Questions tagged [fractions]

Questions on fractions, i.e. expressions (not values) of the form $\frac ab$, including arithmetic with fractions. Not to be confused with the tag (rational-numbers): fractions denote rational numbers, but the same rational number may be written in different ways as a fraction.

A fraction is simply an expression $\frac{a}{b}$, where $a$ and $b$ are typically integers (where $b\neq 0$). This tag may be used, when $a$ and $b$ are more general expressions or algebraic objects; however, consider adding a more specific tag also:

Fractions are distinct from rational numbers because they are a representation: $\frac 34$ and $\frac{30}{40}$ are different fractions that happen to represent the same rational number.

For arithmetic with fractions, this tag is appropriate along with .

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Find the water pumped to flowers using fractions.

A certain tank has water filled to $\frac{1}{5}$ of it's capacity. A persons opens a tap and allows the tank to fill upto to $\frac{3}{4}$ of it's capacity. Then he uses the water in the tank and finally $\frac{1}{3} $ water remains in the…
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How do I know that this is the LCD (Lowest Common Denominator)

When presented with the following expression : $$\frac{1}{(x+1)(x+2)}-\frac{2}{x+1}+\frac{3}{x+2}$$ I have used an online calculator to show me the LCD, which is : $$(x+2)(x+1)$$ Although I can work out the LCD for different algebraic expressions, I…
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Hard question simplify as much as possible following

$$\frac{x^3-49x}{ x^4-13x^3+50x^2-56x}$$ I get answer $\frac {x+3} {x-1}$ but my friend say it's wrong I dont understand please help me please greetings from russia
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Converting sum of individual fraction to a combined fraction

I have following scenario. I want this combined fraction $\frac{A+B+C}{X+Y+Z}$ But Some How I am a little unfortunate and have results in the form of $\frac AX$, $\frac BY$ and $\frac CZ$. How can I use this information to calculate the combined…
Edison
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How to come up with unit rate for 1 day when give 1.5 days?

Question: A gerbil drinks 2/3 of a water bottle every 1.5 days. Use a unit rate to discover how many water bottles the gerbil drinks in 5 days. When given problems like this before, I have used whole numbers and was easily able to figure out a unit…
Chloe
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Simplifying $\csc(\frac{5\pi }{12})$

I need to simplify $\csc(\frac{5\pi }{12})$ I got to the point $\frac{2 \sqrt[]{2} }{ \sqrt[]{3}+1}$ but I have to get to $\sqrt[]{6}-\sqrt[]{2}\}$ Could someone guide me the way?
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fraction multiplication with square root as the numerator

Can anyone explain how did the author arrived at the answer? I can do multiplication of fractions like 1/2 * 1/3 etc... but I stumbled at this question $$3/5 * \sqrt(3)/2 = 3/10 \sqrt3$$
ilovetolearn
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Determine fraction of inch from decimal

I am working with data for the width and height of books. The data is in decimal form, such as 7.563, which I need to display as a fraction: 7 9/16 in. The denominator can vary and the decimal value isn't always rounded the same. Here is some sample…
cantera
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Simplify $\frac{\frac{x+3}{x-6-2}}{\frac{x+3}{x-6+8}}$

$$\frac{\frac{x+3}{x-6-2}}{\frac{x+3}{x-6+8}}$$ How would I simplify this complex fraction? I know what the answer is, but I am just not sure how they got there. I have tried multiplying both sides by $(x-6)$ but I am getting $x^2-3x-18$? Any…
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Simplifying square numbers in a fraction (elementary school lol)

I have the following question in a practice booklet: If $\frac{2^{26} - 2^{23}}{2^{26} + 2^{23}}$ = $\frac{x}{9}$ What is $x$? I know the answer is 7 because it's easy enough when you manually figure out $2^{26}$ etc. but is there a faster way? Can…
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Fraction and Decimal: Reciprocal of x's non-integer

The reciprocal part of $x$'s non-integer decimal part equals $x+1$, and $x>0$. What is $x$? Solution: I tried this way- Let's $n$= integer part of $x$ $1/x-n = x+1$ or, $1=(x-n)(x+1)$ or, $1= x^2+x-nx-n$ or, $x^2+ (1-n)x -(n+1)=0$ but, stucked…
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Help with some algebra

Can anybody explain to me how they went from this $$y − y_1 = \frac{y_2 − y_1}{x_2 − x_1} (x − x_1)$$ to this. $$(y_1 − y_2 )·x − (x_1 − x_2)·y − (y_1 − y_2 )·x_1 + (x_1 − x_2)·y_1 = 0$$ Its confusing..
dranec
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Please help me understand this simple fraction

I got started learning about fractions a few days ago, The tutorial I'm using for this, is limited to fractions like this Now as I'm trying to find further exercices, I keep stumbling upon fraction-based problems that are built like this…
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Can fractions be written with a one under them and can problems be solved this way

How would you write $\frac{a}{0.1}$? Are either of these ways acceptable? $$ \frac{\frac{a}{1}}{\frac{\frac{1}{10}}{1}} = \frac{a}{1} \times \frac{1}{\frac{1}{10}} $$ or $$ \frac{\frac{a}{1}}{\frac{1}{10}} = \frac{a}{1} \times \frac{10}{1} $$
Jacob
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Why is the coefficient of a fraction $\frac{1}{denominator}$ instead of simply 1?

Why is the coefficient of a fraction $\frac{1}{denominator}$ instead of simply $1$? Wouldn't the result be the same?