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Mathematics LibreTexts

8.4: Homework

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  • Page ID 70331

  • Julie Harland
  • MiraCosta College
  • Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
  • Start a new module on the front side of a new page and write the module number on the top center of the page.
  • Answers without supporting work will receive no credit.
  • Some solutions are given in the solutions manual.
  • You may work with classmates but do your own work.

Find GCF(252, 350) using:

Find GCF(140, 315) using:

Use the Euclidean Algorithm to compute the greatest common factor of the numbers given. Use correct notation, and show each step. Then, show how you check your answer. Also, compute the LCM of the two numbers.

State whether each of the following statements is true or false. If it is false, provide a counterexample. If it is true, provide an example.

a. If (a + b)|c, then a|c and b|c

b. If a|b and a|c, then a|(bc)

c. If a|b and a|(b + c), then a|c

d. If a|bc, then a|b and a|c

e. If a|b and a|c, then a|(b + c)

Write the prime factorization for the following numbers. If it is prime, write "prime" and explain how you know it is prime.

Assume m and n are composite whole numbers in each of the following. Find the following. Then provide an example using numbers for m (and n where used). Remember not to use prime numbers in your example.

a. GCF(m,m) =

b. LCM(m,m) =

c. GCF(m,0) =

d. GCF(m,1) =

e. If GCF(m,n) = 1, then LCM(m,n) =

f. If GCF(m,n) = m, then LCM(m,n) =

g. If LCM(m,n) = mn, then GCF(m,n) =

Find the following sums using methods from this module: Show all work

a. 1 + 2 + 3 + . . . + 313 + 314 + 315 =

b. 111 + 112 + 113 + . . . + 287 + 288 + 289 =

c. 15 + 30 + 45 + . . . + 900 + 915 + 930 =

d. 102 + 105 + 108 + . . . + 300 + 303 + 306 =

On each number line, state all whole number possibilities less than 100 that the man could be standing on.

The factors of a number that are less than the number itself are called proper factors . For instance, the proper factors of 10 are 1, 2 and 5. A number is classified as deficient if the sum of its proper factors is less than the number itself. 10 is a deficient number since 1 + 2 + 5 < 10. A number is classified as abundant if the sum of its proper factors is greater than the number itself. For instance, the proper factors of 18 are 1, 2, 3, 6, and 9. 18 is a deficient number since 1 + 2 + 3 + 6 + 9 > 18. A number is classified as perfect if the sum of its proper factors equals the number itself. For each number, list its proper factors. Then find the sum of its proper factors. Then, classify each number as deficient, abundant or perfect.

Are prime numbers deficient, perfect, or abundant? ________ Explain why.

Answer true or false for each of the following. If it is true, provide an example. If it is false, provide a counterexample.

a. Every prime number is odd.

b. If a number is divisible by 6, then it is divisible by 2 and 3.

c. If a number is divisible by 2 and 6, then it is divisible by 12.

d. If a number is divisible by 3 and 4, then it is divisible by 12.

e. If a \(\neq\) b, then GCF(a, b) < LCM(a, b).

f. If 6 is a factor of mn, then 6 is a factor of m or a factor of n.

g. If 5 is a factor of mn, then 5 is a factor of m or a factor of n.

Can the sum of two odd prime numbers be a prime number? Explain why or why not.

Find the least common multiple of the following sets of numbers:

a. LCM(2, 4, 5, 7, 8, 12, 14, 15)

b. LCM(3, 4, 6, 8, 9, 10, 12, 18)

If GCF(30, x) = 6 and LCM(30, x) = 180, then what is x? (Hint: see page 65)

The theory of biorhythm states that your physical cycle is 23 days long, your emotional cycle is 28 days long, your intellectual cycle is 33 days long. If your cycles all occur on the same day, how many days until your cycles again occur on the same day? About how many years is this?

Is your free T4 really in the normal range

Is your Free T4 really in the Normal Range? Optimal vs Normal levels & More

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Evidence-Based

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Chances are VERY high that your Free T4 level isn’t actually normal even though it may be in the “normal range”.

Most people tend to blow off their Free T4 level because it isn’t the ‘free and active’ hormone, especially when compared to free T3. 

But that is a big mistake!

Free T4 still has a story to tell and it’s not something you want to miss out on.

For instance, your Free T4 level can actually help you determine how efficient your thyroid is converting T4 into T3 and may explain why you have a “low” TSH when you still feel terrible . 

In this article, I’m going to help you understand what your Free T4 level means and teach you how to determine if it is really in the “normal range”…

Is your Free T4 Normal & Optimal?

Unfortunately, it isn’t quite that easy…

There is no magic number that your Free T4 level needs to be in order for you to suddenly start feeling amazing.

It is just one small piece of a larger puzzle that is your entire health.

I’ve seen patients with low Free T4 levels who are asymptomatic, and I’ve seen patients with Free T4 levels in the upper 1/3 range who feel terrible . ​

Like other tests in medicine, it needs to be used in conjunction with your symptoms and other lab tests.

But before we get into the nitty-gritty, let’s talk about how to look at your own Free T4 level…

Consider the example below:

thyroid lab tests with free t4 and free t3 levels highlighted which are in the normal range but still represent abnormal values.

​Going off of lab tests alone you can see that this patient’s Free T4 levels fall within the lower 1/3 of the reference range. (Ignore her other lab values, we will get into those later)

If your Doctor were to see these labs he would absolutely tell you that your lab tests were “normal”, but is that really the case? 

In treating hundreds of patients I can tell you honestly that MOST patients feel significantly better when their Free T4 levels are towards the higher range, usually in the upper half.

And this correlates well with newer studies that show that patients with hypothyroidism require a higher free T4 to achieve a normal TSH (1). 

This study showed that, while treating patients with hypothyroidism, the goal should be to obtain a free thyroxine level in the upper part of the reference range . 

​ If you recall from basic Thyroid physiology , your Free T4 levels act as a reservoir or pool to draw upon when your body needs to create the active thyroid hormone Free T3 . 

So when thinking logically about this…

As your free T4 level increases, the more you can draw upon this pool to create the active hormone… right?

It turns out that this is the way that most Doctors (and subsequently patients) think about the thyroid.

Unfortunately, for at least 15% of the population, it isn’t true (2).

And that leaves us with a big problem:

highlight of a study which discusses the concept of tissue level hypothyroidism as a reason for why thyroid patients are so unhappy.

We are basing treatment recommendations on an incomplete picture and we are wondering why our thyroid patients feel terrible and are so unhappy (3).

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Your Free T4 and Thyroid Function

Here’s where things can get a little bit tricky, and why many Doctors may actually be telling you that your thyroid is “fine” when it really isn’t. 

I just said that high levels of Free T4 are good, right?

But that isn’t always the case. 

Refer back to what I said before about Free T4 being a reservoir for Free T3. 

What if you AREN’T converting T4 to T3? (What if your body isn’t utilizing that T4 correctly?). 

Well, let’s just think about this logically again using this example:

I want you to think about your thyroid as a Dam . 

Under normal circumstances, a Dam acts to hold back A LOT of water and only lets a certain amount of water go through in a controlled fashion. 

In this example, the pool of water behind the dam is your Free T4 level, and the water going through is your Free T3. 

What will happen to the system if you suddenly can’t let any water through? 

It all backs up, and the water behind the Dam continues to grow and grow. 

Well…

The same thing happens to your Free T4 level when there is a ‘kink’ in the system. 

But instead of water, your Free T4 level goes higher and higher…

Do you see the problem now?

A kink in the conversion process may actually cause your Free T4 levels to RISE and make you think that your thyroid function is normal when the exact opposite is happening . 

As your Free T4 level rises (because it can’t convert to Free T3) it shows up as high levels of Free T4 in the serum. These high levels of Free T4 actually act to suppress your TSH (because your pituitary doesn’t have the same deiodinases as the rest of the body (4)).

So your lab tests may look something like this:

  • High Free T4
  • Low total T3 and free T3
  • High reverse T3

Meanwhile, you are feeling terrible with every hypothyroid symptom in the book . 

Does this scenario sound familiar?

Don’t worry…

If it is happening to you we are going to discuss how to correctly diagnose it, but first, we need to talk about how T4 can be beneficial. 

Does Your T4 Even Matter?

​It’s easy to think that T4 doesn’t mean much because it isn’t the active thyroid hormone in your body . 

And it makes sense, but there is still some value in using and testing for it.

T4 levels give you an idea about how you are converting T4 into T3.

In keeping with the analogy I described above, your T4 level helps you to understand how your body is processing your T4 and T3 thyroid hormones (5).

High levels of T4 with correspondingly low levels of T3 may indicate that you need to focus on improving your T4 to T3 conversion.

You can read more about how to naturally increase your T3 levels and thus thyroid conversion here . ​

T4 levels can give you an idea if you are properly absorbing thyroid hormone (6).

Another huge benefit of testing your T4 levels is understanding if your body is actually absorbing your thyroid hormone. 

a list of reasons that cause t4 malabsorption taken from a clinical study.

Naturally, your T4 levels should increase as you take thyroid hormone (though it is important to realize that your symptoms may not improve just because your T4 level increases).

By testing your T4 level both before and after you start thyroid hormone (this only applies to T4 only thyroid medication) you can get a rough idea as to whether or not you are absorbing the medication .

Believe it or not, absorption of thyroid hormone is a big deal and something that is frequently missed (7).

You can learn more about how to properly take your thyroid medication in this post which explains how changing the time of day you take your thyroid medication can actually improve thyroid absorption and thyroid function. 

T4 levels can help you determine if you need to focus on improving your thyroid conversion vs increasing thyroid hormone production.

This is primarily helpful for patients who know that they have hypothyroidism, but whose physician is unwilling to treat them with thyroid hormone. 

Most physicians are willing to at least test both TSH and free T4 levels which can give you, as the patient, a lot of information.

If you know that your T4 and T3 levels are low then you can focus on  taking supplements and taking action to increase your thyroid hormone production .

On the other hand, if your T4 levels are high and your T3 levels are low – you as the patient can focus on taking  supplements designed to boost T4 to T3 conversion .

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Over 13 nutrients are involved in thyroid hormone production  (8) and some supplements may help thyroid conversion. 

It turns out that many patients (even those on thyroid hormone) have deficiencies in some of these nutrients which may lead to poor thyroid hormone production and conversion.

If you have Hashimoto’s then the supplements you should consider using are slightly different from the list above and you  can find more information on which supplements are best for autoimmune thyroiditis here . 

​T4 levels can help you determine if you would benefit from adding T3 thyroid medication. 

Let’s say that you are taking T4-only thyroid medication (like Synthroid) and your T4 level is high (so you know you are absorbing it) but your T3 level is still low and you are still having symptoms of hypothyroidism. 

Even in the presence of a low reverse T3 (which means you are still converting thyroid hormone ok), this may indicate that you might benefit from the addition of T3 thyroid hormone. 

Recall that T3 thyroid hormone is the most powerful thyroid hormone and is responsible for all of the good things that thyroid hormone does in your body. 

So remember:

While T4 isn’t the best thyroid test, it can still give you plenty of helpful information – especially if your Doctor isn’t willing to order the complete thyroid panel . ​

How T4 Changes with Thyroid Medication

Another very important factor is understanding how your free T4 level changes with different types of thyroid hormone.

This is worth mentioning because it isn’t always intuitive and it can lead some patients into thinking that they are not heading in the right direction even though they might be . ​

T4 on Levothyroxine (Synthroid, generic Levothyroxine, Tirosint)

The way your T4 level changes when taking T4-only thyroid medication is actually quite intuitive.

Assuming you are absorbing enough thyroid hormone, your T4 level should increase as your increase your T4 dose.

Makes sense right?

Sometimes, though, this doesn’t happen and even if it does it doesn’t necessarily mean everything is “all good”.

As I mentioned above, your T4 level might NOT raise if your dose isn’t high enough and/or if you aren’t properly absorbing the medication you are taking.

And, even if it does, there are studies showing (9) that patients who take T4-only thyroid medication show lower T3 levels than healthy populations – indicating that many patients just don’t do well on these T4-only thyroid medications. 

the conclusion of a study which showed that participants using t4 only thyroid medications had lower t3 levels compared to

There are ways that you can improve the function of thyroid hormone if you are taking T4-only thyroid medication and not feeling better:

1) Consider switching to Tirosint. 

Tirosint contains 3 inactive ingredients and can help increase the absorption and effectiveness of thyroid hormone. 

The case can even be made that you should consider switching over to Tirosint if you are currently taking Synthroid or levothyroxine. 

2) Consider switching to 50mcg increments of Levothyroxine

The 50mcg tablet of levothyroxine contains the fewest inactive ingredients out of all of the other Levothyroxine dosages (For example the 100mcg tablet and so on). 

Changing your dose from 1, 100mcg tablet of levothyroxine to 2, 50mcg tablets of levothyroxine may help increase absorption and reduce any symptoms you may be having. ​

3) Consider switching from Levothyroxine to Synthroid or Synthroid to Levothyroxine

While these medications may appear to be the exact same, studies have shown that they are not bioequivalent (10). 

What this means is that your body may process them differently which may result in varying thyroid levels. 

This is an easy test because all you have to do is switch from taking one medication to the other and you may notice a difference. 

  • Bottom line: If you are taking T4-only thyroid medication (Synthroid, Levothyroxine, Levoxyl) then your free T4 level should increase. If it doesn’t then you may have an absorption issue and you may benefit from switching to Tirosint. 

T4 with NDT (Armour, WP thyroid, Naturethroid)

The way that T4 changes with NDT aren’t as straightforward as it is with T4-only medications.

Any thyroid medication that contains T3 thyroid hormone, at high enough doses, will generally cause your free T4 level to drop (11). 

The degree of how much it lowers largely depends on the dose of T3 you are taking. 

study with text highlighted showing that free t4 levels were lower in a group of patients taking only t4 only thyroid medication.

The higher the dose of T3 the lower your free T4 will go. 

The reason for this has to do with how T3 and T4 influence pituitary function. 

T3 thyroid hormone is 3-4 times more potent at lowering the TSH (12) than T4 is alone. 

As your TSH lowers your body produces less T4 thyroid hormone by itself (and becomes more reliant upon medications to supplement thyroid hormone levels). 

As long as you have a functioning thyroid gland (assuming it isn’t taken out or destroyed by radioactive ablation) then your thyroid will be producing SOME T4 and T3 even if you are taking thyroid medication .

But as you increase the dose of T3 you are taking then that amount your thyroid produces drops. ​

​This will usually result in a decrease in your Free T4 level. 

As you know NDT (natural desiccated thyroid) contains mostly T4 and some T3.

This ratio is close to 80% T4 and 20% T3, which means that the medication is still mostly T4 thyroid hormone.

But even that small amount of T3 is enough to shoot up T3 levels and drop T4 levels in the body.

One mistake I see patients (and doctors make) is increasing the NDT dose while trying to get to some mythical and optimal T4 level in the serum.

In some ways this is futile, as you increase your NDT dose it will drive down your T4 level in the serum which leads to higher and higher levels of NDT.

This can actually backfire and result in high levels of reverse T3 and very high levels of free T3 . 

If you are taking 4+ grains of NDT and still experiencing symptoms of hypothyroidism, then this may be happening inside your body. ​

  • Bottom line: With lower doses of NDT your free T4 level may actually drop somewhat. Higher doses of NDT (greater than 4 grains) will usually cause the free T4 to increase but this isn’t necessarily helpful. 

T4 with T3 Medications Like Cytomel and Liothyronine

This is where things get really interesting. 

Taking T3-only thyroid medication like Cytomel or liothyronine will cause your free T4 to drop below the “normal” range completely and even flag as low.

This has to do with the fact that you are suppressing the TSH with the T3 and so endogenous production of T4 decreased dramatically.

Taking T3-only thyroid medication also causes reverse T3 levels to drop too low levels as well (this is usually a good thing).

To recap what happens on T3-only thyroid medication:

  • TSH level falls
  • Free T3 level increases
  • Free T4 level decreases
  • Reverse T3 level drops

What you really need to get out of all of this is the fact that your free T4 levels do not necessarily need to be in some magical “optimal” range for you to feel good. 

Basing your treatment on these ranges may lead to suboptimal treatment as you chase all the wrong results. 

Instead of laser focusing on your free T4, make sure that you look at your T4 in context with other thyroid lab tests . 

  • Bottom line: Taking T3-only thyroid medication will dramatically reduce your free T4 level and this isn’t necessarily a bad thing. 

Symptoms of Low T4 & T3

​Low free T3 and free T4 levels may indicate low thyroid function, but they may also indicate a condition known as euthyroid sick syndrome or low T3 syndrome . 

This condition is very similar to hypothyroidism, but some patients with it may not experience symptoms, whereas all patients with hypothyroidism will experience symptoms. 

If you suffer from low T3 and/or low T4 then you are also very likely to experience all of the symptoms of hypothyroidism, but with some other slight changes. 

Symptoms of low T3 and low T4 include:

  • Constant fatigue
  • Reduced response to T4-only thyroid medications
  • Weight gain (even while on thyroid medication) 
  • Low resting heart rate
  • Low body temperature

Many of these symptoms result from low T3 levels directly or from the reduced conversion of T4 to T3. 

Patients who are taking thyroid medication (who still have low T4 levels) may experience many of these symptoms (13) which should spark a further investigation by your physician.

If you fall into that category make sure that you properly evaluate how effective your conversion is, and how effective your native thyroid hormone production is (use examples above). ​

Why you need the Complete Thyroid Panel

Because testing for thyroid hormone levels isn’t always intuitive, it’s very important that each time you check your thyroid levels you obtain a complete panel. 

While not all lab tests may be necessary EACH and every time you get blood work, it’s still a good idea to get all of these tests to create baseline values that you can compare further testing to. 

Let’s go back to the initial example we used at the beginning of this post:

the same image showed at the beginning of the post used here for emphasis which displays normal t4 and t3 values which are not optimal.

At first glance, you may be thinking that this patient is completely normal. 

Her TSH is in the 1-2 range, her Free T3 is in the mid-range, and it’s only her Free T4 that is in the low range.

But she is actually quite hypothyroid and I know this because I treated her!

It isn’t until you order her Reverse T3 level that you finally get a better picture as to what is happening…

the repeat image form the beginning of the article used here for emphasis to show that a normal reverse t3 level is not optimal.

​Once you see and understand her Reverse T3 level you begin to understand her thyroid physiology.

The only reason her Free T3 levels even look moderately normal is that her Reverse T3 levels are inappropriately blocking any Free T3 that she has.

Remember that Reverse T3 and Free T3 both compete for cellular binding (14).

If you take into account her high Reverse T3 level, her Free T3 level suddenly starts to make more sense. 

In her case, her Free T4 level never got into the ‘optimal high’ range, but you can definitely tell that it is also inappropriately high for her, given that she can barely convert T4 to T3. 

​The bottom line:

You need a Complete Thyroid Panel if you want to have ANY idea of what is going on with your thyroid .

That means you need the following tests:

  • Thyroid Antibodies
  • Sex hormone-binding globulin

​And remember:

Just ordering the tests isn’t going to be enough.

You need to make sure that you and your Doctor know how to actually interpret them so you don’t fall victim to the trap I just showed you above. ​

Conclusion + Recap

Your Free T4 levels can give you amazing insight into how well your Thyroid is functioning, but you need to remember that they are only a small piece of an even larger puzzle. 

It is possible that your Free T4 levels may be inappropriately elevated ​and that isn’t always a good thing. 

If your Free T4 levels are high and you still feel terrible, then you need to make sure you are also checking your Free T3 levels and your Reverse T3 levels.

​Using these lab values together, in combination with your symptoms, will help you to understand how well your thyroid is functioning. 

So what should your T4 levels be?

If you aren’t taking thyroid hormone, then optimal levels are generally in the upper 50% of the reference range .

If you are already taking thyroid hormone then the upper 50% of the reference range doesn’t always hold, instead, you need to be focusing on other factors . 

Now I want to hear from you: 

Are your free T4 levels high but you still feel terrible?

Is your doctor willing to order the RIGHT tests?

What has helped you feel better in this situation?

Leave your comments or questions below!

Scientific References

#1. https://www.ncbi.nlm.nih.gov/pubmed/18753096

#2. https://www.ncbi.nlm.nih.gov/pubmed/19190113

#3. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3169863/

#4. https://www.ncbi.nlm.nih.gov/pubmed/6595194

#5. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3887425/

#6. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3857600/

#7. https://www.ncbi.nlm.nih.gov/pubmed/28153426

#8. https://www.ncbi.nlm.nih.gov/books/NBK285550/

#9. https://academic.oup.com/jcem/article-lookup/doi/10.1210/jc.2016-2660

#10. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3565118/

#11. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5873391/

#12. https://www.ncbi.nlm.nih.gov/pubmed/402379

#13. https://www.ncbi.nlm.nih.gov/pubmed/29381251

#14. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5869352/

how to tell if your free t4 is normal versus optimal pinterest image.

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About Dr. Westin Childs

Hey! I'm Westin Childs D.O. (former Osteopathic Physician). I don't practice medicine anymore and instead specialize in helping people like YOU who have thyroid problems, hormone imbalances, and weight loss resistance. I love to write and share what I've learned over the years. I also happen to formulate the best supplements on the market (well, at least in my opinion!) and I'm proud to say that over 80,000+ people have used them over the last 7 years. You can read more about my own personal health journey and why I am so passionate about what I do.

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Note If you entered the wrong number of slips, you have to exit T4 Web forms and re-enter the correct number of slips.

Below we give a brief description for each field. See T4 information for details.

What type of slip is this? (This question appears if you selected "Amended" in the previous page.) Select Amended to correct a slip you have already submitted, or select Cancelled to delete a slip you have already submitted.

Employee's name: Enter the employee's last name, followed by the first name and initial.

Employee's address: Enter the employee's address, including the province, territory, or U.S. state, Canadian postal code or U.S. zip code, and country.

Year: Enter the four digits of the calendar year in which you paid the remuneration to the employee.

Box 10 - Province of employment: Select the employee's province of employment.

Box 12 - Social insurance number: Enter the employee's social insurance number (SIN) as it appears on the employee's SIN card.

Box 14 - Employment income: Report the total income before deductions.

Box 16 - Employee's CPP contributions: Enter the amount you deducted from the employee for contributions to the Canada Pension Plan (CPP).

Box 17 - Employee's QPP contributions: Enter the amount you deducted from the employee for contributions to the Quebec Pension Plan (QPP).

Box 18 - Employee's EI contributions: Enter the amount of EI premiums you deducted from the employee's earnings.

Box 20 - RPP contributions: Enter the total amount the employee contributed to a registered pension plan (RPP). Leave the box blank if the employee did not contribute to a plan.

Box 22 - Income tax deducted: Enter the total income tax you deducted from the employee's remuneration. This includes the federal, provincial (except Quebec), and territorial taxes that apply. Leave the box blank if you did not deduct tax.

Box 24 - EI insurable earnings: Enter the total amount you used to calculate the employee's EI premiums.

Box 26 - CPP/QPP pensionable earnings: In most cases, you will leave this box blank. However, you may have to complete the box in some situations. See the T4 section of the employer's guide for more information.

Box 28 - Exempt (CPP/QPP, EI and Provincial Parental Insurance Plan): Do not complete the CPP/QPP part of this box if you entered an amount in box 16, 17, or 26. Enter an "X" under CPP/QPP only if the earnings were exempt for the entire period of employment. Do not complete the EI part of this box if you entered an amount in box 18 or 24. Enter an "X" under EI only if the earnings were exempt, or if they were not eligible for the entire reporting period of employment. Do not complete the PPIP part of this box if you entered an amount in box 55 or 56. Enter an "X" under PPIP only if the earnings were exempt for the entire period of employment in the province of Québec.

Box 29 - Employment code: Enter the appropriate code in this box if one the following situations applies. Otherwise, leave it blank.

Do not complete Box 14, Employment income , if you are using employment codes 11, 12, 13, or 17.

  • 11 - Placement agency - self-employed
  • 12 - Driver of taxi or other passenger-carrying vehicle
  • 13 - Barber or hairdresser
  • 14 - Withdrawal from prescribed salary deferral arrangement plan
  • 15 - Seasonal Agricultural Workers Program
  • 16 - Detached employee-social security agreement
  • 17 - Fishers - Self employed

Box 44 - Union dues (completed at employer's option): If you and the union agree that the union will not issue receipts for union dues to employees, enter the amount you deducted from the employee's earnings for union dues. Include amounts you paid to a parity or advisory committee that qualify for a deduction.

Box 46 - Charitable donations (completed at employer's option): Enter the amount you deducted from the employee's earnings for donations to registered charities in Canada.

Box 50 - RPP or DPSP registration number: Enter the seven-digit registration number we issue for a registered pension plan (RPP) or a deferred profit sharing plan (DPSP), or the seven-digit plan identification number we issue for an unregistered foreign pension plan under which you report a pension adjustment (PA).

Box 52 - Pension adjustment: If you have a registered pension plan (RPP) or a deferred profit sharing plan (DPSP), enter only the dollar amount of the employee's pension adjustment (PA) for the year.

Box 55 - Employee's PPIP contributions: Enter the amount of PPIP premiums you deducted from the employee's earnings.

Box 56 - PPIP insurable earnings: Enter the total amount you used to calculate the employee's PPIP premiums.

Other information: These fields have boxes where you enter codes and amounts relating to employment commissions, taxable allowances and benefits, deductible amounts, and other entries, if they apply.

The Summary of financial information section will display the total amounts for the financial fields on the T4 slips after you select the Calculate summary button.

  • Box 19 - Employer's EI premiums: Enter the total employer's EI premiums.
  • Box 27 - Employer's CPP contributions: Enter the employer's total CPP contributions.
  • Box 82 - Remittances: Enter the employer's total remittances.

No input is required for the following fields, as T4 Web forms will automatically calculate the amounts.

  • Box 14 - Employment income
  • Box 16 - Employee's CPP contributions
  • Box 18 - Employee's EI premiums
  • Box 20 - RPP contributions
  • Box 22 - Income tax deducted
  • Box 52 - Pension adjustment
  • Box 80 - Total deductions reported

After you have completed your T4 information return, select the Calculate summary button. T4 Web forms will then:

  • validate and accept the data you have input,
  • calculate the Summary of financial information fields, and
  • return you to the Employer information section.

Scroll down and review your information return.

If data is invalid or missing, a red circle will appear beside the fields to be verified or corrected. Underneath the box there will be a linked Error number . Select the link for a detailed explanation of the error and how you may be able to correct it.

You have to review fields with a yellow triangle to ensure those entries are correct. These entries will not prevent you from filing the return.

Scroll down and correct each error. Once you have corrected all the errors, select the Calculate summary button.

You will not be allowed to file your information return until you correct all the errors. If no errors are found, select the Continue button. If you notice an error after you file your electronic return, see Amending returns.

Step 3 - Print your T4 information return

After you select the Continue button, the first T4 slip will be displayed for printing (two copies of each slip). Print the slip using your browser's print function. Select the Next Slip button to view the second slip. Continue to do this until all the slips are printed. On the last slip, select Continue to Summary to get to your Summary form. Again, you may print a copy for your records.

Submission number

The Submission number is your confirmation that the CRA has received your information return.

Amending returns

You may need to amend your return after it is processed . For example, after you file your return, you may notice that you made an error when preparing the slips. You will have to file amended slips and an amended return to correct the information.

We are interested in your comments. We invite you to complete the survey on the Confirmation of Receipt page.

After we have processed your return

We may contact you to verify your supporting documentation. This does not mean you are being audited. It is simply part of the verification process we apply to all paper and electronic information returns.

The minimum computer requirements for T4 Web Forms are:

  • Intel or compatible 486DX/66 MHz processor or higher
  • 16 MB RAM or higher
  • Microsoft Windows NT or higher
  • Web browser supporting Transport Layer Security (TLS)
  • 28,800-baud modem or faster
  • System 7.6.1 or higher
  • Intel or compatible Pentium processor
  • 64 MB RAM or higher
  • Mandrake Linux 8.0 or higher

Note While you may access T4 Web forms with any browser, problems may occur if you attempt to use T4 Web forms with browsers we did not test. The CRA does not provide support for browsers.

Why can't I change my browser setting while I'm in a secure session? Your browser setting should not be modified while in a secure T4 Web forms session because it may cause your browser to freeze or the secure T4 Web forms session to end.

The T4 Web forms secure Web pages do not display properly. Why? A number of factors may affect how these pages will display on your system. We recommend the following:

  • Use the default browser settings.
  • Maximize your browser window.
  • Close the Favorites window.
  • Use the browser's Reload or Refresh button.
  • Ensure you have sufficient RAM for your browser's requirements.

I was away from my computer for 30 minutes. Can I still complete my return? For security reasons, after 18 minutes of inactivity our servers will end a secure T4 Web forms session. You will be required to reauthenticate yourself and re-enter your data as any data you may have entered will have been lost.

I lost the connection to the T4 Web forms secure site. What do I do? Reasons to lose your connection include telephone line interruptions, system crashes, and power failures. You will be required to reauthenticate yourself and re-enter your data, as any data you may have entered will have been lost.

I was able to print but not file my return. What do I do? You will be required to reauthenticate yourself and re-enter your data as any data you may have entered will have been lost.

I filed my return but I did not get a Submission Number. What do I do? If you filed your return but you did not receive a Submission Number, call our Help Desk at 1-877-959-5525 to confirm that we have received your return. Wait 48 hours before calling our help desk as our systems may take 48 hours to update .

If the return was not received, you will be required to reauthenticate yourself and re-enter your data, as any data you have entered will have been lost.

Page details

CPM Homework Banner

Home > CC1 > Chapter 4 > Lesson 4.2.4 > Problem 4-82

Use an algebraic expression to represent each sequence of lengths shown below.  

A line segment with 3 sections, and labeled as follows: x, 1, and x.

Think of this as being a tightrope for Croakie to cross. How would you describe his path using this picture?

A line segment with 4 sections. 3 equal sections are each labeled, m, with last section labeled 5.

Use parts (a) and (b) as guides if you are having trouble. Remember that the variable represents a number, so you can use it in an expression just as you would a number.

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