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3 years ago

Which one is bigger 5 1/4 or 5 5/6

Mathematics

2 answers:

8090 [49]3 years ago

6 0

Answer:

5 5/6

Step-by-step explanation:

Since the whole number for both mixed numbers is 5, you don't really have to look at that. 1/4 is smaller than 5/6 so 5 5/6 would be the bigger of the two mixed numbers.

VashaNatasha [74]3 years ago

6 0

Answer:

5 5/6

Step-by-step explanation:

5/6 its closer to a whole than 1/4

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denis23 [38]

Answer:

$a = \dfrac{x^2}{3} \quad \textsf{and} \quad b = \dfrac{x^3}{7}$

Step-by-step explanation:

Given expression:

$\dfrac{3x^{8} \cdot 7x^{3} }{3x^{6} \cdot 7 }$

There are several ways this problem can be approached, and therefore many different answers. The goal is to reduce the given expression to a simple product of two terms in x, set that to the given form 3a⋅7b then solve for a and b.

$\implies \dfrac{3x^{8} \cdot 7x^{3} }{3x^{6} \cdot 7}$

Cancel the common factors 3 and 7:

$\implies \dfrac{\diagup\!\!\!\!3x^{8} \cdot \diagup\!\!\!\!7x^{3} }{\diagup\!\!\!\!3x^{6} \cdot \diagup\!\!\!\!7}$

$\implies \dfrac{x^8 \cdot x^3}{x^6}$

Separate the fraction:

$\implies \dfrac{x^8}{x^6} \cdot x^3$

$\textsf{Apply the quotient rule of exponents} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies x^{8-6} \cdot x^3$

$\implies x^{2} \cdot x^3$

Now equate the simplified expression to the given form:

$\implies x^{2} \cdot x^3=3a \cdot 7b$

Therefore:

$\begin{aligned}x^{2} &=3a \:\: &\textsf{ and }\:\: \quad x^3 &=7b\\ \Rightarrow a & = \dfrac{x^2}{3} & \Rightarrow b & = \dfrac{x^3}{7}\end{aligned}$

However, we could also separate them as:

$\begin{aligned}x^{3} &=3a \:\: &\textsf{ and }\:\: \quad x^2 &=7b\\ \Rightarrow a & = \dfrac{x^3}{3} & \Rightarrow b & = \dfrac{x^2}{7}\end{aligned}$

Another way of writing them would be to go back a few steps and separate the fraction in x terms differently:

$\implies \dfrac{x^8 \cdot x^3}{x^6}=x^8 \cdot \dfrac{x^3}{x^6}=x^8 \cdot x^{-3}$

Therefore, this would give us:

$\begin{aligned}x^{8} &=3a \:\: &\textsf{ and }\:\: \quad x^{-3} &=7b\\ \Rightarrow a & = \dfrac{x^8}{3} & \Rightarrow b & = \dfrac{1}{7x^3}\end{aligned}$

As the given expression reduces to x⁵, we can separate the x term in any way we like, so long as the coefficient of a is ¹/₃ and the coefficient of b is ¹/₇. Therefore, there are many possible answers.

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OlgaM077 [116]

Answer:

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Step-by-step explanation:

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