03.01.2020

If a:b =2:3 write b as a fraction of a

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09.07.2023, solved by verified expert
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given ,

If a:b =2:3 write b as a fraction of a, №18010974, 03.01.2020 03:25

According to Question ,

we've to write b as a fraction of a.

thus , we know that

If a:b =2:3 write b as a fraction of a, №18010974, 03.01.2020 03:25

now to represent b as a fraction of a ,

we'll have to consider the ratio as b : a

which means ,

If a:b =2:3 write b as a fraction of a, №18010974, 03.01.2020 03:25

_____________________________

_____________________________

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b = If a:b =2:3 write b as a fraction of a, №18010974, 03.01.2020 03:25 a

Step-by-step explanation:

express the ratios in fractional form

If a:b =2:3 write b as a fraction of a, №18010974, 03.01.2020 03:25 = If a:b =2:3 write b as a fraction of a, №18010974, 03.01.2020 03:25 ( cross- multiply )

2b = 3a ( divide both sides by 2 )

b = If a:b =2:3 write b as a fraction of a, №18010974, 03.01.2020 03:25 a

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Faq

Mathematics
Step-by-step answer
P Answered by Specialist

given ,

\fbox{a:b = 2:3}

According to Question ,

we've to write b as a fraction of a.

thus , we know that

a:b =  \frac{a}{b}  \\  \\ \dashrightarrow{2:3 =  \frac{2}{3} }

now to represent b as a fraction of a ,

we'll have to consider the ratio as b : a

which means ,

b:a = inverse \: of \: a:b \\ \dashrightarrow{ b:a =   \frac{b}{a}  = \frac{3}{2} }

_____________________________

_____________________________

hope helpful :D

Mathematics
Step-by-step answer
P Answered by PhD

"D"

Step-by-step explanation: 5 and 2/3 is already a mixed number so we leave it how it is. Now we just have to write 5 and 2/3 as an improper fraction.

To write a mixed number as an improper fraction, first multiply the denominator by the whole number and then add the numerator. Finally, we put our new number over our original denominator.

Therefore, 5 and 2/3 can be written as the improper fraction 17/3.


Write 5 and 2 thirds as an improper fraction and as a mixed number a. 7/5, 2 3/5 b.13/5,2 3/5 c.15/3
Mathematics
Step-by-step answer
P Answered by PhD

"D"

Step-by-step explanation: 5 and 2/3 is already a mixed number so we leave it how it is. Now we just have to write 5 and 2/3 as an improper fraction.

To write a mixed number as an improper fraction, first multiply the denominator by the whole number and then add the numerator. Finally, we put our new number over our original denominator.

Therefore, 5 and 2/3 can be written as the improper fraction 17/3.


Write 5 and 2 thirds as an improper fraction and as a mixed number a. 7/5, 2 3/5 b.13/5,2 3/5 c.15/3
Mathematics
Step-by-step answer
P Answered by Master
I believe the correct response is D.

D. 7/3 = 2 1/3 = 2.333.
Mathematics
Step-by-step answer
P Answered by Specialist

1. Using 3, 5 and 8 we can write the proper fractions (when numerator is less than the denominator) as \frac{3}{5} , \frac{3}{8} , \frac{5}{8}. As we can see these are just 3 in number.

Likewise, improper Fraction will be when the numerator is greater than the denominator and they are \frac{5}{3}, \frac{8}{5} , \frac{8}{3}. As we can see even these are just three in number.

2. a 11 is the numerator and 20 is the denominator

b 7 is the numerator and 512 is the denominator

c 12 is the numerator and 10 is the denominator

d 0 is the numerator and 78 is the denominator

3 Please keep in mid that a fraction is proper when the numerator is lesser than the denominator and is improper when the numerator is greater than or equal to the denominator. Thus, keeping in mind this rule let us proceed and check the given fractions.

a Proper

b Improper

c Proper

d Improper

4. When the numerator is equal to denominator, the fraction's value will always be equal to 1. When the numerator is greater than the denominator the fraction's value will always be greater than 1 and when the numerator is less than the denominator the fraction's value will always less than 1. Keeping these rules in mind let us proceed with the fractions given.

a. =

b. <

c. <

d. >

Mathematics
Step-by-step answer
P Answered by Specialist

1. Using 3, 5 and 8 we can write the proper fractions (when numerator is less than the denominator) as \frac{3}{5} , \frac{3}{8} , \frac{5}{8}. As we can see these are just 3 in number.

Likewise, improper Fraction will be when the numerator is greater than the denominator and they are \frac{5}{3}, \frac{8}{5} , \frac{8}{3}. As we can see even these are just three in number.

2. a 11 is the numerator and 20 is the denominator

b 7 is the numerator and 512 is the denominator

c 12 is the numerator and 10 is the denominator

d 0 is the numerator and 78 is the denominator

3 Please keep in mid that a fraction is proper when the numerator is lesser than the denominator and is improper when the numerator is greater than or equal to the denominator. Thus, keeping in mind this rule let us proceed and check the given fractions.

a Proper

b Improper

c Proper

d Improper

4. When the numerator is equal to denominator, the fraction's value will always be equal to 1. When the numerator is greater than the denominator the fraction's value will always be greater than 1 and when the numerator is less than the denominator the fraction's value will always less than 1. Keeping these rules in mind let us proceed with the fractions given.

a. =

b. <

c. <

d. >

Mathematics
Step-by-step answer
P Answered by PhD

QUESTION 1

We want to find the digit that should fill the  blank space to make



3,71-



divisible by 9.



If a number is divisible by 9 then the sum of the digits should be a multiple of 9.



The sum of the given digits is,



3 + 7 + 1 = 11



Since


11 + 7 = 18


which is a multiple of 9.



This means that


3,717


is divisible by 9.



The correct answer is B



QUESTION 2



The factors of the number 30 are all the numbers that divides 30 exactly without a remainder.



These numbers are ;



1,2,3,5,6,10,15,30



The correct answer is A.



QUESTION 3.

We want to find the prime factorization of the number 168.



The prime numbers that are factors of 168 are



2,3 \: and \: 7



We can write 168 as the product of these three prime numbers to obtain,



168={2}^{3}\times 3\times7



We can also use the factor tree as shown in the attachment to write the prime factorization of 168 as



168 ={2}^{3}\times 3\times7



The correct answer is B.



QUESTION 4.



We want to find the greatest common factor of


140\:\:and\:\:180



We need to express each of these numbers as a product of prime factors.



The prime factorization of 140 is



140={2}^{2}\times 5\times7.



The prime factorization of 180 is



180={2}^{2} \times{3}^{2}\times5.



The greatest common factor is the product of the least degree of each common factor.



GCF={2}^{2}\times5



GCF=20


The correct answer is A.



QUESTION 5.



We want to find the greatest common factor of


15,30\: and\:60.



We need to first find the prime factorization of each number.



The prime factorization of 15 is



15=3\times5.



The prime factorization of 30 is


30=2\times 3\times 5.



The prime factorization of 60 is



60={2}^{2}\times3 \times5



The greatest common factor of these three numbers is the product of the factors with the least degree that is common to them.



GCF=3 \times5



GCF=15



The correct answer is C.



QUESTION 6



We want to determine which of the given fractions is equivalent to


\frac{3}{8}.



We must therefore simplify each option,



A.\: \: \frac{15}{32}=\frac{15}{32}



B.\:\:\frac{12}{32}=\frac{4\times 3}{4\times8}=\frac{3}{8}



C.\:\:\:\:\frac{12}{24}=\frac{12\times1}{12\times 2}=\frac{1}{2}



D.\:\:\frac{9}{32}=\frac{9}{32}



The simplification shows that


\frac{12}{32}\equiv \frac{3}{8}



The correct answer is  B.



QUESTION 7.



We want to express


\frac{10}{22}


in the simplest form.



We just have to cancel out common factors as follows.



\frac{10}{22}=\frac{2\times5}{2 \times11}



This simplifies to,



\frac{10}{22}=\frac{5}{11}



The correct answer is C.



QUESTION 8.



We were given that Justin visited 25 of the50 states.

The question requires that we express 25 as a fraction of 50.



This will give us


\frac{25}{50}=\frac{25\times1}{25\times2}



We must cancel out the common factors to have our fraction in the simplest form.



\frac{25}{50}=\frac{1}{2}



The correct answer is C.



QUESTION 9.



We want to write


2\frac{5}{8}


as an improper fraction.



We need to multiply the 2 by the denominator which is 8 and add the product to 5 and then express the result over 8.



This gives us,



2 \frac{5}{8}=\frac{2\times8+5}{8}



this implies that,


2\frac{5}{8}=\frac{16+5}{8}



2\frac{5}{8}=\frac{21}{8}



Sarah needed


\frac{21}{8}\:\:yards



The correct answer is D.



QUESTION 10



See attachment



QUESTION 11



We wan to write


3\: and\:\:\frac{7}{8}



as an improper fraction.



This implies that,



3+\frac{7}{8}=3\frac{7}{8}



To write this as a mixed number, we have,



3\frac{7}{8}=\frac{3\times8+7}{8}



This implies that,



3\frac{7}{8}=\frac{24+7}{8}



This gives



3\frac{7}{8}=\frac{31}{8}



The correct answer is B.


QUESTION 12


We want to find the LCM of 30 and 46 using prime factorization.


The prime factorization of 30 is 30=2\times 3\times 5


The prime factorization of 46 is 40=2\times 23.


The LCM is the product of the common factors with the highest degrees. This gives us,



LCM=2\times \times3 5\times 23


LCM=690


The correct answer is D.


QUESTION 13

We want to find the least common multiple of 3,6 and 7.


The prime factorization of 3 is 3.


The prime factorization of 6 is 6=2\times 3.


The prime factorization of 7 is 7.


The LCM is the product of the common factors with the highest degrees. This gives us,

LCM=2\times3 \times7


LCM=42.


The LCM is 42, therefore 42 days will pass before all three bikes will at the park on the same day again.


The correct answer is B.


See attachment for continuation.



1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the
1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the
1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the
1. find the digit that makes 3,71_ divisible by 9. a. 3 b. 7 c. 1 d. 5 2.list all the factors of the

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