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 .

2981 questions
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Fraction Decomposition

I have the following problem: Suppose $x + y + z = 0$. Show that $$\frac{x^5 + y^5 + z^5}{5}= \frac{x^3 + y^3 + z^3}{3} \times \frac{x^2 + y^2 + z^2}{2}$$ and $$\frac{x^7 + y^7 + z^7}{7}= \frac{x^2 + y^2 + z^2}{2} \times \frac{x^5 + y^5 +…
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Proof from adding and subtracting fractions

In adding or subtracting fractions with two or more terms, the resulting denominator is always the product of the denominators of the terms. Can someone prove or disprove this statement. I'm pretty sure this isn't true, but I don't know how to…
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How to sum up these fractions?

Found this question in a competitive math test for elementary students. The long way is to add all the decimal values but is there a pattern/trick to solve this question (or these types)? I don't know how to solve this except by the long method of…
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Evaluate $1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{...}}}}$ when you see $15$ fraction lines

Evaluate $1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{\ddots}}}}$ when you see $15$ fraction lines. I have solved this problem but using a quater calculating I come from down to up 15 times and found the answer $\frac{987}{610}$. And the time of…
Taha Akbari
  • 3,559
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How to articulate where the extra 1 came in this easy question

"Albert owns 5/9ths of the stock in the North West Chocolate Company. His sister, Rena, owns half as much stock as Albert. What part of stock is owned by NEITHER Albert nor Rena?" The answer is obviously 1/6 (or 3/18). However, a friend reasoned:…
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Unit Fraction Addition

My teacher challenged us: "Can you express the fraction $55\over 108$ as the sum of two unit fractions$?$" I figured out that ${1\over 54} + {1\over 2} = {56\over 108}$ but I could not figure out a way to get $55\over 108$ as a sum of two unit…
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SAT math problem about solute and solution

There are two solutions $P$ and $Q$. There are $50 g$ of $P$, which has $30\%$ benzene by mass, and $200 g$ of $Q$, which has $70\%$ benzene by mass. If $20 g$ of solution $P$ is added to $20 g$ of solution $Q$, what is the percent of benzene by…
Amber
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How to solve for $x$ in ${\sqrt{9+2x}} - {\sqrt{2x}} = \frac{5}{\sqrt{9+2x}}$

How can I solve for $x$ in the following equation? ${\sqrt{9+2x}} - {\sqrt{2x}} = \frac{5}{\sqrt{9+2x}}$
celis
  • 55
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Integers and fractions

How would I write this as an integer or a fraction in lowest terms? $(1-\frac12)(1+\frac 12)(1-\frac13)(1+\frac13)(1-\frac14)(1+\frac14).....(1-\frac1{99})(1+\frac1{99})$ I really need to understand where to start and the process if anyone can help…
SNS
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Multiplying fractions to answer story problems.

My daughter had a math question about finding how far someone walked using multiplication of fractions. The distance was $1 \frac 78$ and he walked $\frac 23$ of the way. The problem wanted to know how far he walked. How does multiplying…
lizanne
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Simplify $\frac{x}{c} - \frac{x}{c-d}$

There's a long time that I don't solve questions like this one. I'm having problems to simplify this one: $$\frac{x}{c} - \frac{x}{c-d}$$
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can fractions be done on a regular caculator?

I am wondering if I can use me standard calculator to solve fraction problems which include: adding, subtracting, multiplying, and dividing fractions, or do I need to buy a scientific calculator to solve them?
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Simplifying fraction with square root as denominator

I'm trying to find the integral of: $$\dfrac {2\sqrt{x} - 3x + x^2}{\sqrt{x}}$$ but I first need to simplify it so I tried dividing by the $\sqrt{x}$ for each of the numbers on the top like so: $$\dfrac {2\sqrt{x}}{\sqrt{x}}$$ and did the same for…
jn025
  • 989
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If you add the same constant to the numerator and denominator, what is the relation between the new fraction and the original fraction?

If I add a constant $\varepsilon < 1$ to the numerator and denominator of a fraction, is the new fraction always greater than the original? That is, do I have $$ \frac{a}{b} \leq \frac{a+\varepsilon}{b+\varepsilon},\ \forall a,b\in\mathbb{R} $$
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Suggested formula for curving test results

Take a test score represented by the fraction ${a\over b}$. This test score could be curved by removing a wrong answer to get ${a\over b-1}$ or adding a correct answer to get ${a+1\over b+1}$. Sometimes the former will cause a greater increase to…