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## How do you simplify (5/6)/(1 1/4)?

Shwetank Mauria
Featured 2 months ago

$\frac{\frac{5}{6}}{1 \frac{1}{4}} = \frac{2}{3}$

#### Explanation:

Let us first convert mixed fraction $1 \frac{1}{4}$ into improper fraction

$1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}$

Now dividing by a fraction $\frac{a}{b}$ is equivalent to multiplying by its reciprocal $\frac{b}{a}$

Hence $\frac{\frac{5}{6}}{1 \frac{1}{4}}$

= $\frac{\frac{5}{6}}{\frac{5}{4}}$

= $\frac{5}{6} \times \frac{4}{5}$

= $\frac{\cancel{5}}{{\cancel{6}}^{3}} \times \frac{{\cancel{4}}^{2}}{\cancel{5}}$

= $\frac{2}{3}$

## Jessica bought 3/4 lb of berries. Mary bought 1/6 lb of berries less than Jessica. Help?

Tony B
Featured 2 months ago

$A \to \text{ Mary bought } \frac{7}{12} p o u n \mathrm{ds}$
$B \to \text{Total weight bought is } 1 \frac{1}{3} p o u n \mathrm{ds}$

Solution given in a lot of detail.

#### Explanation:

$\textcolor{b l u e}{\text{Important facts}}$

A fraction's structure is that of:

$\left(\text{count")/("indicator of size of what you are counting")->("numerator")/("denominator}\right)$

You can not $\underline{\text{directly}}$ add or subtract the 'counts' unless the size indicators are the same.

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way something looks without changing its true value.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering question A}}$
Badly worded but you will get my point.

$M a r y = J e s s i c a - \frac{1}{6}$

$M a r y = \frac{3}{4} - \frac{1}{6} \leftarrow \text{ in pounds}$

Note that both 4 and 6 will divide exactly into 12

color(green)(Mary=[3/4color(red)(xx1)]-[1/6color(red)(xx1)]

color(green)(Mary=[3/4color(red)(xx3/3)]-[1/6color(red)(xx2/2)]

$\textcolor{g r e e n}{M a r y = \text{ "9/12" "-" } \frac{2}{12}}$

$9 - 2 = 7$ giving

$M a r y = \frac{7}{12} p o u n \mathrm{ds}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering question B}}$

Total weight bought $= \frac{3}{4} + \frac{7}{12}$

color(green)("Total weight bought "=[3/4color(red)(xx1)]+7/12

color(green)("Total weight bought "=[3/4color(red)(xx3/3)]+7/12

$\text{Total weight bought } = \frac{9}{12} + \frac{7}{12} = \frac{16}{12} p o u n \mathrm{ds}$

but 4 will divide exactly into both 16 and 12

$\frac{16}{12} \equiv \frac{16 \div 4}{12 \div 4} = \frac{4}{3} = 1 \frac{1}{3}$

Total weight bought is $1 \frac{1}{3} p o u n \mathrm{ds}$

$\frac{1}{3}$ as a decimal is not precise so leave it in fraction form

## Aunt Carol's peanut brittle recipe calls for 1/3 pound of peanuts per batch. If she makes 8 batches, how many pounds of peanuts will she use?

EZ as pi
Featured 3 weeks ago

$\frac{8}{3} = 2 \frac{2}{3}$ pounds

#### Explanation:

The maths involved in questions like these is usually very easy. It is more about understanding the information given and the question asked, and then deciding which operation to do.

We are told that $1$ batch needs $\frac{1}{3}$ of a pound of peanuts
She is going to make $8$ batches, each one needs $\frac{1}{3}$ pound.

It is a multiplication:

$\frac{1}{3} \times 8$

$= \frac{1}{3} \times \frac{8}{1} \text{ } \leftarrow$ nothing cancels, multiply straight across

$= \frac{8}{3}$

This would be easier to say in everyday language as $2 \frac{2}{3}$ pounds

## A piece of cardboard had 2/5 of its usable area cut off. How much of the original piece of cardboard remains?

smendyka
Featured 3 weeks ago

A whole piece of cardboard is $\frac{5}{5}$ or 1 piece of cardboard.

If $\frac{2}{5}$ was taken away we can subtract this from the original piece giving:

$\frac{5}{5} - \frac{2}{5} = \frac{5 - 2}{5} = \frac{3}{5}$

$\frac{3}{5}$ of the piece of cardboard is left.

## Five eighths of 24?

Moksha
Featured 1 week ago

Five eighths of 24 is 15!

#### Explanation:

Lets makes this question into an equation. You may be thinking,"But it's already an equation? Isn't it?" Well no, it's not an equation yet. An equation is like, $2 + 2$ or something like that. So now let's make it into an equation, then!

5 eighths means $\frac{5}{8}$ and the word of in any math problem means the multiplication symbol, $\times$.

Before: What is five eights of 24?
After: 5/8times24=?

Don't you think we made the problem way easier? Anyways lets solve our equation and get our answer!

$8$ goes into $24$, 3 times. Therefore, now our our equation is $5 \times 3$! And what is the answer to $5 \times 3$? It's $15$!

So the answer to "Five eighths of 24?" aka 5/8times24=? is $15$!

My source is my knowledge! :)

$$                                       Answer Written by: Moksha


## 0.054 with 54 repeating as a decimal?

smendyka
Featured 3 days ago

Think you want this as a fraction as it is already a decimal.

See a solution process below:

#### Explanation:

First, we can write:

$x = 0.0 \overline{54}$

Next, we can multiply each side by $100$ giving:

$100 x = 05.4 \overline{54}$

Then we can subtract each side of the first equation from each side of the second equation giving:

$100 x - x = 5.4 \overline{54} - 0.0 \overline{54}$

We can now solve for $x$ as follows:

$100 x - 1 x = \left(5.4 + 0.0 \overline{54}\right) - 0.0 \overline{54}$

$\left(100 - 1\right) x = 5.4 + 0.0 \overline{54} - 0.0 \overline{54}$

$99 x = 5.4 + \left(0. \overline{054} - 0.0 \overline{54}\right)$

$99 x = 5.4 + 0$

$99 x = 5.4$

$\frac{99 x}{\textcolor{red}{99}} = \frac{5.4}{\textcolor{red}{99}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{99}}} x}{\cancel{\textcolor{red}{99}}} = \frac{10 \times 5.4}{10 \times 99}$

$x = \frac{54}{990}$

$x = \frac{18 \times 3}{18 \times 55}$

$x = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{18}}} \times 3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{18}}} \times 55}$

$x = \frac{3}{55}$

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