Why is the expression $(((30 / 2) / 2) / 2)$ same as $30 / 2^3$Order of operations: problem evaluating an expressionExpression with last digits differentWhy exactly does the distributive property work?What values will make this expression realIs $frac5x3$ The Same As $frac53x$?How to evolve an expression with two denominatorsWhy diferent calculators give different values for same expression?magnitude of a root of complex expression plus complex expressionExpression for Change in temperatureWhy do addition and subtraction have the same precedence?
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Why is the expression $(((30 / 2) / 2) / 2)$ same as $30 / 2^3$
Order of operations: problem evaluating an expressionExpression with last digits differentWhy exactly does the distributive property work?What values will make this expression realIs $frac5x3$ The Same As $frac53x$?How to evolve an expression with two denominatorsWhy diferent calculators give different values for same expression?magnitude of a root of complex expression plus complex expressionExpression for Change in temperatureWhy do addition and subtraction have the same precedence?
$begingroup$
Why is the expression $$(((30 / 2) / 2) / 2)$$ same as $$30 / 2^3$$
arithmetic
$endgroup$
add a comment |
$begingroup$
Why is the expression $$(((30 / 2) / 2) / 2)$$ same as $$30 / 2^3$$
arithmetic
$endgroup$
1
$begingroup$
A parenthesis is missing?
$endgroup$
– Dr. Sonnhard Graubner
11 hours ago
$begingroup$
Yes! It is correct
$endgroup$
– HAMIDINE SOUMARE
11 hours ago
$begingroup$
$30/2=15$, $15/2=7.5$, $7.5/2=3.75$. Then $30/2^3=30/8=3.75$.
$endgroup$
– thesmallprint
10 hours ago
add a comment |
$begingroup$
Why is the expression $$(((30 / 2) / 2) / 2)$$ same as $$30 / 2^3$$
arithmetic
$endgroup$
Why is the expression $$(((30 / 2) / 2) / 2)$$ same as $$30 / 2^3$$
arithmetic
arithmetic
edited 5 hours ago
Asaf Karagila♦
308k33441774
308k33441774
asked 11 hours ago
Michael MuntaMichael Munta
111111
111111
1
$begingroup$
A parenthesis is missing?
$endgroup$
– Dr. Sonnhard Graubner
11 hours ago
$begingroup$
Yes! It is correct
$endgroup$
– HAMIDINE SOUMARE
11 hours ago
$begingroup$
$30/2=15$, $15/2=7.5$, $7.5/2=3.75$. Then $30/2^3=30/8=3.75$.
$endgroup$
– thesmallprint
10 hours ago
add a comment |
1
$begingroup$
A parenthesis is missing?
$endgroup$
– Dr. Sonnhard Graubner
11 hours ago
$begingroup$
Yes! It is correct
$endgroup$
– HAMIDINE SOUMARE
11 hours ago
$begingroup$
$30/2=15$, $15/2=7.5$, $7.5/2=3.75$. Then $30/2^3=30/8=3.75$.
$endgroup$
– thesmallprint
10 hours ago
1
1
$begingroup$
A parenthesis is missing?
$endgroup$
– Dr. Sonnhard Graubner
11 hours ago
$begingroup$
A parenthesis is missing?
$endgroup$
– Dr. Sonnhard Graubner
11 hours ago
$begingroup$
Yes! It is correct
$endgroup$
– HAMIDINE SOUMARE
11 hours ago
$begingroup$
Yes! It is correct
$endgroup$
– HAMIDINE SOUMARE
11 hours ago
$begingroup$
$30/2=15$, $15/2=7.5$, $7.5/2=3.75$. Then $30/2^3=30/8=3.75$.
$endgroup$
– thesmallprint
10 hours ago
$begingroup$
$30/2=15$, $15/2=7.5$, $7.5/2=3.75$. Then $30/2^3=30/8=3.75$.
$endgroup$
– thesmallprint
10 hours ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Note that
$$beginalign colorblue(30/2)/2 &= frac302times frac12\
&=colorteal frac302^2
endalign.$$
Hence
$$beginalign
(colorblue(30/2)/2)/2 &= colortealleft(frac302^2right)bigg/2\
&= frac302^2times frac12\
&= frac302^3.
endalign$$
$endgroup$
add a comment |
$begingroup$
$$30div2div2div2=frac302div2div2$$
$$=frac302^2div2$$
$$=frac302^3$$
$endgroup$
2
$begingroup$
Looking at this as a multiplication by a fraction is the only way to prove it?
$endgroup$
– Michael Munta
11 hours ago
add a comment |
$begingroup$
Recall:
$(30/2)=30cdot dfrac12;$
$((30/2)/2)=(30cdot dfrac12)cdot dfrac12;$
$(30/2)/2)/2=$
$((30 cdot dfrac12)cdot dfrac12)cdot dfrac12= 30 cdot (dfrac12)^3= dfrac302^3$
Used: Associative law of multiplication.
$endgroup$
add a comment |
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Note that
$$beginalign colorblue(30/2)/2 &= frac302times frac12\
&=colorteal frac302^2
endalign.$$
Hence
$$beginalign
(colorblue(30/2)/2)/2 &= colortealleft(frac302^2right)bigg/2\
&= frac302^2times frac12\
&= frac302^3.
endalign$$
$endgroup$
add a comment |
$begingroup$
Note that
$$beginalign colorblue(30/2)/2 &= frac302times frac12\
&=colorteal frac302^2
endalign.$$
Hence
$$beginalign
(colorblue(30/2)/2)/2 &= colortealleft(frac302^2right)bigg/2\
&= frac302^2times frac12\
&= frac302^3.
endalign$$
$endgroup$
add a comment |
$begingroup$
Note that
$$beginalign colorblue(30/2)/2 &= frac302times frac12\
&=colorteal frac302^2
endalign.$$
Hence
$$beginalign
(colorblue(30/2)/2)/2 &= colortealleft(frac302^2right)bigg/2\
&= frac302^2times frac12\
&= frac302^3.
endalign$$
$endgroup$
Note that
$$beginalign colorblue(30/2)/2 &= frac302times frac12\
&=colorteal frac302^2
endalign.$$
Hence
$$beginalign
(colorblue(30/2)/2)/2 &= colortealleft(frac302^2right)bigg/2\
&= frac302^2times frac12\
&= frac302^3.
endalign$$
edited 11 hours ago
answered 11 hours ago
Minus One-TwelfthMinus One-Twelfth
3,328413
3,328413
add a comment |
add a comment |
$begingroup$
$$30div2div2div2=frac302div2div2$$
$$=frac302^2div2$$
$$=frac302^3$$
$endgroup$
2
$begingroup$
Looking at this as a multiplication by a fraction is the only way to prove it?
$endgroup$
– Michael Munta
11 hours ago
add a comment |
$begingroup$
$$30div2div2div2=frac302div2div2$$
$$=frac302^2div2$$
$$=frac302^3$$
$endgroup$
2
$begingroup$
Looking at this as a multiplication by a fraction is the only way to prove it?
$endgroup$
– Michael Munta
11 hours ago
add a comment |
$begingroup$
$$30div2div2div2=frac302div2div2$$
$$=frac302^2div2$$
$$=frac302^3$$
$endgroup$
$$30div2div2div2=frac302div2div2$$
$$=frac302^2div2$$
$$=frac302^3$$
answered 11 hours ago
Peter ForemanPeter Foreman
6,1811317
6,1811317
2
$begingroup$
Looking at this as a multiplication by a fraction is the only way to prove it?
$endgroup$
– Michael Munta
11 hours ago
add a comment |
2
$begingroup$
Looking at this as a multiplication by a fraction is the only way to prove it?
$endgroup$
– Michael Munta
11 hours ago
2
2
$begingroup$
Looking at this as a multiplication by a fraction is the only way to prove it?
$endgroup$
– Michael Munta
11 hours ago
$begingroup$
Looking at this as a multiplication by a fraction is the only way to prove it?
$endgroup$
– Michael Munta
11 hours ago
add a comment |
$begingroup$
Recall:
$(30/2)=30cdot dfrac12;$
$((30/2)/2)=(30cdot dfrac12)cdot dfrac12;$
$(30/2)/2)/2=$
$((30 cdot dfrac12)cdot dfrac12)cdot dfrac12= 30 cdot (dfrac12)^3= dfrac302^3$
Used: Associative law of multiplication.
$endgroup$
add a comment |
$begingroup$
Recall:
$(30/2)=30cdot dfrac12;$
$((30/2)/2)=(30cdot dfrac12)cdot dfrac12;$
$(30/2)/2)/2=$
$((30 cdot dfrac12)cdot dfrac12)cdot dfrac12= 30 cdot (dfrac12)^3= dfrac302^3$
Used: Associative law of multiplication.
$endgroup$
add a comment |
$begingroup$
Recall:
$(30/2)=30cdot dfrac12;$
$((30/2)/2)=(30cdot dfrac12)cdot dfrac12;$
$(30/2)/2)/2=$
$((30 cdot dfrac12)cdot dfrac12)cdot dfrac12= 30 cdot (dfrac12)^3= dfrac302^3$
Used: Associative law of multiplication.
$endgroup$
Recall:
$(30/2)=30cdot dfrac12;$
$((30/2)/2)=(30cdot dfrac12)cdot dfrac12;$
$(30/2)/2)/2=$
$((30 cdot dfrac12)cdot dfrac12)cdot dfrac12= 30 cdot (dfrac12)^3= dfrac302^3$
Used: Associative law of multiplication.
edited 8 hours ago
answered 10 hours ago
Peter SzilasPeter Szilas
11.8k2822
11.8k2822
add a comment |
add a comment |
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1
$begingroup$
A parenthesis is missing?
$endgroup$
– Dr. Sonnhard Graubner
11 hours ago
$begingroup$
Yes! It is correct
$endgroup$
– HAMIDINE SOUMARE
11 hours ago
$begingroup$
$30/2=15$, $15/2=7.5$, $7.5/2=3.75$. Then $30/2^3=30/8=3.75$.
$endgroup$
– thesmallprint
10 hours ago