Boost Your Pre-Algebra Skills with Examples and Solutions

High School
Algebra
Pre-Algebra

Compose a number expression and find its value quotient from dividing the sum of the numbers 4/9 and - 5/6 by the number - 14/27 difference between the product of the sum and the difference of the numbers -1.5 and 4 and the number 2 product of sum and difference of numbers -1.9 and 0.9 cube of difference between numbers 6 and 8.

ghulamu51 2022-09-14

The temperature in Hillsville was $20^{\circ}$ Celsius. What is the equivalent of this temperature in degrees Fahrenheit?

maredilunavy 2022-09-14

minimum value of $f (x)$ without the use of derivative
Although I have solved it using derivative. But did not understand how can i solve
without derivative, Help Required, Thanks

babuliaam 2022-09-14

Convert the following as instructed
1.) Change 3 oz to Tablespoons
2.) Change 12 tsps to Tablespoons
3.) Change 45 ml to tsps.
4.) Change 2 Tablespoons to ml
5.) Change 5 Tablespoons to tsp

profesorluissp 2022-09-14

Can we divide two terms in finding solution for Linear Inequalities?
Solve the following inequality.
$\frac{| x - 2 |}{x - 2} > 0$
If x is greater than or equal to 2, it becomes: $\frac{x - 2}{x - 2} > 0$ , which can become $1 > 0$ , which is true for all $x > 2$ for when $x = 2$ ,its value will become undefined. Is my solution correct?

albiguguiismx 2022-09-14

Identify the domain of the following rational expression: $\frac{x + 4}{x^{2} + x - 12}$

manudyent7 2022-09-14

Dividing by Fractions in Algebra
You can divide by a fraction by multiplying by its reciprocal (i.e. $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ ). Given the equation $\frac{1}{2} x = 5$ , intuitively, you could either multiply both sides by two or divide both sides by $\frac{1}{2}$ . Both of these solutions give the same result, $x = 10$
My maths teacher says that, when showing your work, you can only multiply by two. Subjectively, this is simpler. Is this an accepted rule, or is it just personal preference?
P.S. One of my previous teachers did teach to divide by fractions in this case.

Jaylen Dudley 2022-09-14

Integer expression
Expression
$\frac{a}{b + c} + \frac{b}{a + c} + \frac{c}{a + b}$
takes an integer value $2$ when $a = t, b = t, c = 3 t$ . Are there any other integer values of variables for integer value of expression?

batystowy2b 2022-09-14

I'm trying to prove that the best moment tail bound is no worse than the best Chernoff bound. I have all pieces other than this little frustration here:
If $c \leq \frac{a_{i}}{b_{i}} \forall i$ , then $c \leq \frac{\sum_{i = 1}^{\infty} a_{i}}{\sum_{i = 1}^{\infty} b_{i}}$

Ciolan3u 2022-09-14

How many integers are between 5 roots of 7 and 7 roots of 5?

Beckett Henry 2022-09-14

Calculate the value of a numeric expression: 4 7/15 - 3 3/23 * 23/27 - 1 1/5 * 1/6.

Kathryn Sanchez 2022-09-14

Find all natural values of x for which the inequality is true: 3 11\15

Jonah Jacobson 2022-09-14

Find the unknown term of the proportion: x/5=5.4/3.6

Staffangz 2022-09-14

Compute the expressions.
690:3*205-47150+850

Makayla Reilly 2022-09-14

Simplify $\frac{1}{\sqrt{x^{2} + 1}} - \frac{x^{2}}{(x^{2} + 1)^{3 / 2}}$
I want to know why
$\frac{1}{\sqrt{x^{2} + 1}} - \frac{x^{2}}{(x^{2} + 1)^{3 / 2}}$
can be simplified into
$\frac{1}{(x^{2} + 1)^{3 / 2}}$
I tried to simplify by rewriting radicals and fractions. I was hoping to see a clever trick (e.g. adding a clever zero, multiplying by a clever one? Quadratic completion?)
$\begin{aligned} \frac{1}{\sqrt{x^{2} + 1}} - \frac{x^{2}}{(x^{2} + 1)^{3 / 2}} & = \\ = (x^{2} + 1)^{- 1 / 2} - x^{2} * (x^{2} + 1)^{- 3 / 2} \\ = (x^{2} + 1)^{- 1 / 2} * (1 - x^{2} * (x^{2} + 1)^{- 1}) \\ = . . . \end{aligned}$
To give a bit more context, I was calculating the derivative of $\frac{x}{\sqrt{x^{2} + 1}}$ in order to use newtons method for approximating the roots.

tamola7f 2022-09-14

How to resolve this fraction with change of divisors
If i have an equation like this:
$\frac{a}{b \cdot \frac{c}{d - \frac{f}{g}}}$
With what should I multiply to get g?
Should I multiply it with $d - \frac{f}{g}$ ? Or is this incorrect?

Makayla Reilly 2022-09-14

Simplify fraction in numerator when fraction is part of sum
I have the result of a quotient rule:
$\frac{\frac{x}{8 + x} - l n 8}{x^{2}}$
Should I just leave it? Would it be appropriate to separate the fraction into a product of fractions with denominator $x^{2}$ , simplify the left side, and give the result as a product of two fractions?
Any soln using addition or subtraction of fractions is unacceptable and messier than just leaving as is.

Damon Cowan 2022-09-14

Prove $\frac{n - 1}{n} + \frac{n - 1}{n} \frac{n - 3}{n - 2} + \frac{n - 1}{n} \frac{n - 3}{n - 2} \frac{n - 5}{n - 4} + . . . = \frac{n - 1}{3}$ without induction
I found this identity using Maple. Is there a (simple) way to prove it without using induction? Using induction, the proof is quite easy.
Prove for odd n that
$\sum_{k = 1}^{(n + 1) / 2} \prod_{j = 0}^{k - 1} (\frac{n - 2 j - 1}{n - 2 j}) = \frac{n - 1}{n} + \frac{n - 1}{n} \frac{n - 3}{n - 2} + \frac{n - 1}{n} \frac{n - 3}{n - 2} \frac{n - 5}{n - 4} + . . . = \frac{n - 1}{3}$

Makayla Reilly 2022-09-13

The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. The lift of a wing with an area of 300 square feet is 12,000 pounds when the plane is going 110 miles per hour. Find the lifting force on the wing if the plane slows down to 100 miles per hour.

Getting your pre Algebra solved becomes much easier when you have all the answers to your questions by taking a closer look at the various examples dealing with Pre-Algebra subjects. We have intentionally collected the list of pre-algebra equations and various solving equations with decimals problems to help you see various examples that explain how certain solutions are found. Still, if something sounds unclear or you are concerned about some solution that has been provided, approach pre-algebra with reverse engineering approach (going backwards).

Pre-Algebra

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