3
votes
5answers
218 views

How do I solve this fraction addition problem?

$4\frac{2}{9} + -9\frac{1}{2}$ yeilds result of $-5\frac{13}{18}$ but WolframAlpha says the answer is $-5\frac{5}{18}$ fixed.
2
votes
4answers
67 views

How do you add two fractions?

I have a fraction I am trying to solve. I know the answer already, as Wolfram says it is $\frac{143}{300}$. The fraction is: $$\frac{5}{12} + \frac{3}{50} = \space ?$$ Please explain why and how your ...
0
votes
2answers
55 views

How do you solve this fraction?

The problem is : $ \frac{2}{3} + \frac{-1}{16} $ The answer I got was $ \frac{1}{48} $ . I believe it to be incorrect. Three does not divide into $16,$ so I cross multiplied. What am I doing wrong? ...
1
vote
1answer
69 views
+200

Is there a simple closed form of $|\alpha(\sqrt{n}-\left\lfloor \sqrt{n} \right \rfloor) + \beta(\sqrt{n}-\left\lfloor \sqrt{n} \right \rfloor)|$?

Let $d_n(x)$ denote the $n$'th digit after the decimal point in $x$. Examples: $d_8(e) = 2,\;d_5(\pi) = 9$ $\alpha(x)$ and $\beta(x)$ are defined this way: $$d_n(\alpha(x)) = \left\{ ...
3
votes
4answers
87 views

Is there an example to demonstrate why $\frac{1}{(1/2)}$ equals $2$?

To explain why $\frac{1}{2}=\frac{2}{4}$ I use slices of pizza and show how eating one slice of a pizza cut in half is the same thing as eating two slices of a pizza cut in quarters. Is there a way ...
1
vote
1answer
41 views

The elementary question on sign of Rational numbers

The under picture show that $$+\dfrac{8}{3}=\dfrac{+8}{3}$$ Similarly we can show $-\dfrac{8}{3}=\dfrac{-8}{3}.$ Now How do can show that $$-\dfrac{8}{3}=\dfrac{8}{-3}?$$
0
votes
2answers
25 views

multiply fraction with what number to get a whole number?

I'm solving some programming puzzle and it has come down to this: I've a fraction, say 12/13, and I need to multiply it with a smallest possible natural number (say x) to get a whole number. How do I ...
0
votes
1answer
35 views

Comparing Fractional Numbers

Does a formula exist for comparing two fractional numbers, without resolving to using anything other than integers and fractions? (Thus not real numbers). In other words: given $\dfrac{a}{b}$ and ...
26
votes
14answers
5k views

Logic behind dividing negative numbers

I've learnt in school that a positive number, when divided by a negative number, and vice-versa, will give us a negative number as a result.On the other hand, a negative number divided by a negative ...
2
votes
2answers
53 views

A property of proportions: if $a/b=c/d$, then $(ma+nb)/(pa+qb)$ is equal to $ (mc+nd)/(pc+qd)$

If $\large\frac{a}{b}=\frac{c}{d}$ how we can obtain $\displaystyle{\frac{ma+nb}{pa+qb}=\frac{mc+nd}{pc+qd}}$? I can get $\large\frac{ma}{qb}=\frac{mc}{qd}$ and $\large\frac{nb}{pa}=\frac{nd}{pc}$ , ...
1
vote
2answers
61 views

How do you simplify an algebraic expression?

Please explain how to simplify an expression that is similar to this one $\displaystyle\frac{a+3}{6}+\frac{a-4}{4}+\frac{a+2}{-3}$
4
votes
3answers
1k views

Can you give me a visual representation on 1/6 of 4/5 to get 4/30?

I'm trying to understand fractions more by using a visual representation, and I having a hard time making a visual representation of the 1/6 of 4/5 and getting a visual understandable representation ...
0
votes
1answer
52 views

Why is the word “of” equivalent to multiplying in fraction word problems?

I know this is a very easy problem, but I'm having a hard time getting my head around this concept, consider this example from a book. *Jerry bought a pie and ate 1⁄5 of it. Then his wife Doreen ate ...
1
vote
1answer
38 views

Why does $ \frac {a}{b}$ of $c$ means $ \frac {a}{b} \cdot c$ [closed]

Why does it multiply when the preposition "of" appears?
1
vote
1answer
35 views

My small theory…

It is given that 'a,b,c' are whole nos. Now 'a' is an odd no. while 'b' is an even no. Prove that:- a/b + c = x where 'x' is a fraction, equal to 'n/d' where n is an odd no. and d is an even no. and ...
-1
votes
2answers
35 views

How to solve fraction which is divided by decimal fraction [closed]

$$\dfrac{\;\;\;\frac{5}{12}\;\;\;}{\frac{0.25}{0.5}}=?$$ I need to solve this. I'm a beginner in math and I got a exam tomorrow...
0
votes
2answers
60 views

Rationalising the Surds

Please help me rationalise and simplify: $$ \frac{1}{\sqrt[3]{2} - 1} \ - \ \frac{2}{\sqrt{3} - 2} \ . $$ I have tried using the cube of the denominator and the square of the denominator on the ...
7
votes
2answers
218 views

Rationalizing the denominator 3

It is a very difficult question. How can we Rationalizing the denominator? $$\frac{2^{1/2}}{5+3*(4^{1/3})-7*(2^{1/3})}$$
0
votes
2answers
57 views

solve ratio word problem without algebra

Four gallons of yellow paint plus two gallons of red paint make orange paint. I assume this makes six gallons. So the ratio is 4:2, or 2:1. Question: how many gallons of yellow paint, and how many ...
1
vote
2answers
81 views

Converting fractions / decimals to percentages

Can someone show me the methodology on how to convert 1.2794 to a percentage form? If I multiply it by 100, I get 127.94%, which is the correct answer. I'm not really sure 'why' I multiplied it by ...
1
vote
4answers
133 views

change $0.684 210 526 3$ into a fraction

I am a non-mathematician who quit with math after middle school. Now I face a practical problem which I cannot solve. Suppose I want to turn $0.684 210 526 3$ into a fraction, how would I do that ...
0
votes
4answers
101 views

Why does $ \frac {\frac {1}{\sqrt{x}}}{x} = \frac {\sqrt{x}}{x^2} $?

A homework question recently asked for me to simplify: $\frac{1}{\sqrt{7}} \div {7}$ It's easy to see that this becomes $\frac{1}{7\sqrt{7}}$ But according to wolfram alpha this is also equal to ...
5
votes
4answers
3k views

What's the algebraic property where you can flip the fractions in an equation?

Earlier in algebra, we spent over 20 minutes trying to figure out $$ \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_e} \,\,\,\, \text{solve for }R_2 $$ when the teacher said "What you start out with is ...
1
vote
2answers
67 views

Calculating percentage to compensate for percent discount.

Missing something very basic here and cannot pin point it. We need to charge a client \$100 for a product. Let's say our payment processor charges us 10% on every transaction. We make this ...
0
votes
6answers
287 views

Why Not Define $0/0$ To Be $0$?

For every number $x$, $x\times 0=0$, hence $\dfrac{0}{0}$ can be any number! So $\dfrac{0}{0}$ "is knows as indeterminate" [1]. But what if we define it to be $0$? I already have an answer, but ...
1
vote
1answer
104 views

Simplifying square root with fraction

I'm not sure about this equality $$4(-3+\sqrt {15})/4)^2 = (9-6 \sqrt{15} +15)/4$$ Hope some one can enlighten me. I will be facing more of such fractions, please guide me on how to solve/simplify ...
0
votes
2answers
39 views

Percentage of Amounts

I'm studying and I'm not that sure how to answer this question. Is $97.1%$ $=$ $650,000,000$? I was going to find $2.9%$ of $650,000,000$ however this would be wrong as I would finding our the ...
2
votes
1answer
83 views

Percentage of an amount?

I'm totally confused, we were doing a question in class and there are two answers but I'm not sure why one works and the other one doesn't. For example; there are 6000 pandas now and over 10 years ...
6
votes
1answer
145 views

How to best understand Euclid's definition of equal ratios? How does it relate to Dedekind cuts?

This is something I've been wondering about. When I think of "ratios" $x/y$ and $z/w$ as being "equal", with $x$, $y$, $z$, and $w$ being real numbers, this means the results of dividing the real ...
0
votes
1answer
97 views

Finding percentage which is less

The number that is 50% greater than $60$ is what percentage less than the number that is 20% less than $150$ ? My try : I considered a number is 50% of $130$ which is greater than the $60$ and 20% ...
1
vote
4answers
102 views

Simplifying compound fraction: $\frac{3}{\sqrt{5}/5}$

I'm trying to simplify the following: $$\frac{3}{\ \frac{\sqrt{5}}{5} \ }.$$ I know it is a very simple question but I am stuck. I followed through some instructions on Wolfram which suggests that I ...
0
votes
2answers
324 views

Ratio - Basic Question

If ratio of A:B = 1:2 if it is doubled , should it be not 2:4 i see many problems where they are simply multiplying numerator by 2 please can some one explain
0
votes
4answers
86 views

breaking up fractions

I have these two fractions ${11 \over 31 }+{-11 \over 61}$ Adding them gives $330 \over 1891$ But how do I go back to the two fractions, once I've added them? I can get the denominators just by ...
17
votes
12answers
3k views

Why is $\frac{1}{\frac{1}{X}}=X$?

Can someone help me understand in basic terms why $$\frac{1}{\frac{1}{X}} = X$$ And my book says that "to simplify the reciprocal of a fraction, invert the fraction"...I don't get this because isn't ...
5
votes
1answer
283 views

Is it possible to rationalize a denominator containing two cube roots?

The fraction in question is $$-\frac{12}{\sqrt[3]{12\sqrt{849} + 108} - \sqrt[3]{12\sqrt{849} - 108}}$$ And was reached in calculating the solution to $x^4 - x - 1 = 0$. I've tried all the standard ...
1
vote
2answers
96 views

when the numerator is less than the denominator

when the numerator is less than the denominator the result is always between 0 and 1? for example if I have a number like x/y where x<y then the result will be ...
0
votes
2answers
109 views

When is a fraction simplified?

When is a fraction simplified? "A fraction is simplified if the numerator and denominator do not have any common factors other than 1." This is what I read on this website: ...
0
votes
2answers
95 views

Aproximate calculation in decimals

I am trying to refresh on precision of calculations. If we have the decimal fractions: $.234673$, $.322135$, $.114342$, $.563217$ each known to be correct to six figures why are each of the decimals ...
3
votes
2answers
832 views

How do I get the integer part of a number by using basic arithmetic?

While it is trivial to simply remove the fractional part of an irrational or rational number, and in programming I could just use the floor() or ...
0
votes
1answer
113 views

Find the set of all natural number that make $(n+1)/(n+3)$ reducible

Lets assume $d$ is a natural number which makes $(n+1)/(n+3)$ reducible, then $d|n+1$ and $d|n+3$. $d|[n+3-(n+1)] = d|2$ which means $d=1$ or $d=2$. $n+1$ and $n+3$ must be divisible by $2$ so all ...
2
votes
1answer
69 views

Fraction comparison and addition

On Monday, Leo memorizes $\frac{3}{5}$ of his trumpet solo. On Tuesday, he memorizes $\frac{1}{3}$ more. What fraction of his solo does he have left to memorize?
1
vote
3answers
63 views

Please explain how this ratio is being calculated

A,B and C are partners of a company. A receives $\frac{x}{y}$ of profit. B and C share the remaining profit equally among them. A's income increases by $I_a$ if overall profit increases from P% to ...
3
votes
3answers
89 views

How to combine ratios? If $a:b$ is $2:5$, and $c:d$ is $5:2$, and $d:b$ is $3:2$, what is the ratio $a:c$?

How would I go about solving this math problem? if the ratio of $a:b$ is $2:5$ the ratio of $c:d$ is $5:2$ and the ratio of $d:b$ is $3:2$, what is the ratio of $a:c$? I got $a/c = 2/5$ but that is ...
0
votes
1answer
429 views

Equivalency of percentage formulas

I know 3 methods for calculating percentages, one example, find 70% of 50: 1) 50/100 * 70 2) 70/(100/50) 3) 70/100 * 50 I do not undertand how this 3 methods can be equivalent, also conceptually ...
1
vote
1answer
91 views

Simplifying a fraction?

$$\frac {n-2}{n} \cdot \frac {n-3}{n-1} \cdot \frac {n-4}{n-2} \cdots \frac{2}{4} \cdot \frac{1}{3} = \frac {1}{n(n-1)}$$ Why is this true? Notice the denominators and numerators cancel out, but ...
1
vote
4answers
728 views

Fastest way to compare fractions

Which is the fastest method to compare the below fractions with minimum calculation possible and finding which is greatest and which the smallest?? $$\frac{26}{686},\quad \frac{48}{874},\quad ...
3
votes
1answer
95 views

How fast is a low denominator encountered, when using only mediants?

This question is (remotely) related to How to find a "simple" fraction between two other fractions?, but is not answered in that older post. Let $f_1=\frac{a}{b}$ and $f_2=\frac{c}{d}$ be ...
3
votes
1answer
100 views

Is there a direct proof of this inequality between quotients of integers?

Let $\frac{a}{b}$ and $\frac{c}{d}$ be two reduced fractions with $bc-ad > 1$ (and hence $\frac{a}{b} \lt \frac{c}{d}$) and $a,b,c,d$ positive. It is well known that there are integers $u,v$ ...
2
votes
1answer
298 views

How to calculate percentage of comment lines in a code?

I have a file within which I have 6 lines of code and 8 lines of comment. What's the formula to calculate how much percent of the whole file comments have?
3
votes
1answer
134 views

Ways to teach fractions

I'm tutoring elementary-level kids on equivalent fractions and am not doing a very good job of explaining it. I've tried using the example of a pizza or a pie and have shown them how they can come up ...