Since changing the order of the division did not give the same result,
division is not commutative . The commutative properties only apply to addition and multiplication!
Addition and multiplication
are commutative.
Subtraction and Division
are not commutative.
If you were asked to simplify this expression, how would you do it and what would your answer be?
$7+8+2$
Some people would think
$7+8\phantom{\rule{0.2em}{0ex}}\text{is}\phantom{\rule{0.2em}{0ex}}15$ and then
$15+2\phantom{\rule{0.2em}{0ex}}\text{is}\phantom{\rule{0.2em}{0ex}}17.$ Others might start with
$8+2\phantom{\rule{0.2em}{0ex}}\text{makes}\phantom{\rule{0.2em}{0ex}}10$ and then
$7+10\phantom{\rule{0.2em}{0ex}}\text{makes}\phantom{\rule{0.2em}{0ex}}17.$
Either way gives the same result. Remember, we use parentheses as grouping symbols to indicate which operation should be done first.
When multiplying three numbers, changing the grouping of the numbers gives the same result.
You probably know this, but the terminology may be new to you. These examples illustrate the
associative property .
Associative property
$\begin{array}{cccc}\mathbf{\text{of Addition}}\hfill & & & \text{If}\phantom{\rule{0.2em}{0ex}}a,b,c\phantom{\rule{0.2em}{0ex}}\text{are real numbers, then}\phantom{\rule{0.2em}{0ex}}(a+b)+c=a+(b+c)\hfill \\ \mathbf{\text{of Multiplication}}\hfill & & & \text{If}\phantom{\rule{0.2em}{0ex}}a,b,c\phantom{\rule{0.2em}{0ex}}\text{are real numbers, then}\phantom{\rule{0.2em}{0ex}}(a\xb7b)\xb7c=a\xb7(b\xb7c)\hfill \end{array}$
When adding or multiplying, changing the
grouping gives the same result.
Let’s think again about multiplying
$5\xb7\frac{1}{3}\xb73.$ We got the same result both ways, but which way was easier? Multiplying
$\frac{1}{3}$ and
$3$ first, as shown above on the right side, eliminates the fraction in the first step. Using the associative property can make the math easier!
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Got questions? Get instant answers now!
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Susanna if the first cooler holds five times the gallons then the other cooler. The big cooler holda 40 gallons and the 2nd will hold 8 gallons is that correct?
Georgie
@Susanna that person is correct if you divide 40 by 8 you can see it's 5 it's simple
Ashley
@Geogie my bad that was meant for u
Ashley
Hi everyone, I'm glad to be connected with you all. from France.
Keshad gets paid $2,400 per month plus 6% of his sales. His brother earns $3,300 per month. For what amount of total sales will Keshad’s monthly pay be higher than his brother’s monthly pay?