This module covers the multiplication of rational expressions.
Multiplying fractions is easy: you just multiply the tops, and multiply the bottoms. For instance,
Now, you may notice that
can be simplified, since 7 goes into the top and bottom.
. So
is the correct answer, but
is
also the correct answer (since they are the same number), and it’s a good bit simpler.
In fact, we could have jumped straight to the simplest answer first, and avoided dealing with all those big numbers, if we had noticed that we have a 7 in the numerator and a 7 in the denominator, and
cancelled them before we even multiplied!
This is a great time-saver, and you’re also a lot less likely to make mistakes.
When multiplying fractions...
If the same number appears on the top and the bottom, you can cancel it before you multiply. This works regardless of whether the numbers appear in the
same fraction or different fractions .
But it’s critical to remember that this rule
only applies when you are multiplying fractions : not when you are adding, subtracting, or dividing.
As you might guess, all this review of basic fractions is useful because, once again, rational expressions work the same way.
Multiplying rational expressions
The problem
Always begin rational expression problems by factoring! Note that for the first element you begin by factoring out the common 3, and then factoring the remaining expression.
When multiplying fractions, you can cancel anything on top with anything on the bottom, even across different fractions
Now, just see what you’re left with. Note that you could rewrite the top asbut it’s generally easier to work with in factored form.
Dividing rational expressions
To divide fractions, you flip the bottom one, and then multiply.
After the “flipping” stage, all the considerations are exactly the same as multiplying.
Dividing rational expressions
This problem could also be written as:
. However, the
symbol is rarely seen at this level of math.
is written as
.
Flip the bottom and multiply. From here, it’s a straight multiplication problem.
Always begin rational expression problems by factoring! Now, cancel a factor of
and an
and you get...
That’s as simple as it gets, I’m afraid. But it’s better than what we started with!
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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