Evaluate 7*15-8+6*6*9.

Matilda Webb
2022-05-09
Answered

Evaluate 7*15-8+6*6*9.

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empatteMattmkezo

Answered 2022-05-10
Author has **12** answers

Simplify each term.

$105-8+324$

Simplify by adding and subtracting.

$421$

asked 2022-03-12

When is the lcm of a fraction sum the actual denominator.

Consider a sum

$\frac{a}{b}+\frac{c}{d}=\frac{x}{y}$

where each fraction is reduced. Alternatively using the familiar process of lowest common denominators, we have

$\frac{a}{b}+\frac{c}{d}=\frac{a\cdot \frac{d}{(b,d)}+c\cdot \frac{b}{(b,d)}}{\begin{array}{cc}b& d\end{array}}$

where$(b,d)$ denotes the gcd and $[b,d]$ denotes the lcm. My question is, when is it true that $y=[b,d]$ ? For example, this does not hold for

$\frac{5}{6}+\frac{1}{14}=\frac{38}{42}=\frac{19}{21}$

where$21\ne \text{}[14,6]$

Are there any simple necessary and sufficient conditions for$y=[b,d]$ ?

Edit It has been suggested that

$y=[b,d]\iff (b,d)=1$

is a necessary and sufficient condition. I'm interested in either a proof or a counterexample if possible.

Edit 2 After a bit of searching, I've found

$\frac{1}{24}+\frac{1}{16}=\frac{5}{48}$

as a counterexample.

I am still looking for nice conditions for this to be satisfied and I feel that I should give an explanation of exactly what type of condition I am seeking. Angela has provided a necessary and sufficient condition, but it does not seem to be "simpler" than simply adding the fraction and seeing if it reduces. This is perhaps ambitious, but I am looking for a condition which is simple enough to use by inspection for simple fractions.

Consider a sum

where each fraction is reduced. Alternatively using the familiar process of lowest common denominators, we have

where

where

Are there any simple necessary and sufficient conditions for

Edit It has been suggested that

is a necessary and sufficient condition. I'm interested in either a proof or a counterexample if possible.

Edit 2 After a bit of searching, I've found

as a counterexample.

I am still looking for nice conditions for this to be satisfied and I feel that I should give an explanation of exactly what type of condition I am seeking. Angela has provided a necessary and sufficient condition, but it does not seem to be "simpler" than simply adding the fraction and seeing if it reduces. This is perhaps ambitious, but I am looking for a condition which is simple enough to use by inspection for simple fractions.

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Is .6 a rational number?

asked 2022-04-15

manipulation of subtraction

I am trying to solve an induction problem and got stuck at this part.

$1-\frac{n+2}{(n+2)!}+\frac{n+1}{(n+2)!}=1-\frac{(n+2)-(n+1)}{(n+2)!}$

Shouldn't it be

$1-\frac{n+2}{(n+2)!}+\frac{n+1}{(n+2)!}=1-\frac{(n+2)+(n+1)}{(n+2)!}$

How do you get the left expression to the right expression?

I am trying to solve an induction problem and got stuck at this part.

Shouldn't it be

How do you get the left expression to the right expression?

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For Exercise, solve the equation.

$\frac{x+3}{5x}+2=\frac{x-4}{x}$

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Convert 25%, 50%, 75%, and 100% to fractions. Do you notice a pattern? Explain what the pattern is.

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In the following exercises, approximate the(a) circumference and (b) area of each circle. If measurements are given in fractions, leave a answer in fraction form.

radius$=18.6m$

a) Approximate the circumference of circle with radius 18.6m.

b) Approximate the area of circle with radius 18.6m.

radius

a) Approximate the circumference of circle with radius 18.6m.

b) Approximate the area of circle with radius 18.6m.

asked 2021-11-14

Solve the equation. Express number as integers or simplified fractions.

$\frac{1}{12}x-\frac{1}{4}=-\frac{1}{8}x+\frac{3}{2}+\frac{3}{8}x$