.3cm} \text{ *Multiply both 1 and 10 by 8} \\\\ & =8+80 \hspace{1.8cm} \text{ *Add the partial products back together} \\\\ & =88 \end{aligned}
4. Which of the following equations shows 3 \times 7 using the distributive property?
The numbers are being multiplied, so the distributive property can be used.
\begin{aligned} & 3 \times 7 \\\\ & =3 \times(1+3+3) \hspace{1.8cm} \text{ *Break 7 up into 1 + 3 + 3}\\\\ & =(3 \times 1)+(3 \times 3)+(3 \times 3) \hspace{0.3cm} \text{ *Multiply 1, 3 and 3 by 3} \\\\ & =3+9+9 \hspace{2.6cm} \text{ *Add the partial products back together} \\\\ & =21 \end{aligned}
5. Which of the following equations is NOT a way to solve 10 \times 5 using the distributive property?
This strategy is NOT a way to solve with the distributive property.
All the other equations break 10 or 5 up into a sum and add the products of the parts, using the distributive property correctly:
6. Which of the following equations is NOT a way to solve 9 \times 8 using the distributive property?
This strategy is NOT a way to solve 9 \times 8 with the distributive property.
All the other equations break 9 or 8 up into a sum and add the products of the parts, using the distributive property correctly:
Yes, the distributive property can be used with integers (including negative numbers) and rational numbers (including fractions and decimals), as long as the numbers are all being multiplied. In middle and high school, students will learn how to use the distributive property with any real number and/or algebraic expression.
No, even though the associative property also uses parentheses, they are different properties. The associative property says you can change the grouping of numbers when adding or multiplying and the sum or product will be the same. This is different from the distributive property.
Yes, this is called the distributive property of multiplication over subtraction.
This is a general term and means the same as the distributive property.
No, because of the order of operations (or PEMDAS), the products will be found first and then added together. However, it is good practice to group each partial product with parentheses.
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Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.
40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!