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3 years ago

Oliver uses the gcf and the distributive property to rewrite this summer 64+96

Mathematics

1 answer:

Rashid [163]3 years ago

6 0

64+96 = 32 (2 + 3)

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Use decimals and fractions in the same equation showing the Commutative Property. Repeat for the Associative Property.

Anna71 [15]

For Commutative Property of Addition

Let us take a decimal number $2.14$ and a fraction $\frac{5}{20}$

Now, according to the Commutative property of Addition:

For any two numbers $a$ and $b$ :

$a+b = b+a$

So, for $2.14$ and $\frac{5}{20}$

Let us add

$2.14+\frac{5}{20} = \frac{214}{100} +\frac{5}{20}$

$=\frac{214}{100} + \frac{5 \times 5}{20 \times 5} \\ \\=\frac{214}{100} + \frac{25}{100} \\ \\= 2.14 + 0.25 \\ \\ = 2.39$

Also,

$\frac{5}{20} + 2.14 = \frac{5}{20} + \frac{214}{100}$

$= \frac{5 \times 5}{20 \times 5} +\frac{214}{100} \\ \\= \frac{25}{100} + \frac{214}{100} \\ \\= 0.25 + 2.14 \\ \\ = 2.39$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Commutative Property of Addition is satisfied.

For Associated Property of Addition

Let us take two same decimal numbers $2.14$ , $7.25$ and a fraction $\frac{5}{20}$

Now, according to the Associated property of Addition:

For any three numbers $a$ , $b$ and $c$

$a + (b+c) =(a+b) + c$

So, for $2.14$ , $7.25$ and $\frac{5}{20}$

The Left hand side:

$a + (b+c)$

$2.14 + (7.25 + \frac{5}{20}) = 2.14 + (\frac{725}{100} + \frac{5 \times 5}{20\times 5})$

$= 2.14 + (\frac{725}{100} + \frac{25 }{100})$

$= 2.14 + (\frac{750}{100} )$

$= \frac{214}{100} + \frac{750}{100}$

$= \frac{964}{100}$

$=9.64$

The Right hand side:

$(a + b )+c$

$(2.14 + 7.25 )+ \frac{5}{20}= ( 9.39 ) + \frac{5 }{20}$

$= 9.39 + \frac{5 \times 5 }{20 \times 5}$

$= 9.39 + \frac{25}{100}$

$= 9.39 + 0.25$

$= 9.64$

Thus,

$(2.14 + (7.25 + \frac{5}{20} )= (2.14 + 7.25 )+ \frac{5}{20}$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Associative Property of Addition is satisfied.

8 0

3 years ago

Which input in this table is incorrect?

ycow [4]

Answer:

I would say its D. 9.00

Step-by-step explanation:

6 0

4 years ago

637 x 3 find the products. Show your thinking. The first row gives some ideas for showing your thinking

Colt1911 [192]

Answer:

1,911

Step-by-step example

3 x 7

3 x 30

3 x 600

then add it all up to get the 1,911

6 0

3 years ago

I need awnsers please

romanna [79]

$y=f(x) =12\sqrt x\\\\\text{Replace x with y and then solve for y:}\\ \\~~~~~~~x = 12\sqrt y\\\\\implies \sqrt y = \dfrac{x}{12}\\ \\\implies y = \dfrac{x^2}{144}\\\\\implies f^{-1} (x) = \dfrac{x^2}{144} \\\\\text{Hence the inverse of the function is}~ \dfrac{x^2}{144}$

5 0

2 years ago

A bag contains 10 marbles: 3 are green, 2 are red, and 5 are blue. Jose chooses a marble at random, and without putting it back,

Ludmilka [50]

We know that
g=3
r=2
b=5
total marbies=g+r+b------> 3+2+5----> 10

a) probability that the first marble is red
P(red)=r/total marbies------------> 2/10-----> 1/5

b) probability that the second marble is blue
in this case total marbles-------> 9
P(blue)=b/total marbles----------> 5/9

c) the probability that the first marble is red and the second is blue
(1/5)*(5/9)=1/9

the answer is
1/9

6 0

3 years ago