Divide the fractions and simplify the answer 60 / 2 2/3

2 answers:

6 0

2 2/3 as a decimal is 2.66666667. 60 divided by 2.66666667 is 22.5.
As a fraction, the answer will be 22 5/10

Please mark my answer as the brainliest answer, I'd really appreciate it, thanks!

ElenaW [278]3 years ago

3 0

Hey there, make 60 a fraction, 60=60/1, 2 2/3 as an improper fraction is 8/3. Now, we have 60/1÷8/3, change the ÷ sign into a × sign. Flip 8/3 into 3/8, now we have 60/1×3/8. 60×3=180 and 1×8=8. Now, we have a fraction of 180/8. Then, we simplify 180/8. The GCF of 180 and 8 is 4 so we divide by 4, 180÷4=45 and 8÷4=2, So, 180/8 simplified is 45/2, 45 is bigger than 2 so we make 45/2 as a mixed number, 45/2 as a mixed number is 22 1/2. Therefore, 60 ÷ 2 2/3 = 22 1/2

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1.Simplify 5 to the 5th over 5 to the 8th.

timurjin [86]

Q1. The answer is 1 over 5 to the 3rd power.

5 to the 5th is 5⁵
5 to the 8th is 5⁸
5 to the 5th over 5 to the 8th is $\frac{ 5^{5} }{ 5^{8} }$
To simplify, we will use two rules:
$\frac{ x^{a}}{ x^{b} } = x^{a-b} \\ x^{-a} = \frac{1}{ x^{a}}$
Therefore:
$\frac{ 5^{5} }{ 5^{8} } = 5^{5-8} =5^{-3}= \frac{1}{5^{3}}$
$\frac{1}{5^{3}}$ is the same as 1 over 5 to the 3rd power.

Q2. The answer is (53)−4.

The exponents are multiplied when are expressed in the form:
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So, $(5^{3} )^{-4}=5^{3*(-4)}=5^{-12}$

Other choices are incorrect:
one third to the 4th times one third to the 7th is $( \frac{1}{3} )^{4} *( \frac{1}{3} )^{7}=( \frac{1}{3} )^{4+7}$
3 to the 7th over 3 to the 15th is $\frac{ 3^{7} }{3^{15}} =3^{7-15}$
45 ⋅ 42 is $4^{5}* 4^{2} = 4^{5+2}$