Reminders
• If you missed your exam/quiz due to illness or other grounds, you
send an e-mail/write a request for Deferred Assessment. You must
submit your request/e-mail to auditor.e@pnu.edu.ph and include
appropriate documentation to support the grounds on which you are
requesting your assessment to be deferred.
• Grounds and their associated documentation could include the
following:
• Illness—medical certificate (or a letter signed by your
parents/guardians if you have difficulty obtaining a medical
certificate)
• Technical Issues - timestamped screenshot or proof of help
request/Declaration (e.g. PLDT announcement)
• Other compassionate circumstances—Declaration (Announcement)
etc.
• Homework/Task is your teachers' way of
evaluating how much you understand of what's
going on in class. But it can seem overwhelming at
times. Luckily, you can do a few things to make
homework less work.
Review LCM and GCF
The greatest common factor, or GCF, is the
greatest factor that divides two numbers.
The Least Common Multiple ( LCM ) is also referred to as the Lowest Common
Multiple ( LCM ) and Least Common Divisor ( LCD) . For two numbers the LCM is
the smallest positive number that is evenly divisible by both a and b. For
example, LCM(2,3) = 6 and LCM(6,10) = 30.
What is the Ladder Method Anyway?
---It is a simple technique that uses
prime numbers and visualization in
the form of staggering lines (in a way
that looks like a ladder) to help you
understand math problems
• So, the first step is defining and identifying prime
numbers. ---prime numbers are those that are
greater than 1 and have no positive divisors other
than 1 and itself---Prime numbers are numbers
that have only 2 factors: 1 and themselves.
• For example, the first 5 prime numbers are 2, 3, 5,
7, and 11. By contrast, numbers with more than 2
factors are call composite numbers.
How to Use the Ladder Method to Simplify Fractions
When you have a fraction like 24/36 and you need to simplify, you’ll use the
ladder method just like in the example above. To account for both numbers, you
will simply add another column.
Identify both the numerator (the number on top of the fraction) and the
denominator (the number on the bottom), putting them in separate columns:
N
D
| 24 | 36 |
Using the ladder Method, think about the smallest prime number that will go into
both 24 and 36.
Answer is “2”, ask them how many times 2 goes into both 24 and 36. You’ll write
the answers in the separate rungs below the numbers.
This is how the first two rungs of the ladder should look at this point:
2 | 24 | 36 |
2 | 12 | 18 |
Repeat the process for the next two numbers, which are also divisible by 2:
2 | 24 | 36 |
2 | 12 | 18 |
|6|9|
Now we have the numbers 6 and 9.
When we start with the lowest prime number, 2, we notice that it goes evenly into 6, but not 9. That means we can’t
use it. So, you must move to the next prime number.
Does 3 go into both numbers evenly?
If you divide 6 by 3, we get 2; a nice even number. And you can divide 9 by 3 and to get 3, a prime number. So we’ll
add another rung to the ladder.
N D
2 | 24 | 36 |
2 | 12 | 18 |
3|6|9|
2 3
At this point, you’ve reached a prime number and will not be able to add any more rungs. So we’ll revisit the original
problem: how to simplify the fraction 24/36 .
The correct answer is in the bottom rung of the ladder: ?
Easy peasy, right?
Since we’ve already done all this math, let’s use this same example to find the greatest common factor and the least
common multiple.
How to Use the Ladder Method to Find the Greatest Common Factor
The greatest common factor (GCF) is the largest number that divides evenly into all of the numbers you’re
comparing.
It’s easy to find the GCF using the ladder method because all you have to do is look at the factors of each
number on the left side of the ladder and multiply them.
Can you find the greatest common factor in the example below?
N D
2 | 24 | 36 |
2 | 12 | 18 |
3|6|9|
2 3
If you answered 12, you are correct because 2 x 2 x 3 = 12.
That means no other number higher than 12 can be divided evenly into both 24 and 36.
How to Use the Ladder Method to Find the Lowest Common Multiple
To show you how to do this, we’ll use the ladder we built earlier with 24 and 36.
Then, you’ll simply multiply all the numbers that form an “L” on the left side of
the ladder.
2 | 24 | 36 |
2 | 12 | 18 |
3 |6|9|
|2|3|
So the LCM is found with the following equation: 2 x 2 x 3 x 2 x 3 = 72.
This is a much easier way to find the solution than identifying all the individual
multiples of these numbers!
Share
Operations with Fractions
Addition, subtraction, multiplication and division
Multiplication first, it’s the easiest one to do…
1
2
1
3
=
1
6
Multiplication RULE: Multiply across the top
(the numerators), then multiply across the
bottom (the denominators).
If necessary, reduce the fraction to lower terms.
Multiply these fractions now
3
4
1
3
=
2
3
1
5
=
Multiply these fractions now
3
4
1
3
2
3
1
5
=
3
12
=
2
15
3
3
÷
3
12
=
1
4
Division of Fractions… also easy,
but with a “1st step” to do first!
2
1
÷
3
5
=
2
3
5
1
=
10
3
=
1
33
We don’t really ever “divide” fractions… we change the ÷ sign
to the x sign, FLIP the 2nd fraction over, then just multiply, and
Divide these fractions now
3
1
÷
5
3
=
7
1
÷
10 2
=
Divide these fractions now
3
1
÷
5
3
7
1
÷
10 2
3
5
=
=
7
10
2
1
3
1
=
=
14
10
9
5
=
4
15
4
2
110 =15
=
Addition of Fractions… make sure you have
COMMON DENOMINATORS, make sure the
bottom numbers are the same before you add.
1
3
+
5
5
=
1
2
+
4
4
=
Addition of Fractions… make sure you have
COMMON DENOMINATORS, make sure the
bottom numbers are the same before you add.
1
3
+
5
5
1
2
+
4
4
=
4
5
=
3
4
Both of these addition
problems STARTED with
common denominators, all
you have to do is add them up.
Easy!
This is not quite the same, these fractions have
different bottom numbers, different denominators.
1
1
+
2
4
=
You need to figure out a common denominator first,
then add. (hint, it’s FOUR!)
This is not quite the same, these fractions have
different bottom numbers, different denominators.
1
1
+
2
4
2
1
+
4
4
=
1
2
x2=
x2=
=
3
4
2
4
The four can’t be lowered to a 2, but the two can be doubled to four.
If you double the bottom, double the top
Add these fractions.
1
1
+
3
6
=
Becomes…
1
1
+
3
6
=
2
2
2
1
+
6
6
=
3
6
=
1
2
Add these fractions.
2
1
+
3
5
=
3
3
2
1
+
3
5
=
5
5
10 3
+
15 15
=
This is important:
13
15
3
3
=1
and
5
5
=1
We are changing the “name” of the
fractions, but not their values.
Add these fractions.
1
3
+
3 15
=
Add these fractions.
1
3
+
3 15
=
5
5
3
5
+
15 15
=
8
15
Subtract these fractions.
3
1
−
4
2
=
3
1
−
4
2
=
Same process, make the denominators
the same, then just subtract the
numerators. No big deal at all. .
Subtract these fractions.
3
1
−
4
2
3
1
−
4
2
=
=
Same process, make the denominators
the same, then just subtract the
numerators. No big deal at all. .
3
2
−
4
4
=
1
4
Subtract these fractions.
5
1
−
10 5
=
Subtract these fractions.
5
1
−
10 5
=
5
2
−
10 10
=
3
10
https://www.homeschoolmath.net/worksheets/tablefractions.php?op=adsu&col=2&row=4&dup=1&neg=1&ntype1=fraction&n1_min=1&n1_
max=9&n1_list=&d1_min=2&d1_max=10&d1_list=&w1_min=2&w1_max=5&w1_list=&n
type2=fraction&n2_min=1&n2_max=12&n2_list=&d2_min=2&d2_max=10&d2_list=&w2
_min=2&w2_max=5&w2_list=&numbers=2&extraspace=6&font=Arial&FontSize=12pt&p
ad=9&border=on&color=teal&ptitle=&Submit=Submit
https://www.homeschoolmath.net/worksheets/fraction.php
Do your homework.