The following important fact is illustrated in the preceding examples.
Mixed number = natural number + proper fraction
Mixed numbers are the
sum of a natural number and a proper fraction. Mixed number = (natural number) + (proper fraction)
For example
can be expressed as
The fraction
can be expressed as
.
It is important to note that a number such as
does
not indicate multiplication. To indicate multiplication, we would need to use a multiplication symbol (such as ⋅)
means
and
not
, which means 5 times
or 5 multiplied by
.
Thus, mixed numbers may be represented by improper fractions, and improper fractions may be represented by mixed numbers.
Converting improper fractions to mixed numbers
To understand how we might convert an improper fraction to a mixed number, let's consider the fraction,
.
Thus,
.
We can illustrate a procedure for converting an improper fraction to a mixed number using this example. However, the conversion is
more easily accomplished by dividing the numerator by the denominator and using the result to write the mixed number.
Converting an improper fraction to a mixed number
To convert an improper fraction to a mixed number, divide the numerator by the denominator.
The whole number part of the mixed number is the quotient.
The fractional part of the mixed number is the remainder written over the divisor (the denominator of the improper fraction).
Sample set a
Convert each improper fraction to its corresponding mixed number.
Divide 5 by 3.
The improper fraction
.
. Divide 46 by 9.
The improper fraction
.
. Divide 83 by 11.
The improper fraction
.
Divide 104 by 4.
The improper fraction
.
Practice set a
Convert each improper fraction to its corresponding mixed number.
62
Converting mixed numbers to improper fractions
To understand how to convert a mixed number to an improper fraction, we'll recall
mixed number = (natural number) + (proper fraction)
and consider the following diagram.
Recall that multiplication describes repeated addition.
Notice that
can be obtained from
using multiplication in the following way.
Multiply:
Add:
. Place the 5 over the 3:
The procedure for converting a mixed number to an improper fraction is illustrated in this example.
Converting a mixed number to an improper fraction
To convert a mixed number to an improper fraction,
Multiply the denominator of the fractional part of the mixed number by the whole number part.
To this product, add the numerator of the fractional part.
Place this result over the denominator of the fractional part.
Sample set b
Convert each mixed number to an improper fraction.
Multiply:
.
Add:
.
Place 47 over 8:
.
Thus,
.
Multiply:
.
Add:
.
Place 50 over 3:
Thus,
Practice set b
Convert each mixed number to its corresponding improper fraction.
Exercises
For the following 15 problems, identify each expression as a proper fraction, an improper fraction, or a mixed number.
improper fraction
proper fraction
mixed number
improper fraction
mixed number
mixed number
proper fraction
mixed number
For the following 15 problems, convert each of the improper fractions to its corresponding mixed number.
or
For the following 15 problems, convert each of the mixed numbers to its corresponding improper fraction.
Why does
not qualify as a mixed number?
See the definition of a mixed number.
Why does 5 qualify as a mixed number?
See the definition of a mixed number.
… because it may be written as
, where
is any positive whole number.
Exercises for review
(
[link] ) Round 2,614,000 to the nearest thousand.
(
[link] ) Determine if 41,826 is divisible by 2 and 3.
(
[link] ) Find the least common multiple of 28 and 36.
252
(
[link] ) Specify the numerator and denominator of the fraction
.
Questions & Answers
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
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A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
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D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product