3
Active contributors today

## How do you evaluate #22- 2( 13- 7+ 3)#?

Nathan
Featured 1 month ago

4

#### Explanation:

For this problem, we will need to have knowledge of the order of operations.

Parentheses
Exponents
Multiplication
Division
Subtraction.

In order from top to bottom.

..................................................................................................................

Using the order of operations we know that first we need to solve what is inside the parentheses.

$22 - 2 \left(13 - 7 + 3\right)$

$22 - 2 \left(6 + 3\right)$

$22 - 2 \left(9\right)$

..................................................................................................................

Now, we are going to do the multiplication, because that is before subtraction on our order of operations.

$22 - 2 \left(9\right)$

$22 - 18$

..................................................................................................................

Now, we just have to do basic subtraction.

$22 - 18 = 4$

This brings us to our final answer of 4.

## The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost$3.68. How do you find the cost of each?

Gió
Featured 4 weeks ago

I found:
Oranges: #$0.26# Apples: #$0.32#

#### Explanation:

Let us call the cost of oranges $O r$ and apples $A p$. We can write:

$12 O r + 7 A p = 5.36$
and
$8 O r + 5 A p = 3.68$

we can extract from the first:

$O r = \frac{5.36 - 7 A p}{12}$

we substitute this into the second equation for $O r$:

${\cancel{8}}^{2} \cdot \frac{5.36 - 7 A p}{\cancel{12}} ^ 3 + 5 A p = 3.68$

solve for $A p$:

$10.72 - 14 A p + 15 A p = 11.04$

$A p = 0.32$

use this value bach into the first equation:

$O r = \frac{5.36 - 7 A p}{12} = \frac{5.36 - 7 \cdot 0.32}{12} = 0.26$

## How do you write the prime factorization of 900?

sjc
Featured 3 weeks ago

$900 = 2 \times 2 \times 3 \times 3 \times 5 \times 5$

or$\text{ } 900 = {2}^{2} \times {3}^{2} \times {5}^{2}$

#### Explanation:

Split the number up into a product pair where one of them is a prime number, then split the remaining non-prime number up in the same way; continue until all the factors are prime numbers.

$900 = \textcolor{red}{2} \times 450$

$900 = \textcolor{red}{2 \times 2} \times 225$

$900 = \textcolor{red}{2 \times 2 \times 5} \times 45$

$900 = \textcolor{red}{2 \times 2 \times 5 \times 5} \times 9$

$900 = \textcolor{red}{2 \times 2 \times 5 \times 5 \times 3 \times 3}$

## How do you solve #(- 2) + ( - 8) + ( - 6)#?

Tony B
Featured 3 weeks ago

$- 16$

#### Explanation:

Sometimes the idea about subtraction is a little thought provoking.

$\textcolor{b r o w n}{\text{Very important fact}}$

The natural way to count on the number line is increasingly positive. Often drawn so that it is towards the right. The number line is the same sort of thing as the x-axis on a graph.

$\textcolor{b r o w n}{\text{Always think of starting to count to the right on the number line.}}$
$\textcolor{b r o w n}{\text{The minus sign means change direction of count}}$

$+ \text{ " -> "Count right}$
$- \text{ "-> "Reverse direction count so you count left}$

$- - \text{ "->"Reverse direction of count twice. You end up}$
$\text{ going in the positive direction}$

$\left(- 2\right) \to$ Count to the left

$+ \left(- 8\right) \to$ + is count right but the - instructs change direction. So you end up counting left. So this is the same as just $- 8$

$+ \left(- 6\right) \to$+ is count right but the - instructs change direction. So you end up counting left. So this is the same as just $- 6$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it all together}}$

$\left(- 2\right) + \left(- 8\right) + \left(- 6\right) \text{ "->" } - 2 - 8 - 6 = - 16$

## How do you evaluate #16\div ( 0.8\div 0.04)#?

Tony B
Featured 2 weeks ago

$\frac{4}{5} = 0.8$

#### Explanation:

$\textcolor{b l u e}{\text{Step 1}}$

Do the brackets first so we have: $0.8 \div 0.04$

$\textcolor{g r e e n}{\frac{0.8}{0.04} \equiv \frac{0.8}{0.04} \textcolor{red}{\times 1} \text{ " =" } \frac{0.8}{0.04} \textcolor{red}{\times \frac{100}{100}}}$

$\text{ "=" } \textcolor{g r e e n}{\frac{80}{4} = 20}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Step 2}}$

Divide the contents of the brackets into the 16 giving

$\text{ } \textcolor{g r e e n}{\frac{16}{20} \equiv \frac{16 \textcolor{red}{\div 4}}{20 \textcolor{red}{\div 4}} = \frac{4}{5}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Step 3}}$

Make the answer the same format as the question which is decimal.

$\textcolor{b r o w n}{\text{Notice that the denominator of 20 in "16/20" is } 2 \times 10}$

#" "color(green)(16/20-=(16color(red)(-:2))/(20color(red)(-:2)) = 8/10 = 0.8#

## Name four fractions whose value are between 1/5 and 1/3?

Don
Featured yesterday

there are an infinite amount of answers but here are some:

$\frac{13}{60}$

$\frac{7}{30}$

$\frac{15}{60}$

$\frac{4}{15}$

#### Explanation:

first let's find a common denominator just to make the problem easier.

$\frac{1}{5}$ = $\frac{3}{15}$ = .2

$\frac{1}{3}$ = $\frac{5}{15}$ = .333333333333

so essentially we want to find numbers larger than $\frac{3}{15}$ and smaller than $\frac{5}{15}$.. . so $\frac{4}{15}$ would be a great place to start. actually $\frac{4}{15}$ could actually be one of your answers.

but let's have some fun with these numbers.

$\frac{3}{15}$ = $\frac{6}{30}$ = $\frac{12}{60}$ we get this from multiplying the numerator and denominator by the same number (2).

$\frac{5}{15}$ = $\frac{10}{30}$ = $\frac{20}{60}$ we get this from multiplying the numerator and denominator by the same number (2).

So to rephrase the question:
find 4 fractions between $\frac{12}{60}$ and $\frac{20}{60}$

Here they are:

$\frac{13}{60}$

$\frac{14}{60}$ this is the same as $\frac{7}{30}$

$\frac{15}{60}$

$\frac{16}{60}$ this is the same as the $\frac{4}{15}$ we saw earlier

also. . .

$\frac{17}{60}$

$\frac{18}{60}$

$\frac{19}{60}$

we can check by converting to decimal and seeing if the number is larger than .2 and smaller than .3333

when i put 13/60 in my calculator it says .21666 so I know it's right because
.2 < .216 < .333

##### Questions
• · 2 days ago
• · 2 days ago
• · 2 days ago
• · 2 days ago
• · 2 days ago
• · 2 days ago
• · 2 days ago
• · 2 days ago
• · 2 days ago
• · 2 days ago
• · 2 days ago
• · 3 days ago
• · 3 days ago
• · 3 days ago · in Square Root
• · 3 days ago
• · 3 days ago
• · 3 days ago
• · 3 days ago · in Ratios and Proportions
• · 4 days ago · in Negative Numbers
• · 4 days ago
• · 4 days ago · in Rates
• · 4 days ago · in Order of Operations
• · 4 days ago · in Rates
• · 5 days ago
• · 5 days ago · in Scientific Notation
• · 5 days ago
• · 5 days ago
• · 5 days ago · in Unit Conversions
• · 6 days ago
• · 6 days ago · in Unit Conversions
• 6 days ago · in Absolute Value
• · 6 days ago
• · 6 days ago
• · 6 days ago · in Rates
• · 6 days ago · in Comparing Fractions
• · 6 days ago · in Comparing Fractions
• · 6 days ago · in Prime Factorization
• 1 week ago
• · 1 week ago · in Exponents
• · 1 week ago
• · 1 week ago