Commutative Property — Definition & Examples
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- (Video) Commutative and Associative Properties of Addition by mathman1024 This video by mathman1024 explains the commutative and associative properties. Summary\large{\text{Summ…
By Alex Federspiel, Zora Gilbert, Jonathan Heller
- Commutative Properties The four operations, addition, subtraction, multiplication, and division, are important skills in pre-algebra. It is important to realize that oftentimes …
By Joshua Siktar, Eunji Kwon, Alex Federspiel, Jonathan Heller
- Here are some examples: Commutative Property of Addition 3+1=1+321+19=19+21x+y=y+x\begin{align} 3+1&=1+3\\ 21+19&=19+21\\ x+y&=y+x \end{align}3+121+19x+y=1+3=19+21=y+x Commut…
By Caroline K, Alex Federspiel, Jonathan Heller
Problems 115
- 9+5=5+?9+5=5+{?}9+5=5+?
- 3×12=12 × ?3 \times 12=12 \,\times\, ?3×12=12×?
- 4+6=?+?4+6={?}+{?}4+6=?+?
- 5×8=?×?5\times8={?}\times{?}5×8=?×?
- 11+?=7+?11+{?}=7+{?}11+?=7+? Select all that apply.
- 2×?=9×?2 \times {?}=9 \times {?}2×?=9×?
- 1+(2+3)1+(2+3)1+(2+3) is equal to which of the following? Select all that apply.
- Which of the following operations are commutative?
- True or False\text{True or False}True or False === If multiplication and addition are both commutative, then you can switch between those operations in any expression.
- 13+8=8+?13+8=8+{?}13+8=8+?
- 13+7=7+?13+7=7+{?}13+7=7+?
- 13+7=7+?13+7=7+{?}13+7=7+?
- 88×?=π×?88\times{?}=\pi\times{?}88×?=π×?
- Is subtraction a commutative operation on the set of integers?
- What does (3+6)+5=?\left(3+6\right)+5={?}(3+6)+5=?
- 7a3b2c+abc=?7a^3b^2c+abc={?}7a3b2c+abc=?
- 34+(99+5+8)34+(99+5+8)34+(99+5+8) is equivalent to?
- What is (−4)+(−6)\left(-4\right)+\left(-6\right)(−4)+(−6) equal to?
- What is a+b+ca+b+ca+b+c equivalent to?
- What does 5⋅3⋅7=5\cdot3\cdot7=5⋅3⋅7=?
- What does (8⋅7)⋅(10)⋅(3⋅2)\left(8\cdot7\right)\cdot\left(10\right)\cdot\left(3\cdot2\right)(8⋅7)⋅(10)⋅(3⋅2) equal?
- What types of operations do NOT satisfy the commutative property?
- What does xyzxyzxyz equal?
- If y=7⋅9y=7\cdot9y=7⋅9, then 636363 equals which of the following? (Mark all that apply.)
- Find values for the question marks, in order, such that 5x+3y+z=?y+?z+?x5x+3y+z = {?}y+{?}z+{?}x5x+3y+z=?y+?z+?x holds for all x,y,zx,y,zx,y,z.
- If ab=21ab=21ab=21, then ba=?ba=?ba=?
- Can xy<yxxy<yxxy<yx? Why or why not?
- If yx=5yx=5yx=5, yz=3yz=3yz=3, and ya=2ya=2ya=2, then what does (xy)(yz)(ya)(xy)(yz)(ya)(xy)(yz)(ya) equal?
- If b×y=34b\times y=34b×y=34, then what is y×b=?y\times b=?y×b=? (Mark all that apply.)
- If a=5+7a=5+7a=5+7, then
- Suppose you go to the store and buy a notebook for 444 dollars, scissors for 222 dollars, and a pen for 111 dollar. Which of the following represents the value of the cost of al…
- You go to the store to purchase ice cube trays for a large event you are hosting. You first notice 222 trays that hold 444 rows of 333 ice cubes each on sale for 5\55. Right nex…
- (538)+7+(3+5)+2=?\left(538\right)+7+\left(3+5\right)+2={?}(538)+7+(3+5)+2=?
- If (x⋅8)⋅2=2⋅(3⋅8)\left(x\cdot8\right)\cdot2=2\cdot\left(3\cdot8\right)(x⋅8)⋅2=2⋅(3⋅8), what could xxx equal?
- If (7⋅2)⋅(10⋅x)=(10⋅2)⋅(7⋅3)\left(7\cdot2\right)\cdot\left(10\cdot x\right)=\left(10\cdot2\right)\cdot\left(7\cdot3\right)(7⋅2)⋅(10⋅x)=(10⋅2)⋅(7⋅3), what could xxx be?
- xyab=?\frac{xy}{ab}=?abxy=? (Check all that must be equal.)
- If x=3+7x=3+7x=3+7, then x=?x=?x=? (Select all that apply.)
- 5348xyz=?5348xyz=?5348xyz=? (Select all choices that must be equal.)
- Which team is in the lead at the start of the ninth inning?
- 1×2×3=?×2×11 \times 2 \times 3 = {?} \times 2 \times 11×2×3=?×2×1
- If I get 222 cartons with 121212 eggs each, how many cartons with 222 eggs each would you have to buy to have the same amount of eggs?
- If I work 333 hours a day for 666 days, how many hours per day would you have to work for 333 days to match my total?
- If I run 222 miles in the morning and 555 miles at night, and you ran 555 miles in the morning, how many miles should you run at night to match my mileage for the day?
- In basketball, if I score a 222 point shot, then hit a 333, then you hit a 333, what kind of shot could you hit to tie the game?
- The commutative property holds true for which of the following statements? (select all that apply)
- Ruby and Kyle received a box of cupcakes. Ruby counted them by flavors and Kyle counted them by toppings. Will they reach the same conclusion?
- We know multiplication is commutative, meaning a×b=b×aa\times b = b\times aa×b=b×a. If we change the multiplication sign to division sign, is it still true? In other words, does…
- Will is arranging some Lego pieces in an array. There are 333 different kinds of shape and 555 different kinds of color. If Will's array has 555 rows, how many columns will he h…
- Finn plans on throwing out his out storage unit and getting a new one. His old unit has 222 rows and 333 columns, like the picture above. Finn wants a new unit with the same amo…
- aaa and bbb represent two numbers. \\ If 12×a=b×1212\times a = b \times 1212×a=b×12, what can we say about aaa and bbb?
- Every number in this equation is positive. What does the equation equal to?
- What numbers could be in the blue and yellow box?
- Does the commutative property of multiplication apply when we have negative numbers? \\ Hint: think of some examples with real numbers
- 2×3×11=?×1×62\times 3 \times 11 = {?} \times 1 \times 62×3×11=?×1×6, what does ??? equal to?
- You and your friend are picking fruit at the local orchard. Each person is allowed to pick 101010 pieces of fruit. Your friend picks 777 pears and 333 apples. You pick 333 pears…
- 4+12+6=12+6+?4+12+6 = 12+6+{?}4+12+6=12+6+?
- You buy 444 bunches of balloons where each bunch has 121212 balloons. How many bunches of balloons would you need to buy to get the same number of balloons if each bunch of ball…
- 11+12+13=13+12+?11 + 12 + 13 = 13 + 12 +{?}11+12+13=13+12+?
- 12×24×36=24×36×?12\times24\times36=24\times36\times {?}12×24×36=24×36×?
- How many unique ways are there to plug in the numbers?
- Which one of the following is true for sure? \\ \\
- Which of the following is true? \\ Note that, for example: 2 and 32\text{ and }32 and 3 and 3 and 23\text{ and }23 and 2 are two identical pairs of number, even though they are …
- Which of the following is true? \\ Note that, for example: 2 and 32\text{ and }32 and 3 and 3 and 23\text{ and }23 and 2 are two identical pairs of numbers, even though they are…
- Logan and his twin brother Lucas both have two kids. One of Logan's kids is 888. One of Lucas' kids is 111111. Coincidentally, the sum of Logan's kids' age is equal to the sum o…
- Both Lexi and Ran got the maximum amount they can get. Lexi got 111 original cheesecake. Ran got 333 original cheesecake. In total, how many green tea cheesecake did Lexi and Ra…
- There are a bunch of Lego pieces on the desk. After sorting them by shape, Dan and Lynn decide to count them. \\ Each shape has a good amount of pieces. Dan and Lynn counted the…
- Toby picked up some sweet potatoes and russet potatoes. He wanted to count how many he got in total. Does the order he counts them in matter?
- What goes in place of the question mark? 5+123=123+?5 + 123 = 123+{?}5+123=123+?
- 24+x=5+9+2424 + x = 5 + 9 + 2424+x=5+9+24What is xxx?
- How many ways are there to complete the 101010-box row?
- You have one of each colored piece. How many unique are there to arrange the 333 pieces so they fill up the 101010-box row? \\\\ hint: try putting down each at the left-most pos…
- Using the two remaining pieces, how many ways (or arrangements) are there to finish the puzzle?
- How many unique ways are there to arrange the 333 pieces? Unique means each arrangement looks different.
- 37+540=540+?37 + 540 = 540 + {?}37+540=540+? What is ?
- We know addition is commutative, meaning a+b=b+aa + b = b + aa+b=b+a. Does this hold if one of a,ba, ba,b is negative?
- Subtraction is not commutative. However, can we somehow apply the commutative property of addition to 2−12 - 12−1?
- Aly got an assortment of fruits. She starts counting them, by kind. However, she messed up half way through and decided to start over again. She forgot the order she counted the…
- While playing basketball the opposing team scores two 333-Point shots. How many 222-Point shots do you need to score to get the same number of points as the opposing team?
- Do these properties hold if one of a,ba, ba,b is negative? If both a,ba, ba,b are negative?
- True or False\text{True or False}True or False === 5+9=9+55+9=9+55+9=9+5
- Solve for nnn in the equation 15×13=13×n15 \times 13= 13 \times n15×13=13×n.
- Which of the following satisfies z×2×4=2×n×9z \times 2 \times 4 = 2 \times n \times 9z×2×4=2×n×9?
- Which property is the following: 14+23=23+14\frac14+\frac23=\frac23+\frac1441+32=32+41
- Which of the following is equal to 1+1001+1001+100? Select all that apply.
- Calculate the following: 4×13×54\times 13\times54×13×5
- Calculate the following: 32+16+1832+16+1832+16+18
- Select everything (xy)+(xz)×(yz)(xy)+(xz)\times(yz)(xy)+(xz)×(yz) is equivalent to.
- We know that 4x=94x=94x=9. What is 4×(3x)4\times (3x)4×(3x)?
- If a+b+c=0a+b+c = 0a+b+c=0, can we show a+c+b=0a+c+b = 0a+c+b=0 with the commutative property?
- If a+b=πa+b=\pia+b=π, what is a+5+ba+5+ba+5+b?
- True or False\text{True or False}True or False === Can we apply the commutative property to the addition in the expression 5x−4x+35x - 4x + 35x−4x+3? In other words, is it true …
- Using the commutative property, calculating the following: 23+54+4723+54+4723+54+47
- Take advantage of the commutative property of multiplication and calculate the following: 25×13×425\times 13\times 425×13×4
- If Jack and Jill both did the math correctly, should they get the same answer?
- Which of the following properties apply to the set of rational numbers? Select all that apply.
- Which property is expressed by: a+b=b+aa+b=b+aa+b=b+a
- You get on an elevator and go down 222 floors and then up 888 floors. The next day you get on at the same place and go up 888 floors and then down 222 floors. Do you arrive at t…
- What number could xxx equal? 23+19−4=−4+x23+19-4=-4+x23+19−4=−4+x
- Since rational numbers follow the commutative property, we know that the value of xxx will be: 38+15=15+x16\frac38+\frac15=\frac15+\frac{x}{16}83+51=51+16x
- What is the commutative property of addition?
- True or False\text{True or False}True or False == The commutative property of addition doesn't work for negative numbers.
- Who won?
- Here are two completed rows from a Sudoku game. Will these rows equal the same number when added together?
- According to the commutative property, which expressions are equal to x+3+y+7+zx+3+y+7+zx+3+y+7+z?
- True or False\text{True or False}True or False === Suppose you 333 legos of different heights. No matter how you stack the legos on top of each other, the result will always be …
- Liza wrote 151515 problems on Monday and 252525 solutions on Tuesday. Alex wrote 252525 problems on Monday and 151515 solutions on Tuesday. Is there a difference in what they wr…
- Which of the following demonstrates the commutative property of addition?
- Sylvia is buying soda at a restaurant. The soda costs 1\11, but there is a 20%20\%20% discount as well as a 6%6\%6% state tax. Does Sylvia get a better deal if she gets the disc…
- Which of the following are equivalent to a×b×ca\times b\times ca×b×c?
- Which of the following are equivalent to a+b+ca+b+ca+b+c?
- Liza wrote 101010 problems on Monday and 202020 problems on Tuesday. Alex wrote 202020 problems on Monday and 101010 problems on Tuesday. Is there a difference in the number of …
- Alex has 333 bowls, and each of them has 444 fish. Caroline has 444 bowls, and each of them has 333 fish. How many more fish does Alex have than Caroline?
- Sylvia spends 888 hours on a normal day solving her Rubiks Cube and Caroline spends 151515 hours on a normal day solving hers. If one day Caroline spends only 888 hours cubing a…
- If a×b=0,a \times b = 0,a×b=0, which of the following must be true, no matter the values of aaa and b?b?b?
- Faith and Shelby go apple picking. Faith has 444 baskets, and each of them has 666 apples. Shelby has 666 baskets, and each of them has 444 apples. What is the difference in the…