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## How do you simplify 3/9?

EZ as pi
Featured 1 month ago

$\frac{3 \div 3}{9 \div 3} = \frac{1}{3}$

#### Explanation:

You can simplify a fraction if you multiply or divide the numerator and denominator by the same number.

This is the same as multiplying or dividing by $1$, which does not change the value of the fraction, but creates an equivalent fraction.

in $\frac{3}{9}$, both $3 \mathmr{and} 9$ have $3$ as a factor. Divide both by $3$

$\frac{3 \div 3}{9 \div 3} = \frac{1}{3}$

## Angel has a job finding golf balls. He is paid $3 an hour and$3.25 for any ball he finds. If he finds an average of 15 balls an hour, he earns $160.25 for one day. How many hours did he work? smendyka Featured 4 weeks ago #### Answer: See a solution process below: #### Explanation: A formula for this problem can be written as: $e = \left(p \cdot h\right) + \left(r \cdot b\right)$Where: $e$iw Angel's earnings:$160.25 for this problem.

$p$ is Angel's hourly pay rate: $3 per hour for this problem. $h$is the number of hours Angel worked: What we are solving for in this problem. $r$is the rate Angel is paid for each ball found:$3.25 for this problem.

$b$ is the number of balls found. For this problem we are told Angel found 15 balls per hour so we can write this as: $\left(\frac{15}{\text{hr}} \cdot h\right)$

Substituting and solving for $h$ gives:

$160.25 = (($3)/"hr" * h) + ($3.25 * (15/"hr" * h)) $160.25 = (($3)/"hr" * h) + ($3.25 * 15/"hr" * h)

$160.25 = (($3)/"hr" * h) + (($48.75)/"hr" * h) $160.25 = (($3)/"hr" + ($48.75)/"hr")h

$160.25 = ($51.75)/"hr"h

$160.25 xx color(red)("hr")/(color(red)($)color(blue)(51.75)) = ($51.75)/"hr"h xx color(red)("hr")/(color(blue)($)color(blue)(51.75))

color(blue)(cancel(color(black)($)))160.25 xx color(red)("hr")/(cancel(color(blue)($))color(blue)(51.75)) = color(blue)(cancel(color(black)($51.75)))/color(red)(cancel(color(black)("hr")))h xx cancel(color(red)("hr"))/cancel((color(blue)($)color(blue)(51.75)))

$\frac{160.25 \text{hr}}{\textcolor{b l u e}{51.75}} = h$

$3.1 \text{hr} = h$

Angel worked 3.1 hours rounded to the nearest tenth of an hour.

## Which numbers below are prime numbers and which are composite?

Angelina S.
Featured 4 weeks ago

Composite means it has more than two factors
Prime means that it only has one factor that it is itself and one

#### Explanation:

Composite - 25,12,21,15
Prime- 19,41

Factors of 25
5,1,25

Factors of 12
1,2,3,4,6,12

Factors of 21
1,3,7,21

Factors of 15
1,3,5,15

Factors of 19
1,19

Factors of 41
1,41

## What is the LCM of 8, 7, and 12?

VviantheDancer
Featured 4 weeks ago

168.

## What's the greatest common factor of 40 and 42?

smendyka
Featured 1 week ago

See a solution process below:

#### Explanation:

Find the prime factors for each number as:

$40 = 2 \times 2 \times 2 \times 5$

$42 = 2 \times 3 \times 7$

Now identify the common factors and determine the GCF:

$40 = \textcolor{red}{2} \times 2 \times 2 \times 5$

$42 = \textcolor{red}{2} \times 3 \times 7$

Therefore:

$\text{GCF} = \textcolor{red}{2}$

## What is the lowest common multiple of 12,18 and 45?

David Drayer
Featured 2 days ago

180

#### Explanation:

Find the unique prime factors for each number and multiply the factors together.

$12 = 2 \times 2 \times 3$
$18 = 2 \times 3 \times 3$
$45 = 5 \times 3 \times 3$

There are two factors of 2 needed ( the factor of 2 for 18 is a repeat.)

There are two factors of 3 needed ( the factors of 3 in 12 and 45 are repeats.)

There is one unique factor of 5

Multiplying the non repeated or unique factors gives.

The Least Common Multiply $= 2 \times 2 \times 3 \times 3 \times 5$

$2 \times 2 \times 3 \times 3 \times 5 = 180$

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