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3 years ago

Write each fraction as the sum of a whole number and a fraction less than 1

Mathematics

1 answer:

Tpy6a [65]3 years ago

7 0

Given:

The fractions are:

$\dfrac{6}{5},\dfrac{11}{7},\dfrac{21}{4}$

To find:

The each fraction as the sum of a whole number and a fraction less than 1.

Solution:

The given fraction is $\dfrac{6}{5}$ .

$\dfrac{6}{5}=\dfrac{5+1}{5}$

$\dfrac{6}{5}=\dfrac{5}{5}+\dfrac{1}{5}$

$\dfrac{6}{5}=1+\dfrac{1}{5}$

Therefore, the given fraction $\dfrac{6}{5}$ can be written as $1+\dfrac{1}{5}$ .

The given fraction is $\dfrac{11}{7}$ .

$\dfrac{11}{7}=\dfrac{7+4}{7}$

$\dfrac{11}{7}=\dfrac{7}{7}+\dfrac{4}{7}$

$\dfrac{11}{7}=1+\dfrac{4}{7}$

Therefore, the given fraction $\dfrac{11}{7}$ can be written as $1+\dfrac{4}{7}$ .

The given fraction is $\dfrac{21}{4}$ .

$\dfrac{21}{4}=\dfrac{20+1}{4}$

$\dfrac{21}{4}=\dfrac{20}{4}+\dfrac{1}{4}$

$\dfrac{21}{4}=5+\dfrac{1}{4}$

Therefore, the given fraction $\dfrac{21}{4}$ can be written as $5+\dfrac{1}{4}$ .

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3 years ago

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3 years ago

Let a, b, c and x elements in the group G. In each of the following solve for x in terms of a, b, and c.

alina1380 [7]

Answer:

The answer is $x=a^{-1}cb^{-1}$ .

Step-by-step explanation:

First, it is important to recall that the group law is not commutative in general, so we cannot assume it here. In order to solve the exercise we need to remember the axioms of group, specially the existence of the inverse element, i.e., for each element $g\in G$ there exist another element, denoted by $g^{-1}$ such that $gg^{-1}=e$ , where $e$ stands for the identity element of G.

So, given the equality $axb=c$ we make a left multiplication by $a^{-1}$ and we obtain:

$a^{-1}axb =a^{-1}c.$

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Now, in the equality $xb = a^{-1}c$ we make a right multiplication by $b^{-1}$ , and we obtain

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$x=a^{-1}cb^{-1}$ .

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3 years ago

Factor the algebraic expression. 40a+5

Vitek1552 [10]

Answer:

5 (8a + 1)

Step-by-step explanation:

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3 years ago

A rectangular solid and a cube are of equal volume. If the rectangular solid is 20 centimeters long, 5 centimeters wide, and 10

abruzzese [7]

Answer:

10 centimeters.

Step-by-step explanation:

First, we need to remember what's the formula to get the volume of a rectangular solid and a cube.

The volume of the first equals:

Volume = Length x Width x Height

While the volume of the cube is:

$Volume = a^{3}$ where a is the edge.

We are given the measures of the rectangular solid so we can calculate its volume:

$Volume= (20)(5)(10)=1000$ cubic cms.

Now, we know that both the volume of the rectangular solid and the cube are the same so we will use this information to calculate the edge of the cube.

$1000=a^3 \\\sqrt[3]{1000} =\sqrt[3]{a^3} \\10=a$

Thus the length of an edge of the cube is 10 centimeters

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3 years ago