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## Question #95a26

Daniel L.
Featured 2 months ago

See explanation.

#### Explanation:

To compare 2 fractions we have to find their (lowest) common denominator (i.e. the number both denominators can be changed to by multiplying or dividing numerator and denominator by the same number)

Here the fractions are $\frac{6}{9}$ and $\frac{4}{6}$the first fraction can be reduced by $3$:

## $\frac{6}{9} = \frac{2 \cdot \cancel{3}}{3 \cdot \cancel{3}} = \frac{2}{3}$

The second fraction can be reduced by $2$:

## $\frac{4}{6} = \frac{2 \cdot \cancel{2}}{3 \cdot \cancel{2}} = \frac{2}{3}$

Both numbers are reduced to the same fraction $\frac{2}{3}$, so they are equal:

## Question #364e9

John D.
Featured 1 month ago

$3.99 \times {10}^{-} 6$

#### Explanation:

Since all of these numbers are in scientific notation, we can determine which one is the smallest by looking at the exponents.

The number with the smallest exponent is the smallest number.

In this case, the smallest exponent is $\textcolor{red}{- 6}$

Therefore, the smallest number is $3.99 \times {10}^{\textcolor{red}{- 6}}$

## Question #dfce0

sjc
Featured 1 month ago

#1%rarr1/100#

#### Explanation:

#1%#mean 1 out of $100$

so as a common fraction

#1%rarr1/100#

## Question #aeca4

Nimo N.
Featured 1 month ago

See below.

#### Explanation:

The sum of the quotient of a number and 3 and 8 is 16."

One needs to translate from English to mathematics symbols. Sometimes, the words can be translated directly, piece by piece, from left-to-right, then the parts can be put together.

This one is one of those "left-to-right." translations:
$\left(\text{the first thing") + ("the second thing}\right)$

"is" translates to "=". So,
$\textcolor{b l u e}{\left(\text{the first thing") + ("the second thing}\right) = 16}$.

Using "x" for everything can make the eyes sore, so here we use "N" for the unknown Number.

the first thing:
"the quotient of a number and 3". Since "quotient of" means divide the first thing mentioned (an unknown number, N) by the second thing mentioned (3).
$N \div 3 = \frac{N}{3}$

We can fill-in part of the expression:
$\textcolor{b l u e}{\left(\frac{N}{3}\right) + \left(\text{the second thing}\right) = 16}$

the second thing:
The second thing being added is 8.

Now, finish the translation with a full equation:
$\textcolor{red}{\frac{N}{3} + \left(8\right) = 16}$

To solve the math problem, subtract 8 from both sides of the equation, then multiply both sides of the result by 3.

You should get: # color(red)( N = 24 #.

## Question #27b67

EZ as pi
Featured 1 month ago

The prime factors of $1400 \text{ are } 2 , 5 , 7$

$1400 = 2 \times 2 \times 2 \times 5 \times 5 \times 7$

#### Explanation:

The intention of the question is not absolutely clear....

Is it asking which of the factors of $1400$ are prime numbers?

Or

Is it asking for $1400$ to be written as the product of its prime factors.

It will help to write $1400$ as the product of its prime factors anyway..

Divide $1400$ by prime numbers which are factors until you get $1$

$2 | \underline{\textcolor{w h i t e}{.} 1400}$
$2 | \underline{\text{ } 700}$
$2 | \underline{\text{ } 350}$
$5 | \underline{\text{ } 175}$
$5 | \underline{\text{ } 35}$
$7 | \underline{\text{ } 7}$
$\textcolor{w h i t e}{. . w w \ldots} 1$

The prime factors of $1400 \text{ are } 2 , 5 , 7$

As the product of its prime factors:

$1400 = 2 \times 2 \times 2 \times 5 \times 5 \times 7$

## How you test 69,902 for divisibility by 2, 3, 5, 9, or 10?

Shwetank Mauria
Featured 1 week ago

$69902$ is divisible only by $2$ and not by $3 , 5 , 9$ or $10$. Please see below for details.

#### Explanation:

Divisibility by $2$ can be tested by checking the digit at unit's place. If we have $0 , 2 , 4 , 6$ or $8$ at unit's place, then the number is divisible by $2$. Here we have $2$ at unit's place in $69902$, and hence it is divisible by $2$.

Divisibility by $3$ can be tested by checking that sum of all the digits is divisible by $3$ or not. Here sum of digit's in $69902$ is $6 + 9 + 9 + 0 + 2 = 26$, which is not divisible by $3$, therefore $69902$ is not divisible by $3$.

Divisibility by $5$ can be tested by checking the digit at unit's place. If we have $0$ or $5$ at unit's place, then the number is divisible by $5$. Here we have $2$ at unit's place in $69902$, and hence it is not divisible by $5$.

Divisibility by $9$ can be tested by checking that sum of all the digits is divisible by $9$ or not. Here sum of digit's in $69902$ is $6 + 9 + 9 + 0 + 2 = 26$, which is not divisible by $9$, therefore $69902$ is not divisible by $9$. Note that if a number is not divisible by $3$, it is also not divisible by $9$.

Divisibility by $10$ can be tested by checking the digit at unit's place. If we have $0$ at unit's place, then the number is divisible by $10$. Here we have $2$ at unit's place in $69902$, and hence it is not divisible by $10$.

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