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The common factor is 11.

Posted on Mar 28, 2017

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77, 132, 143
Factors of 77

1 7 11 77

Factors of 132

1 2 3 4 6 11 12 22 33 44 66 132

Factors of 143

1 11 13 143

The highest (greatest) common factor, the highest number in each of the factors is 11.

Good luck,

Paul

Posted on Mar 29, 2017

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I interpreted the question as:

(x-2)/(4-x) + 2/3 = (x-2)/12 or

(x-2) 2 (x-2)

------ + --- = -----

(4-x) 3 12

Now to find a common denominator.

I factor all the terms and see what is common, so it can be eliminated to leave the lowest common denominator.

(4 - x) - prime - cannot be factored

3 - prime - cannot be factored

12 - 4 x 3

What is common in the above? The 3, so we can eliminate one 3.

Common denominator - (4 -x) (3)(4)

So, we must multiply the numerator and denominator of the first term by 12 (3 x 4).

The next term's numerator and denominator must be multiplied by 4(4-x).

The term on the right of the equals sign must have the numerator and denominator multiplied by (4-x).

Good luck.

If you need more assistance, post again.

Paul

(x-2)/(4-x) + 2/3 = (x-2)/12 or

(x-2) 2 (x-2)

------ + --- = -----

(4-x) 3 12

Now to find a common denominator.

I factor all the terms and see what is common, so it can be eliminated to leave the lowest common denominator.

(4 - x) - prime - cannot be factored

3 - prime - cannot be factored

12 - 4 x 3

What is common in the above? The 3, so we can eliminate one 3.

Common denominator - (4 -x) (3)(4)

So, we must multiply the numerator and denominator of the first term by 12 (3 x 4).

The next term's numerator and denominator must be multiplied by 4(4-x).

The term on the right of the equals sign must have the numerator and denominator multiplied by (4-x).

Good luck.

If you need more assistance, post again.

Paul

Apr 02, 2018 | Homework

I think you want to reduce the fraction to the lowest terms.

Improper fraction 1 3/4 produces an improper fraction of 7/4 (1 times denominator plus numerator)

To reduce a fraction, we need to divide the numerator (number on top) and the denominator (number on the bottom) by the greatest common factor (GCF).

To get the GCF, find the factors of the numerators and denominators and find the greatest number that is in both lists.

The factors of 2 are 1, 2.

The factors of 10 are 1, 2, 5, 10.

The greatest (largest) number is both lists is 2, so we divide the numerator and denominator by 2 and get 1/5.

Good luck,

Paul

Improper fraction 1 3/4 produces an improper fraction of 7/4 (1 times denominator plus numerator)

To reduce a fraction, we need to divide the numerator (number on top) and the denominator (number on the bottom) by the greatest common factor (GCF).

To get the GCF, find the factors of the numerators and denominators and find the greatest number that is in both lists.

The factors of 2 are 1, 2.

The factors of 10 are 1, 2, 5, 10.

The greatest (largest) number is both lists is 2, so we divide the numerator and denominator by 2 and get 1/5.

Good luck,

Paul

Feb 06, 2018 | Homework

the factors of 65 are

1 x 65

13 x5

so the highest common factor is 13

1 x 65

13 x5

so the highest common factor is 13

Sep 11, 2017 | Homework

We want to divide the top and bottom numbers by the largest possible number to make the numerator and denominator the smallest possible. We can determine that number by factoring both 192 000 and 650 and see what the biggest common factor is. Another approach is to simplify it step by step.

Let's try the step-by-step method.

Since both end in 0, let's divide both by 10.

19 200 : 65

Since they both end with 0 or 5, we can divide both by 5

3 840 : 13

Since 13 is prime (its only factors are 1 and 13) and 13 doesn't go evenly into 3 840, we cannot go any further.

Good luck,

Paul

Let's try the step-by-step method.

Since both end in 0, let's divide both by 10.

19 200 : 65

Since they both end with 0 or 5, we can divide both by 5

3 840 : 13

Since 13 is prime (its only factors are 1 and 13) and 13 doesn't go evenly into 3 840, we cannot go any further.

Good luck,

Paul

May 16, 2017 | Homework

-54k^2+3k
I assume that you want to factor this completely.

I do it one component at a time.

What is the biggest common factor of -54 and 3. I use a trick of adding the digits of the number. If 3 and/or 9 go into that number evenly, than 3 and/or 9, respectively go into the original number. In this case, 5+4 = 9 and since 3 goes into 9 evenly, 3 goes into 54 evenly. Since the factors of 3 are 3 and 1, this must be the greatest common factor of this component.

Onto the next component, what is the greatest common factor of k^2 and k. The answer is k, because k^2 doesn't go evenly into k.

Combining the two, the greatest common factor is 3k.

Next we have to divide 3k into each term.

3k(-18k+1) or -3k(18k-1)

Good luck,

Paul

I do it one component at a time.

What is the biggest common factor of -54 and 3. I use a trick of adding the digits of the number. If 3 and/or 9 go into that number evenly, than 3 and/or 9, respectively go into the original number. In this case, 5+4 = 9 and since 3 goes into 9 evenly, 3 goes into 54 evenly. Since the factors of 3 are 3 and 1, this must be the greatest common factor of this component.

Onto the next component, what is the greatest common factor of k^2 and k. The answer is k, because k^2 doesn't go evenly into k.

Combining the two, the greatest common factor is 3k.

Next we have to divide 3k into each term.

3k(-18k+1) or -3k(18k-1)

Good luck,

Paul

Mar 29, 2017 | Homework

Just want to make sure that we are on the same page.

2^(-3) + 3^(-3)

2 to the exponent -3 + 3 to the exponent -3

Because of BEDMAS, we have to do the exponent calculations first and then do the addition between the two terms last.

The rule of negative exponents is you put 1 over the base to the same exponent, but change the exponent from negative to positive.

=1/(2^3) + 1/(3^3)

= 1/8 + 1/27

To add or subtract numbers, we need a common denominator.

Let's factor 8 and 27 to get the lowest common multiple.

8 - 1 2 4 8

27 - 1 3 9 27

Nothing in common to eliminate, so we have to use 8 x 27 or 216.

27/216 + 8/216 = 35/216

Good luck,

Paul

2^(-3) + 3^(-3)

2 to the exponent -3 + 3 to the exponent -3

Because of BEDMAS, we have to do the exponent calculations first and then do the addition between the two terms last.

The rule of negative exponents is you put 1 over the base to the same exponent, but change the exponent from negative to positive.

=1/(2^3) + 1/(3^3)

= 1/8 + 1/27

To add or subtract numbers, we need a common denominator.

Let's factor 8 and 27 to get the lowest common multiple.

8 - 1 2 4 8

27 - 1 3 9 27

Nothing in common to eliminate, so we have to use 8 x 27 or 216.

27/216 + 8/216 = 35/216

Good luck,

Paul

Mar 11, 2017 | Homework

59/100 is in the simplest form.

it can also be written in decimals, that is 0.59

it can also be written in decimals, that is 0.59

Jan 04, 2017 | Homework

Mar 31, 2018 | Homework

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