Time: Subtracting Weeks and Days

Hello,

In our last post we learned how to add weeks and days together.  Today we are going to learn how to subtract weeks and days.  It is basically the opposite of adding weeks and days.  To add weeks and days, we added the weeks and days together, and then we subtracted 7 from the number of days if it was greater than or equal to 7, and then we increased the weeks by 1.  We would repeat this process if the days were still 7 or greater. 

For subtraction we are going to follow these steps:

1.) Subtract the number of weeks from one another and then subtract the number of days from one another; first, you must check if the second step holds:
2.) If the number of days is less than what you originally started with, you must subtract 1 from the original number of weeks, and then add 7 to the original amount of days.
3.) Once again, subtract the weeks and days. 

Examples:

1.) 6 weeks, 8 days - 5 weeks, 3 days = ?
2.) 5 weeks, 4 days - 3 weeks, 9 days = ?
3.) 7 weeks, 2 days - 2 weeks, 6 days = ?

Solutions:

1.) Since the number of days being subtracted (3) is less than the original days (8), we do not need to worry about our steps.  So, we subtract normally.  6 weeks - 5 weeks = 1 week.  8 days - 3 days = 5 days.  So, our final answer is 1 week, 5 days.

2.) Since the number of days being subtracted (9) is greater than the original amount of days (4), we must follow our steps above.  First, we must subtract 1 from our original amount of weeks, which was 5.  So, now we have 4 weeks.  Now, we add 7 to our original amount of days (4).  4 days + 7 days = 11 days. Now, we can proceed with subtracting.  4 weeks - 3 weeks = 1 week.  11 days - 9 days = 2 days.  So, our final answer is 1 week and 2 days.

3.) Since our number of days that we are subtracting (6) is greater than our original amount of days (2), we must subtract 1 from our original amount of weeks (7-1 = 6 weeks).  Then, we must add 7 to our original amount of days (2 + 7 = 9 days).  Now, subtract normally.  6 weeks - 2 weeks = 4 weeks.  9 days - 6 days = 3 days.  So, our final answer is 4 weeks, 3 days. 

It is confusing at first, but once you practice, I know you'll be able to do it!

The following are links that reiterate how to subtract weeks and days, which will hopefully help you:

1.) How to subtract weeks and days:explanation and example
2.) Subtract weeks and days to a date calendar

Time: Adding Weeks and Days

Hello,

In our last post, we learned about the number of days in each month and how to convert from weeks to days and days to weeks.  In our post today, we are going to learn how to add days and weeks together.

Let's review: 1 week = how many days? If you are thinking 7, you are correct!
Let's go over the rules for days and weeks addition:

1.) Add your days together.
2.) Add your weeks together.
3.) If your days add up to 7 or greater, you will subtract 7 from your days, and then increase your weeks by 1.
4.) If the amount of days is still 7 or greater, then you will repeat step 3. 


Remember that step 3 is the key!

Let's try some examples: Add the following weeks and days.

1.) 2 weeks, 6 days + 3 weeks, 2 days = ?
2.) 1 weeks, 4 days + 9 weeks, 1 day = ?
3.) 7 weeks, 5 days + 4 weeks, 7 days = ?
4.) 3 weeks, 8 days + 8 weeks, 3 days = ?
5.) 6 weeks, 14 days + 2 weeks, 2 days = ?

Solutions:

1.) Add the weeks together first, and then the days together.  2 weeks + 3 weeks = 5 weeks; 6 days + 2 days = 8 days.  Since your number of days is greater than or equal to 7, you're going to subtract 7 from your amount of days (8-7 = 1) and then add 1 to your weeks (5 + 1 = 6).  So, you're final answer is 6 weeks and 1 day.

2.) 1 week + 9 weeks = 10 weeks; 4 days + 1 day = 5 days; so, since your amount of days is less than or equal to 7, you can stop right there, and you're done.  So, you're final answer is 10 weeks and 5 days.

3.) 7 weeks + 4 weeks = 11 weeks; 5 days + 7 days = 12 days; so, here since we have 12, we must subtract 12-7 days = 5 days.  Then, we must add 1 to our 11 weeks = 12 weeks.  So, our final answer is 12 weeks and 5 days.

4.) 3 weeks + 8 weeks = 11 weeks; 8 days + 3 days = 11 days; so, we must subtract 11 days - 7 = 4 days, and then we must add 1 to our 11 weeks = 12 weeks.  So, our final answer is 12 weeks and 4 days.

5.) 6 weeks + 2 weeks = 8 weeks; 14 days + 2 day = 16 days; we must subtract 16 days - 7 = 9 days, and then add 1 to our 8 weeks = 9 weeks.  We must continue because 9 days is still greater than 7.  So, we take 9 days - 7 = 2 days, and then add 1 to our 9 weeks = 10 weeks.  So, our final answer is 10 weeks and 2 days.

The first link below reiterates how to add weeks and days; it has a practice at the bottom of the webpage; the second link is more for fun--you can add and subtract weeks and days from a certain date.  This is useful if you do not have a calendar around to find the date, and it takes less time.

1.) Explanation of how to add weeks and days with an example
2.) Adding and Subtracting weeks and days to a date calendar

I hope this helps!

Time: Days in a Month; Time: Weeks to Days

In our last post, we learned about different conversions of seconds, minutes, and hours.  Today, we are going to learn about two things: days in each month and converting weeks to days and vice versa. 


To memorize how many days are in each month, we will learn a saying to help us remember. The saying goes like this: 


30 days has September, April, June, and November.  All the rest have 31, except February, which has 28, or 29 if it is a leap year.


It is that easy!


So, just to confirm, we will list the number of days in each month:


January:  31
February: 28 or 29
March: 31
April: 30
May: 31
June: 30
July: 31
August: 31
September: 30
October: 31
November: 30
December: 31


Now, we are going to learn how to convert from weeks to days.  First, we must know that there are 7 days in a week.  To convert weeks back into days, we simply multiply the number of weeks given by 7, since each week has 7 days.  For example, to convert 26 weeks into days, we simply multiply 26 x 7 = 182.  So, 26 weeks = 182 days.  


Let's try a few more examples:


Convert the following number of weeks into days.


1.) 5 weeks = ? days
2.) 17 weeks = ? days
3.) 12 weeks = ? days


1.) 35 days; 5 x 7 = 35
2.) 119 days; 17 x 7 = 119
3.) 84 days; 12 x 7 = 84


Now, we are going to convert from days into weeks.  Since we multiply by 7 to convert from weeks to days, we do the opposite operation to convert days into weeks.  We divide the number of days by 7 to find the number of weeks.  The simplest example is: 7 days = ? weeks?  We simply divide 7 / 7 = 1.  So, 7 days = 1 week.  


Let's try a few more examples:


1.) 49 days = ? weeks
2.) 87 days = ? weeks
3.) 14 days = ? weeks


1.) 49 days = 7 weeks because 49 / 7 = 7
2.) 87 days = 12.43 weeks rounded to the nearest hundredth because 87 / 7 = 12.4285714
3.) 14 days = 2 weeks because 14 / 7 = 2


The following are useful links to help you with both topics we have discussed today:


Note: the first two links should only be used to confirm answers, as they are simply conversion calculators.


1.) Converting weeks to days : calculator
2.) Converting days to weeks: Calculator
3.) Website for learning how to remember the days in each month 

Measuring Time: Hours, Minutes, and Seconds

Hello,

In our previous posts we have learned about fractions, decimals, properties of addition, place values, etc.  We are going to move on to measuring time, and we will start with hours, minutes, and seconds.  In this particular post we will learn how to convert minutes to hours and hours to minutes.  We will also learn how to convert from hours to minutes to seconds and vice versa. 

Basically, you need to know that there are 60 minutes in 1 hour.  So, for example, to convert 45 minutes into hours, you would simply divide 45 into 60.  45/60 = 0.75 when you use long division or your calculator. So, 45 minutes = 0.75 hours.  Let's try an example with converting hours back to minutes.  5 hours is equal to how many minutes?  If you multiply 5 x 60, you will find the amount of minutes.  So 5 hours = 300 minutes.  75 hours is equal how many minutes? 75 x 60 = 4,500 minutes.

As a side note, if we were converting from seconds to minutes to hours, we would not only need to know that there are 60 minutes in 1 hour, but that there are 60 seconds in 1 minute.  For example, 35 hours is equal to how many minutes?  35 x 60 = 2100 minutes.  2100 minutes is equal to how many seconds?  2100 x 60 seconds.  In other words, 35 hours = 2100 minutes = 126,000 seconds.  If we were to reverse our problem and convert 126,000 seconds to minutes and hours, we would proceed with the following computations: 126,000/60 = 2,100 minutes and 2,100/60 = 35 hours.   

Hint: Converting from minutes to hours: divide by 60; converting from hours to minutes: multiply by 60; converting from hours to seconds, multiply by 3600; converting from seconds to minutes, divide by 60; converting from seconds to hours, divide by 3600. 

I know that this seems confusing, but it will be much easier as we practice, I promise.

Let's try these worksheets below; Note that the answers are with the worksheet, but try to do the problems yourself before looking at the answers. 

1.) Worksheet: converting from hours to minutes
2.) Worksheet: converting from minutes to hours
3.) Worksheet: converting from minutes to seconds
4.) Worksheet: converting from seconds to minutes
5.) Worksheet: converting hours, minutes, and seconds; more advanced problems ; Answers to worksheet 5

Look at this website for more practice with conversions, specifically minutes to hours, and hours to minutes :  Go to measurement--time, and click on the fist couple links: More practice with time conversions

Equivalent Fractions

These fractions are equivalent, meaning equal.

Hello,

In past posts, we have discussed fractions; we have learned how to add and subtract fractions, how to convert from improper fractions to mixed numbers, and how to convert from mixed numbers to improper fractions.  Today, we are going to learn about equivalent fractions.  Equivalent fractions represent the same part of something, such as a piece of pizza.  If you cut a piece of pizza in half, you have 2 pieces, while piece is 1 out of the two, or 1/2.  If you cut the pizza into 4 pieces, then 2 of the pieces represent 1/2, and so now you have 2 out of the total 4 pieces, or 2/4.  In other words, 1/2 = 2/4.  Common words to describe equivalent fractions other than 'equivalent to' are 'equal to' and 'congruent to.'  Basically, equivalent fractions multiply the same number to the numerator and denominator to get the new fraction.  1/2 = 2/4 because we can multiply 2 to our numerator, 1, and multiply 2 to our denominator, 2, to get 2/4.  1/2 is also congruent to 3/6 because we can multiply numerator and denominator by 3 to get 3/6.  If we multiplied 1/2 by 4 to the numerator and denominator, what would our equivalent fraction be? Our calculation is 1/2 x 4/4 = 4/8, since when you multiply fractions you just multiply straight across, (numerator x numerator) divided by (denominator x denominator), which we will learn in more detail in another post.

Hint: In order to find equivalent fractions, you must multiply by the same number to numerator and denominator to find your new, equivalent fraction, or you must divide by the same number to numerator and denominator to find your new, equivalent fraction.  Dividing numerator and denominator by the same number to get our equivalent fraction means that we are reducing the fraction, usually in lowest terms.

Let's do some examples of finding equivalent fractions and recognizing equivalent fractions.

1.) 1/3 = ?/6
2.) 5/9 = ?/18
3.) 2/6 = 1/?
4.) True or False. 3/4 = 12/16.
5.) 3/5 = 15/?
6.) 7/10 = 14/?
7.) 4/9 = ?/27
8.) True or False. 1/9 = 7/62.
9.) 4/12 = ?/3
10.) 2/7 = ?/49

Try these examples on your own, and then see the solutions attached here: Answer key to equivalent fractions questions 

For more help with equivalent fractions you can view the chart below, as well as the links below:

Website for understanding equivalent fractions , YouTube video describing equivalent fractions with pictures

Improper Fractions and Mixed Numbers Continued

 Advice of the day:

In our last post, we learned how to convert improper fractions to mixed numbers.  Today we will learn how to convert mixed numbers into improper fractions.  Basically, we are working backwards from what we were doing in our last post.  To review, a mixed number is a whole number plus a fraction, while an improper fraction is where your numerator is larger than your denominator.  In order to learn how to convert mixed numbers to improper fractions, we will go over some examples. 

Examples: Convert the following mixed numbers into improper fractions.

1.) 3 1/2 = ?
2.) 5 2/7 = ?
3.) 7 1/8 = ?
4.) 1 3/4 = ?
5.) 10 1/2 = ?
6.) 2 1/9 = ?
7.) 6 7/8 = ?
8.) 4 2/9 = ?
9.) 8 5/6 = ?
10.) 9 3/5 = ?

Let's do a few together, and then you can try the rest on your own and see the attached answers.   

1.) 3 1/2 = [(2x3) + 1] / 2 = 7/2
2.) 5 2/7 = [(7x5) + 2] / 7 = 37/7
3.) 7 1/8 = [(8x7) + 1] / 8 = 57/8

The pattern is: multiply your denominator by your whole number, add your numerator, and then put that number over your original denominator.

 

Go to this link below to see the solutions to the other problems:  

Solutions to problems 4 through 10

For more help with converting mixed numbers into improper fractions, go to the following links: 

Youtube video with teacher providing an example of how to convert a mixed number into an improper fraction,  Worksheet with 24 practice problems 

I hope this helps! 

Improper Fractions and Mixed Numbers

In our last post, we learned about the different properties of addition.  Today, we are going to be learning how to convert improper fractions to mixed numbers.

We discussed fractions before, which consist of a numerator and denominator.  The only difference between a regular fraction and an improper fraction is that an improper fraction has a numerator larger than the denominator.  For example, 7/2 is an improper fraction because the numerator, 7, is larger than 2, the denominator.  Basically, our goal is to convert  our improper fractions to mixed numbers.  Mixed numbers consist of a whole number and a fraction.  An example of a mixed number is 5 1/2 because 5 is a whole number and 1/2 is a fraction; notice that 1/2 is a regular fraction and not an improper fraction.

How to convert from an improper fraction to a mixed number:  Let's start with an example.  Let's use our 7/2 that we used above.  We first ask ourselves: "How many times does our denominator go into our numerator?"  This will be our whole number part of our mixed number.  Next we subtract how ever many times our denominator goes into our numerator by our numerator.  This will give us our new fraction.  It sounds complicated, but let's try it.  So, how many times does 2 go into 7? 3 times.  So, then we subtract 7 - (2 x 3) and we get 1.  1 is our numerator of our new fraction, and we put that over 2 because that's what we originally started with.  So our mixed number is 3 1/2.

More examples: Convert the following improper fractions to mixed numbers.

1.) 17/4 = ?
2.) 9/5 = ?
3.) 19/6 = ?
4.) 15/2 = ?
5.) 24/9 = ?
6.) 13/8 = ?
7.) 11/3 = ?
8.) 16/5 = ?
9.) 12/5 = ?
10.) 28/9 = ?

1.) 4 goes into 17 four times.  4x4 = 16.  17-16 = 1, so our mixed number is 4 1/4.
2.) 5 goes into 9 once. 5x1 = 5.  9-5 = 4, so our mixed number is 1 4/5.
3.) 6 goes into 19 three times.  6x3 = 18.  19-18 = 1, so our mixed number is 3 1/6.
4.) 2 goes into 15 seven times. 2x7 = 14.  15-14 = 1, so our mixed number is 7 1/2.
5.) 9 goes into 24 two times. 9x2 = 18.  24-18 = 6, so our mixed number is 2 6/9, which can be simplified to 2 2/3 because 6/9 = 2/3 since 3 is divisible by 6 and 9.
6.) 8 goes into 13 once. 8x1 = 8.  13-8 = 5, so our mixed number is 1 5/8.
7.) 3 goes into 11 three times. 3x3 = 9.  11-9 = 2, so our mixed number is 3 2/3.
8.) 5 goes into 16 three times. 5x3 = 15.  16-15 = 1, so our mixed number is 3 1/5.
9.) 5 goes into 12 twice.  5x2 = 10.  12-10 = 2, so our mixed number is 2 2/5.
10.) 9 goes into 28 three times.  9x3 = 27.  28-27 = 1, so our mixed number is 3 1/9.

For more help, visit: for practice with converting improper fractions to mixed numbers, 
 YouTube video on further instruction on how to convert improper fractions to mixed numbers

I hope this helps =)

4 Properties of Addition

Hi boys and girls, I hope that you are having a great day!

Today we will be discussing the different properties of addition that will be useful in your future math classes, perhaps even in college, yes I said college!) as these are properties that will never go away.  There are five properties of addition.  They include: commutative, associative, identity, distributive, and inverse.  I will give the general form of each property in a list below.

1.) Commutative property of addition: a + b = b + a (or) a + (b + c) = (b + c) + a
2.) Associative property of addition: (a + b) + c  = a + (b + c)
3.) Identity property of addition: a + 0 = a = 0 + a
4.) Additive inverse property: a + (-a) = 0
5.) Distributive property of addition: a (b + c) = ab + ac 

Now, these may seem confusing or foreign to you, but all you need to do is memorize them, and examples will help you.  If you look at the commutative and associative properties, they look similar.  However, for the commutative property, what is inside the parentheses will NOT change.  For the associative property, what is inside the parentheses WILL change.  And for the first two properties, you are basically adding two or three numbers, but in a different order.  Properties three and four are pretty self-explanatory; for property three, you are simply interested in adding some number to "x" (x being any number) to always get "x."  In this case, we want zero because any number added to zero gives us zero.  For property four, it is called the inverse property of addition because you are adding the 'inverse' of a number to get zero.  Property five is pretty easy.  You must 'distribute' the 'a' to the 'b' and 'c.'  So you are essentially multiplying 'a' to both 'b' and 'c' and then adding them together.

Examples:  Which property of addition holds for the following?

1.) 5 (4 + 9) = 20 + 45.

2.) 8 + (-8) = 0.

3.) 6 + 1 = 1 + 6.

4.) 7 + (1 + 2) = (7 + 1) + 2.

5.) 6 + (-6) = 0.

6.) 3 + 0 = 0 + 3.

7.) 5 + 6 = 6 + 5.

8.) 0 + 4 = 4 + 0.

9.) (1 + 1) + 5 = 1 + (1 + 5).

10.) 9 (4 + 8) = 36 + 72.

Answers: =)

1.) Distributive
2.) Inverse
3.) Commutative
4.) Associative
5.) Inverse
6.) Identity
7.) Commutative
8.) Identity
9.) Associative
10.) Distributive

Do you understand them?

For more help, go to help with associative, commutative, and distributive properties, properties of addition put into different words, YouTube video with properties of addition

Thanks!