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Fractions and Mixed Numbers

A fraction is a number expressed in the form of a part of a whole. A fraction is a number that is either a whole number or a non-whole number. For example, 1/2 and 3/4 are fractions. A mixed number is a number expressed in the form of a decimal number, with a non-whole number as a fraction. For example, 1.7 is a mixed number. The decimal system is the number system used in mathematics, physics, and engineering for representing and manipulating real numbers. Mathematical notation uses a variety of symbols and conventions to denote fractions and mixed numbers, including the use of superscripts, subscripts, and the fraction slash. The fraction slash is a fraction slash symbol used in mathematics to denote a fraction. Fractions are often indicated in the form of a fraction slash. The fraction slash is written between two numbers and represents the fractional part of the second number divided by the fractional part of the first number. The fraction slash can be used to form a mixed number from a fraction. The fraction slash is also used in currency, juxtaposed to the fractional part of a monetary amount such as a penny or a dollar. In mathematics, a number is a real number, which means that it can be expressed as a ratio of two integers, for example, 2.5. If a ratio can be expressed as an algebraic fraction, then it is a real number. For example, the ratio of 3 to 5 is the same as the fraction of 3 over 5 (written as 1/5), which is a real number. A real number can be thought of as a value on a number line, with the distances between each pair of real numbers representing a certain proportion of some quantity. A real number can be thought of as a point or a set of points on the number line. For example, the number 1 is the point at which the number line is divided into two equal parts: the first part to the left of the number 1 is the positive numbers, and the second part to the right of the number 1 is the negative numbers. Thus, the positive half of the number line is to the right of the number 1, and the negative half is to the left of the number 1. A real number is denoted by a decimal, exponential, or integer, followed by a period and then by a decimal or exponential. The decimal or exponential can be followed by an E or another letter, which is a superscript. The superscripts are used to denote the number of decimal places or the exponent, respectively. The rules for writing real numbers are as follows: The exponential of a given number a is written a" and the exponential of the exponential of a number a is written a". The fraction of a number is just a number, which can be a decimal, an exponential, or a rational number. The decimal can be followed by a period and then by a digit or an E. The digit or E can be followed by a period and then by a decimal. The fraction slash can be used to form a mixed number from a fraction. In mathematics, a number is a real number, which means that it can be expressed as a ratio of two integers, for example, 2.5. If a ratio can be expressed as an algebraic fraction, then it is a real number. For example, the ratio of 3 to 5 is the same as the fraction of 3 over 5 (written as 1/5), which is a real number. A real number can be thought of as a value on a number line, with the distances between each pair of real numbers representing a certain proportion of some quantity. A real number can be thought of as a point or a set of points on the number line. For example, the number 1 is the point at which the number line is divided into two equal parts: the first part to the left of the number 1 is the positive numbers, and the second part to the right of the number 1 is the negative numbers. Thus, the positive half of the number line is to the right of the number 1, and the negative half is to the left of the number 1. A real number is denoted by a decimal, exponential, or integer, followed by a period and then by a decimal or exponential. The decimal or exponential can be followed by an E or another letter, which is a superscript. The superscripts are used to denote the number of decimal places or the exponent, respectively. The rules for writing real numbers are as follows: The exponential of a given number a is written a" and the exponential of the exponential of a number a is written a". The fraction of a number is just a number, which can be a decimal, an exponential

An Introduction to Fractions

225 Practice Problems
View More
00:21
Basic Mathematical Skills with Geometry

Write as fractions.
$$65 \%$$

Percents
Writing Percents as Fractions and Decimals
Brandon Fox
00:14
Basic Mathematical Skills with Geometry

Write as fractions.
$$6 \%$$

Percents
Writing Percents as Fractions and Decimals
Brandon Fox
01:11
Basic Mathematical Skills with Geometry

Give the mixed number that names the shaded portion of each diagram. Also write
each as an improper fraction.
(FIGURE CANNOT COPY)

Multiplying and Dividing Fractions
Fraction Basics
Nick Johnson

Multiplying Fractions

191 Practice Problems
View More
00:28
Basic Mathematical Skills with Geometry

Multiply. Be sure to write each answer in simplest form.
$$\frac{3}{7} \cdot 14$$

Multiplying and Dividing Fractions
Multiplying Fractions
Tausaga Pauu
00:56
Basic Mathematical Skills with Geometry

Multiply. Be sure to write each answer in simplest form.
$$\frac{5}{21} \times \frac{14}{25}$$

Multiplying and Dividing Fractions
Multiplying Fractions
Tausaga Pauu
00:28
Basic Mathematical Skills with Geometry

Multiply. Be sure to write each answer in simplest form.
$$\frac{3}{4} \times \frac{5}{11}$$

Multiplying and Dividing Fractions
Multiplying Fractions
Tausaga Pauu

Dividing Fractions

142 Practice Problems
View More
00:28
Basic Mathematical Skills with Geometry

$$\left(\frac{2}{3}\right)^{3} \div 4$$

Multiplying and Dividing Fractions
Dividing Fractions
Michelle Nguyen
00:44
Basic Mathematical Skills with Geometry

Divide. Write each result in simplest form.
$$\frac{\frac{5}{27}}{\frac{25}{36}}$$

Multiplying and Dividing Fractions
Dividing Fractions
Michelle Nguyen
00:17
Basic Mathematical Skills with Geometry

Divide. Write each result in simplest form.
$$\frac{1}{5} \div \frac{3}{4}$$

Multiplying and Dividing Fractions
Dividing Fractions
Michelle Nguyen

Adding and Subtracting Fractions

318 Practice Problems
View More
01:26
Precalculus : Building Concepts and Connections

This set of exercises will draw on the ideas presented in this section and your general math background.
Explain why the following decomposition is incorrect.
$$
\frac{1}{x\left(x^{2}+2 x-3\right)}=\frac{A}{x}+\frac{B x+C}{x^{2}+2 x-3}
$$

Systems of Equations and Inequalities
Partial Fractions
Odera Egbuonu
03:35
Precalculus : Building Concepts and Connections

Write the partial fraction decomposition of each rational expression.
$$\frac{4 x+4}{(x-1)\left(x^{2}+x+1\right)}$$

Systems of Equations and Inequalities
Partial Fractions
Odera Egbuonu
03:37
Precalculus : Building Concepts and Connections

Write the partial fraction decomposition of each rational expression.
$$\frac{3}{x^{2}+3 x+2}$$

Systems of Equations and Inequalities
Partial Fractions
Odera Egbuonu

Multiplying and Dividing Mixed Numbers

95 Practice Problems
View More
03:38
216

Express the number in decimal form.
Cattle population A rancher has 750 head of cattle consisting of 400 adults (aged 2 or more years), 150 yearlings, and
200 calves. The following information is known about this particular species. Fach spring an adult female gives birth to a single calf, and $75 \%$ of these calves will survive the first year. The yearly survival percentages for yearlings and adults are $80 \%$ and $90 \%$, respectively. The male-female ratio is one in all age classes. Estimate the population of each age class
A. next spring
B. last spring

Topics from Algebra
Real Numbers
Christopher Stanley
01:03
216

Express the number in decimal form.
Avogadro's number The number of hydrogen atoms in a mole is Avogadro's number, $6.02 \times 10^{23} .$ If one mole of the gas has a mass of 1.01 grams, estimate the mass of a hydrogen atom.

Topics from Algebra
Real Numbers
Wendi Zhao
01:46
216

Express the number in scientific form.
A. $427,000$
B. 0.000000093
C. $810,000,000$

Topics from Algebra
Real Numbers
Erika Bustos

Adding and Subtracting Mixed Numbers

132 Practice Problems
View More
01:00
216

Replace the symbol $\square$ with either $=$ or $\neq$ to make the resulting statement true for all real numbers $a, b$ $c,$ and $d,$ whenever the expressions are defined.
$$-(a+b) \square-a+b$$

Topics from Algebra
Real Numbers
Harsh Gadhiya
01:07
216

Rewrite the expression without using the ahsolute yalue symbol, ans simnlify the resilit.
$$\left|-x^{2}-1\right|$$

Topics from Algebra
Real Numbers
Harsh Gadhiya
03:19
216

Express the statement as an inequality.
A. $b$ is positive.
B. $s$ is nonpositive.
C. $w$ is greater than or equal to $-4$
D. $c$ is between $\frac{1}{5}$ and $\frac{1}{3}$
E. $p$ is not greater than $-2$
F. The negative of $m$ is not less than $-2$
G. The quotient of $r$ and $s$ is at least $\frac{1}{5}$
H. The reciprocal of $f$ is at most 14
I. The absolute value of $x$ is less than 4

Topics from Algebra
Real Numbers
Harsh Gadhiya

Order of Operations and Complex Fractions

88 Practice Problems
View More
04:02
Prealgebra

Evaluate each expression. See Example 1.
$$\frac{1}{6}+\frac{9}{8}\left(-\frac{2}{3}\right)^{3}$$

Fractions and Mixed Numbers
Order of Operations and Complex Fractions
Jessica Hill
00:50
Prealgebra

Write the denominator of the following complex fraction as an improper fraction.
$$\frac{\frac{1}{8}-\frac{3}{16}}{5 \frac{3}{4}}$$

Fractions and Mixed Numbers
Order of Operations and Complex Fractions
Jessica Hill
01:42
Intermediate Algebra

Simplify the complex fractions by using Method II.
$$\frac{\frac{1}{4+h}-\frac{1}{4}}{h}$$

Rational Expressions and Rational Equations
Complex Fractions

Solving Equations That Involve Fractions

398 Practice Problems
View More
07:00
Precalculus

Solve each problem.
Two chemical plants are polluting a river. If plant A produces a predetermined maximum amount of pollutant twice as fast as plant $\mathbf{B}$, and together they produce the maximum pollutant in 26 hr, how long will it take plant B alone?
$$\begin{array}{c|c|c|c} & \text { Rate } & \text { Time } & \begin{array}{c}\text { Part of Job } \\\text { Accomplished }
\end{array} \\\hline \text { Pollution from A } & \frac{1}{x} & 26 & \frac{1}{x}(26) \\\hline \text { Pollution from B } & & 26 & \\\hline\end{array}$$

Equations and Inequalities
Other Types of Equations and Applications
Supriya Kulkarni
02:58
Precalculus

Solve each equation in Exercises $7-23 .$
(a) $\frac{3}{x-2}=\frac{5}{9 x}$
(b) $\frac{3}{x-2}=\frac{5}{9 x-2}$
(c) $\frac{3}{x-2}=\frac{5}{\frac{5}{3} x-2}$

Fundamentals
Solving Equations
Kerry Thornton-Genova
01:46
Precalculus

Solve each equation in Exercises $7-23 .$
$$\frac{1}{x-5}+\frac{1}{x+5}=\frac{2 x+1}{x^{2}-25}$$

Fundamentals
Solving Equations
Kerry Thornton-Genova

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