Is 5/10 equivalent to 1/6, №18010229, 21.03.2023 13:25

Mathematics

Step-by-step answer

P Answered by Master

No

Step-by-step explanation:

Given the following question:

$\frac{5}{10}$

You can prove 5/10 isn't equivalent to 1/6 by simply reducing 5/10.

$\frac{5}{10}$
$\frac{5}{10}\div5=\frac{1}{2}$
$=\frac{1}{2}$
$\frac{1}{2} \frac{1}{6}$

5/10 isn't equivalent to 1/6, so your answer is "no."

Hope this helps.

Mathematics

Which expression is equivalent to 2^a+1/10a-5/10a/4a^2-1? a 2a/(2a-1)^2 b 50a/(2a+1)^2 c (2a - 1)^2/2a d (2a + 1)^2/50a which expression is equivalent to the expression below? (x/x+4)/x a x/x+4 * x/1 b x/x+4 * 1/x c x+4/x * 1/x d x+4/x * x/1 what is the quotient? n+3/2n-6/n+3/3n-9 a 2/3 b 3/2 c (n+3)^2/6(n-3)^2 d 6(n-3)^2/(n+3)^2 what is the product? a-3/15a * 5/a-3 a 1/3 b 1/3a c 3a d 3 what is the quotient? n+3/2n-6/n+3/3n-9 a 2/3 b 3/2 c (n+3)^2/6(n-3)^2 d 6(n-3)^2/(n+3)^2 what is the product? a-3/15a * 5/a-3 a 1/3 b 1/3a c 3a d 3 what is the

Step-by-step answer

P Answered by PhD

30

1. D

2.B

3.B

4.B

5. B

6.D

Step-by-step explanation:

QUESTION 1

We want to simplify $\frac{\frac{2a+1}{10a-5}}{\frac{10a}{4a^2-1}}$ .

Let us change the middle bar to a normal division sign to obtain,

$\frac{2a+1}{10a-5}\div\frac{10a}{4a^2-1}$ .

We now multiply, the first fraction by the reciprocal of the second fraction to get,

$\frac{2a+1}{10a-5}\times \frac{4a^2-1}{10a}$ .

We now factor to obtain,

$\frac{2a+1}{5(2a-1)}\times \frac{(2a-1)(2a+1)}{10a}$ .

We cancel out common factors to get,

$\frac{2a+1}{5(1)}\times \frac{(1)(2a+1)}{10a}$ .

We now multiply out to get,

$\frac{(2a+1)^2}{50a}$ .

Ans:D

QUESTION 2

The given expression is $\frac{\frac{x}{x+4} }{x}$

We change the middle bar to a normal division sign to get,

$\frac{x}{x+4}\div x$

We now multiply by the reciprocal of the second fraction to obtain,

$\frac{x}{x+4}\times \frac{1}{x}$

Ans:B

QUESTION 3

We want to simplify the quotient,

$\frac{\frac{n+3}{2n-6}}{\frac{n+3}{3n-9}}$ .

We change the middle to a normal division sign to obtain,

$\frac{n+3}{2n-6}\div\frac{n+3}{3n-9}$ .

We now multiply the first fraction by the reciprocal of the second fraction to get,

$\frac{n+3}{2n-6}\times \frac{3n-9}{n+3}$ .

We factor to get,

$\frac{n+3}{2(n-3)}\times \frac{3(n-3)}{n+3}$ .

We cancel out common factors to obtain,

$\frac{1}{2(1)}\times \frac{3(1)}{1}$ .

We simplify to get,

$\frac{3}{2}$ .

Ans:B

QUESTION 4

We want to find the product $\frac{a-3}{15a} \times\frac{5}{a-3}$ .

This multiplication is very simple to do. We just have to cancel out common factors to get,

$\frac{1}{3a} \times\frac{1}{1}$ .

We now multiply out to get,

$\frac{1}{3a}$

Ans:B

QUESTION 5.

We want to find the product $\frac{2a-7}{a} \times \frac{3a^2}{2a^2-11a+14}$ .

We factor the denominator of the second fraction to obtain,

$\frac{2a-7}{a} \times \frac{3a^2}{(2a-7)(a-2)}$ .

We now cancel out common factors to obtain,

$\frac{1}{1} \times \frac{3a}{(1)(a-2)}$ .

We multiply out to get,

$\frac{3a}{a-2}$ .

Ans:B

QUESTION 6

We want to find the quotient $\frac{\frac{a-3}{7}}{\frac{3-a}{21} }$ .

We need to change the middle bar to a normal division sign to get,

$\frac{a-3}{7}\div \frac{3-a}{21}$

We multiply by the reciprocal of the second function to get,

$\frac{a-3}{7} \times \frac{21}{3-a}$

We factor the negative 1 from the denominator of the second fraction to get,

$\frac{a-3}{7} \times \frac{21}{-1(a-3)}$

We now cancel common factors to get,

$\frac{1}{1} \times \frac{3}{-1(1)}$

This simplifies to,

.

Ans: D

Two questions repeated

Mathematics

Which expression is equivalent to 2^a+1/10a-5/10a/4a^2-1? a 2a/(2a-1)^2 b 50a/(2a+1)^2 c (2a - 1)^2/2a d (2a + 1)^2/50a which expression is equivalent to the expression below? (x/x+4)/x a x/x+4 * x/1 b x/x+4 * 1/x c x+4/x * 1/x d x+4/x * x/1 what is the quotient? n+3/2n-6/n+3/3n-9 a 2/3 b 3/2 c (n+3)^2/6(n-3)^2 d 6(n-3)^2/(n+3)^2 what is the product? a-3/15a * 5/a-3 a 1/3 b 1/3a c 3a d 3 what is the quotient? n+3/2n-6/n+3/3n-9 a 2/3 b 3/2 c (n+3)^2/6(n-3)^2 d 6(n-3)^2/(n+3)^2 what is the product? a-3/15a * 5/a-3 a 1/3 b 1/3a c 3a d 3 what is the

Step-by-step answer

P Answered by PhD

30

1. D

2.B

3.B

4.B

5. B

6.D

Step-by-step explanation:

QUESTION 1

We want to simplify $\frac{\frac{2a+1}{10a-5}}{\frac{10a}{4a^2-1}}$ .

Let us change the middle bar to a normal division sign to obtain,

$\frac{2a+1}{10a-5}\div\frac{10a}{4a^2-1}$ .

We now multiply, the first fraction by the reciprocal of the second fraction to get,

$\frac{2a+1}{10a-5}\times \frac{4a^2-1}{10a}$ .

We now factor to obtain,

$\frac{2a+1}{5(2a-1)}\times \frac{(2a-1)(2a+1)}{10a}$ .

We cancel out common factors to get,

$\frac{2a+1}{5(1)}\times \frac{(1)(2a+1)}{10a}$ .

We now multiply out to get,

$\frac{(2a+1)^2}{50a}$ .

Ans:D

QUESTION 2

The given expression is $\frac{\frac{x}{x+4} }{x}$

We change the middle bar to a normal division sign to get,

$\frac{x}{x+4}\div x$

We now multiply by the reciprocal of the second fraction to obtain,

$\frac{x}{x+4}\times \frac{1}{x}$

Ans:B

QUESTION 3

We want to simplify the quotient,

$\frac{\frac{n+3}{2n-6}}{\frac{n+3}{3n-9}}$ .

We change the middle to a normal division sign to obtain,

$\frac{n+3}{2n-6}\div\frac{n+3}{3n-9}$ .

We now multiply the first fraction by the reciprocal of the second fraction to get,

$\frac{n+3}{2n-6}\times \frac{3n-9}{n+3}$ .

We factor to get,

$\frac{n+3}{2(n-3)}\times \frac{3(n-3)}{n+3}$ .

We cancel out common factors to obtain,

$\frac{1}{2(1)}\times \frac{3(1)}{1}$ .

We simplify to get,

$\frac{3}{2}$ .

Ans:B

QUESTION 4

We want to find the product $\frac{a-3}{15a} \times\frac{5}{a-3}$ .

This multiplication is very simple to do. We just have to cancel out common factors to get,

$\frac{1}{3a} \times\frac{1}{1}$ .

We now multiply out to get,

$\frac{1}{3a}$

Ans:B

QUESTION 5.

We want to find the product $\frac{2a-7}{a} \times \frac{3a^2}{2a^2-11a+14}$ .

We factor the denominator of the second fraction to obtain,

$\frac{2a-7}{a} \times \frac{3a^2}{(2a-7)(a-2)}$ .

We now cancel out common factors to obtain,

$\frac{1}{1} \times \frac{3a}{(1)(a-2)}$ .

We multiply out to get,

$\frac{3a}{a-2}$ .

Ans:B

QUESTION 6

We want to find the quotient $\frac{\frac{a-3}{7}}{\frac{3-a}{21} }$ .

We need to change the middle bar to a normal division sign to get,

$\frac{a-3}{7}\div \frac{3-a}{21}$

We multiply by the reciprocal of the second function to get,

$\frac{a-3}{7} \times \frac{21}{3-a}$

We factor the negative 1 from the denominator of the second fraction to get,

$\frac{a-3}{7} \times \frac{21}{-1(a-3)}$

We now cancel common factors to get,

$\frac{1}{1} \times \frac{3}{-1(1)}$

This simplifies to,

.

Ans: D

Two questions repeated

Mathematics

1) State whether the following pairs of fractions are equivalent or not : 2/5,10/15 3/7,6/7 9/7 ,1 2/7 2)Reduce the given fractions to their lowest terms. a) 50/75 b) 65/105 c) 18/81

Step-by-step answer

P Answered by PhD

1

1)

2/5 ≠ 10/15= 2/3 not equivalent

3/7 ≠ 6/7 not equivalent

9/7 = 1 2/7 = 9/7 equivalent

2)

a) 50/75 = 25*2/25*3= 2/3

b) 65/105 = 5*13/5*21= 13/21

c) 18/81 = 9*2/9*9= 2/9

Mathematics

1) State whether the following pairs of fractions are equivalent or not : 2/5,10/15 3/7,6/7 9/7 ,1 2/7 2)Reduce the given fractions to their lowest terms. a) 50/75 b) 65/105 c) 18/81

Step-by-step answer

P Answered by PhD

1

1)

2/5 ≠ 10/15= 2/3 not equivalent

3/7 ≠ 6/7 not equivalent

9/7 = 1 2/7 = 9/7 equivalent

2)

a) 50/75 = 25*2/25*3= 2/3

b) 65/105 = 5*13/5*21= 13/21

c) 18/81 = 9*2/9*9= 2/9

Mathematics

Which of the following is equivalent to a real number? A. (-46)^1/2 B. (-10596)^1/8 C. (-4099)^1/5 D. (-5403)^1/6

Step-by-step answer

P Answered by Specialist

C. (-4099)^1/5

Step-by-step explanation:

$x^{\frac{1}{2} } = \sqrt{x}$

you can not take roots (real roots) of a negative number if the exponent is

even ... A,B,D have even exponents (in the denominator of the exponent.. in other words the index of the radical is even)...

the only odd index is in "B" (the 5 in the 1/5)

Mathematics

Which of the following is equivalent to a real number? A. (-46)^1/2 B. (-10596)^1/8 C. (-4099)^1/5 D. (-5403)^1/6

Step-by-step answer

P Answered by Specialist

C. (-4099)^1/5

Step-by-step explanation:

$x^{\frac{1}{2} } = \sqrt{x}$

you can not take roots (real roots) of a negative number if the exponent is

even ... A,B,D have even exponents (in the denominator of the exponent.. in other words the index of the radical is even)...

the only odd index is in "B" (the 5 in the 1/5)

Mathematics

1. What is the decimal equivalent to start fraction 3 over 50 end fraction? (1 point) 6.0 0.6 0.06 0.006 2. Express 0.54 as a fraction in simplest form. (1 point) fifty-four hundredths over one hundred fifty-four over one hundred twenty-seven over fifty one hundred over fifty-four 3. What makes the statement true? 8–2 = ? (1 point) 64 16 negative one over sixty-four one over sixty-four 4. Evaluate the expression 6–2 • 40. (1 point) 12 48 one over thirty-six 36 5. Write 32 • 3–3 • 36 as a single exponent. (1 point) 34 35 311 275 6. The 2010 census

Step-by-step answer

P Answered by Specialist

7

Step-by-step explanation:

0.0627/501/64 I am not sure but I think it is 1/363⁵Idaho has the smallest population. 0.000857 1.414213562.. 1.5 x 10⁸ .16 3/32 6.2 29/30 I am not sure -1/6 4/9 2.25 .265

Mathematics

1. What is the decimal equivalent to start fraction 3 over 50 end fraction? (1 point) 6.0 0.6 0.06 0.006 2. Express 0.54 as a fraction in simplest form. (1 point) fifty-four hundredths over one hundred fifty-four over one hundred twenty-seven over fifty one hundred over fifty-four 3. What makes the statement true? 8–2 = ? (1 point) 64 16 negative one over sixty-four one over sixty-four 4. Evaluate the expression 6–2 • 40. (1 point) 12 48 one over thirty-six 36 5. Write 32 • 3–3 • 36 as a single exponent. (1 point) 34 35 311 275 6. The 2010 census

Step-by-step answer

P Answered by Master

7

Step-by-step explanation:

0.0627/501/64 I am not sure but I think it is 1/363⁵Idaho has the smallest population. 0.000857 1.414213562.. 1.5 x 10⁸ .16 3/32 6.2 29/30 I am not sure -1/6 4/9 2.25 .265

Mathematics

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 number 30. a. 1, 2, 3, 5, 6, 10, 15, 30 b. 2, 3, 4, 10, 20, 30, 40 c. 1, 2, 4, 5, 10, 15, 30 d. 1, 2, 4, 5, 8, 10, 20, 40 3. find the prime factorization of the number 168. a. 24 x 3 x 7 b. 23 x 3 x 7 c. 24 x 33 x 13 d. 23 x 33 x 7 4. find the gcf of the numbers 140 and 180. a. 20 b. 90 c. 30 d. 10 5. the weights of 3 bags containing footballs are 15 oz, 30 oz, and 60 oz. the greatest common factor of 15, 30, and 60 gives the weight of each ball

Step-by-step answer

P Answered by PhD

64

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 of the states.

The question requires that we express 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 and 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 is .

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

The prime factorization of 7 is .

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

Is 5/10 equivalent to 1/6

Step-by-step answer

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