The distributive law of multiplication over subtraction | Pre-Algebra | Khan Academy
The distributive law of multiplication over subtraction | Pre-Algebra | Khan Academy

Main content

4th grade foundations (Eureka Math/EngageNY)

Distributive property explained

The distributive property tells us how to solve expressions in the form of a(b + c). The distributive property is sometimes called the distributive law of multiplication and division.

Normally when we see an expression like this …

distributive property format

we just evaluate what’s in the parentheses first, then solve it:

distributive property in practice

This is following the official “order of operations” rule that we’ve learned in the past.

With the distributive property, we multiply the ‘4’ first:

distributing values

We distribute the 4 to the 8, then to the 3.
Then we need to remember to multiply first, before doing the addition!

Then we need to remember to multiply first, before doing the addition!

We got the same answer, 44, with both approaches!

Why did we do it differently when we could have easily worked out what was in the brackets first?
This is preparation for when we have variables instead of numbers inside the parentheses.

This is preparation for when we have variables instead of numbers inside the parentheses.

Another example before we start to use variables:

Example of the distributive property using variables:

More examples
a)

a)

b)

Tips

  • We usually use the distributive property because the two terms inside the parentheses can’t be added because they’re not like terms
  • Make sure you apply the outside number to all of the terms inside the parentheses/brackets

Try our stack of practice questions with useful hints and answers! Like this one:

Want to join the conversation?

  • Can the distributive property work if there is multiplication or division inside the parentheses? Like in 9(3/3)?(34 votes)
    • That’s not a failure to distribute due to the fraction/division though, it fails because e it requires a minimum of 2 terms to distribute onto.
      Say the problem is 9(3/3+3/3), then you just handle the multiplication inside just like any other fractions/divisions
      9*3/3+9*3/3 -> 27/3+27/3 -> 9/1+9/1 = 18(0 votes)
  • What if you have two parentheses? Such as (3×6) – (3×3)(14 votes)
    • You can take out the 3 from both terms
      3(6-3) = 18 – 9 = 9. This gives the same answer as multiplying the numbers in the brackets.(0 votes)
  • why is this important for me to know in life(10 votes)
    • i honestly think its for jobs that have to do with math, like welding and being a mechanic there are plenty of jobs that take complex equation’s even animation it takes over hundreds of frames to even get a small clip think of how much algebra you’d have to do(5 votes)
  • Im confused….. What does the 2 in example c mean? Does it mean to divide 12 by the answer of 5+2 by 2? Because that would be logical if it does.😊(7 votes)
    • Sal wrote the 2 there, because he was signifying that when the positive 7 and the negative 5 were combined together, it would equal a positive 2. He then added this positive 2 to the 6+x in the rest of the expression and got 8+x. Did that help?(7 votes)
  • In example c, what does the underneath 5+7 represent?(7 votes)
    • I think you may be talking about example b, in which there is a sort of wiggly line with a downward facing peak in the middle. This is just a symbol Sal uses to indicate a particular part of an expression. I’m not sure of its name, but does it look kind of like this } but lying flat on the ground?(4 votes)
  • What if the expression does not have a operation inside?
    Example: 18(26)(3 votes)
    • Technically,18(26)does have an operation…
      In this instance, the parentheses denote multiplication. Therefore,18(26) = 18*26
      Knowing this, you can now continue with the distributive property.(12 votes)
  • Why do you use a parenthesis instead of a multiplication symbol?(6 votes)
    • The parenthesis helps the problem more understandable rather than doing this 3*4-7(3 votes)
  • What if the format is this
    1/2(2a-6b+8)(3 votes)
    • Distribute the 1/2
      2a (1/2) -6b (1/2) + 8 (1/2)
      It may be easier if you change the other numbers into fractions.
      2a/1 (1/2) -6b/1 (1/2) + 8/1 (1/2)
      Finish the multiplication of each fraction pair and reduce them.
      For example: 2a/1 (1/2) = 2a/2 = a
      I’ll let you finish the rest.
      Hope this helps.(6 votes)
  • one of one my distributive problems is 7-3(-8 + 2)
    do I bring the seven down and do negative 3 times negative 8, or do I do 7-3 = 4, and then multiply 4 and negative 8(3 votes)
    • Order of operations applies…
      You need to multiply (distribute the -3 to the -8 and 2) prior to subtracting with the 7.
      Or, Do the work inside the parentheses 1st (-8+2).
      Then, multiply result with -3
      Last add/subtract with the 7(5 votes)
  • Here is the question Use the distrubitive property to rewrite this product below in two different ways. Simplify your anwsers. Should they still be equal? Why?
    23(79)=
    23(79)=(5 votes)

You are watching: Distributive property explained (article). Info created by Bút Chì Xanh selection and synthesis along with other related topics.