How can greatest common factors and least common multiples help you work with fractions ?

-1/3 + (-7/4)<br> pls help

djverab [1.8K]

Answer:

-25

——— = -2.08333

12

Step-by-step explanation:

Step 1 :

7

Simplify —

4

Equation at the end of step 1 :

1 7

(0 - —) + (0 - —)

3 4

Step 2 :

1

Simplify —

3

Equation at the end of step 2 :

1 -7

(0 - —) + ——

3 4

Step 3 :

Calculating the Least Common Multiple :

3.1 Find the Least Common Multiple

The left denominator is : 3

The right denominator is : 4

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

3 1 0 1

2 0 2 2

Product of all

Prime Factors 3 4 12

Least Common Multiple:

12

Calculating Multipliers :

3.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 4

Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

3.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. -1 • 4

—————————————————— = ——————

L.C.M 12

R. Mult. • R. Num. -7 • 3

—————————————————— = ——————

L.C.M 12

Adding fractions that have a common denominator :

3.4 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-1 • 4 + -7 • 3 -25

——————————————— = ———

12 12

Final result :

-25

——— = -2.08333

12

Processing ends successfully

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2 years ago

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A ladder leaning against a wall forms a triangle and exterior angles with the wall and the ground. What are the measures of the

Paha777 [63]

11x° is interior angle of ladder to the ground
and 7X° is interior angle of ladder to the wall

exterior angle of a ladder to wall is 180-7x
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3 years ago

17. Scott cuts his birthday cake into nine equal pieces and eats two of them.

Roman55 [17]

Answer:

A. 0.2222

B. Repeat indefinitely

Step-by-step explanation:

A. We have that Scott has 9 pieces in total and he eats 2 of them. That means he eats 2 <em>out of </em>the 9, so we have 2 ÷ 9. (see attachment)

The decimal form is: 0.2222.

B. Clearly, we can see that throughout the long division, we keep getting 20 - 18 = 2, which makes another 20 and so on. So, this will repeat indefinitely.

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2 years ago

Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work together, it takes them 2 hours. How

aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood = K hrs

So, the per hour rate of Dwight = $(\frac{1}{K})$

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood = (K- 3) hrs

So, the per hour rate of Joe = $(\frac{1}{K-3})$

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them = $(\frac{1}{2})$

⇒ Per hour rate of ( Dwight + Joe) = $(\frac{1}{2} )$

$\implies (\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})$

Now, solving for the value of K , we get:

$(\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})\\\implies \frac{(K-3) + K}{K (K-3)} = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K + 6= 0\\\implies K^2 - 6K - K + 6= 0\\\implies K(K-6) -1(K - 6)= 0\\\implies (K-6)(K-1) = 0$

Implies either K = 6 Or K = 1

But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.

⇒ K = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

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2 years ago

Haylee opened her savings account with $440 in week 1. each week after this, she deposited $65 in her account. how much money wi

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The answer is 2000 dollars

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