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8/14/2019 documents in math.docx
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8/14/2019 documents in math.docx
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TOPIC: Division of fractions
Example:
3/5%1/4First the numerator of will become the denominator and the
denominator will become the numerator.
3/5 x 4/1
Second multiply it
3/5 x 4/1=12/5
Third if the answer is improper change it to mixed form by
dividing it.
5%12=2 2/5
The final answer is
2 2/5
REMEMBER:
To divide the fractions, multiply the dividend by the
reciprocal of the divisor. Change the answer to its
simplest form, if possible.
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8/14/2019 documents in math.docx
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TOPIC: Multiplication of fractions by mixed numbers
Examples:
5/18x4 =5/182x91/2
Think of the common factor between 9 and 18 it is 9.
Divide: 9%9=1; 18%9=2
Multiply 5 by 1 and 2 by 2
Reduce your answer to lowest term
=5/4 or 1
REMEMBER:
To multiply a fraction by a mixed number, change the mixed
number to an improper fraction, then multiply the numerators.
Have the product over the product of the denominators.
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8/14/2019 documents in math.docx
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Example:
4/8 and 2/5
First multiply the numerator by the denominator. Use crossmultiplication.
4x5=20
Second multiply the denominator by the numerator. Use again
the cross multiplication.
8x2=16
Use the cross multiplication to tell whether , greater than less
than another fraction.
4/8 2/5
20 16
The highest number is 20 so the point to the 16 because its thelowest.
The final answer
20 > 16
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8/14/2019 documents in math.docx
5/27
TOPIC: Renaming decimal as fraction
Example:
.010 is read as 10 thousandths10/1 00010%10= 1/
1000%10=100
1/100=0.010
First divide 10 to 10 then the answer is 1 then 1 is the numeratorthen the 1 will become the denominator and add three zeros
1000 divided by 10 is 100 the answer is 1/100 or 0.010
REMEMBER:
In changing a decimal number to a fraction, read the
decimal number, write it in fraction form and then reducethe fraction to its lowest term
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8/14/2019 documents in math.docx
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TOPIC: Writing fraction
Example:
4/8 % 4= the answer is 4/8 or
5/10 % 5=1/2 the final answer is 5/10 or
REMEMBER:
We write fractions in this way 2/3 2 is the numerator 3
is the denominator
Two different fractions sometimes suggest the same
number of objects in a set or the same part of a region.
Two such fractions are equivalent to each other.
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8/14/2019 documents in math.docx
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TOPIC: Least common multiple (LCM)
Example:
12 and 366/12 36 6x2=12 12x3=36 the LCM is 36
2/ 2 6 if the number is 1 multiply the factors and if
3/ 1 3 its done the answer in the factors is the
/ 1 1 answer in the LCM.
REMEMBER:
The least common multiple (LCM) is the least number
greater than one that can divide 2 or more given numbers
without any remainder.
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8/14/2019 documents in math.docx
8/27
TOPIC: Mixed numbers to improper fractions and vice-versa
Example:
1 2/3 first multiply whole by thedenominator.
1x3=3
Next is Add the answer to the numerator.
3+2=5
The answer is 5/3
REMEMBER:
To change mixed number to an improper fraction, multiply
the whole number by the denominator of the fractional part
then add the product to the Numerator.The denominator of the result of the step above is the same
as the denominator of the fractional part of the mixednumber
To change an improper fraction to a mixed number, divide
the numerator by the denominator.
The quotient is the whole number of the mixed number and
the remainder becomes the numerator while the denominator
remains the same as in the improper fraction.
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8/14/2019 documents in math.docx
9/27
TOPICS: Multiplication of fraction by other fractions
Example:
4/5 and 10/16First use cancellation. Cross the numerator and denominator
4/51, 102/16
Second cross the denominator and numerator
14/51,102/164=2/4
Third express the answer to lowest term if necessary
2/4%2=1/2
The final answer is
2/4 or 1/2
REMEMBER:
To multiply two fractions, find the product of the
numerators and have this over the product of the
denominators. Express the answer in its lowest terms, if
necessary.
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8/14/2019 documents in math.docx
10/27
TOPIC: Multiplication of fractions by whole numbers
Example:
5/8x5First multiply the whole number by the numerator
5x5=25
Second copy the denominator
25/8
third change the product to its simplest form
25/8=5
The final answer is 5
REMEMBER:
To multiply fractions by whole numbers, multiply the
numerator by the whole number and have the product
over the denominator of the fraction. Change the
product to its simplest form, if needed.Cancellation can also be used in multiplying fractions
by whole numbers.
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8/14/2019 documents in math.docx
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TOPIC: Subtraction of dissimilar fractions
Example:
3/4, 1/5, 2/5First get the LCD of the denominators
5/4 5 5
/4 1 1
Second multiply the factors
5x1x1x4=20
Third divide the both denominators and multiply to the
numerator
4%20=5x3=15, 5%20=4x1=4 and 5%20=4x2=8
Fourth subtract all the numerators
15/204/20=11/208/20=3/20
The final answer is
3/20
REMEMBER:
To subtract dissimilar fractions, change them first tosimilar fractions by finding the LCD, then subtract the
numerators and have the difference over the
denominator.
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8/14/2019 documents in math.docx
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TOPIC: Subtraction of similar fractions
Example:
5 8/12 and 2 4/6First subtract the whole number.
52=3
Second subtract the both the numerators.
84=4
Third subtract both the denominators.
126=6
Solution:
5 8/122 4/6=3 4/6
The final answer is:3 4/6
REMEMBER:
To subtract similar fractions, find the difference of the
numerators and have this over the common
denominator.
In cases where the numerator in the minuend is smaller
than the numerator and rename the whole number as a
mixed number with the same denominator.
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8/14/2019 documents in math.docx
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TOPIC: Addition of dissimilar fractions
Example:
1/10, 1/20, 3/15First get the LCD then multiply the factors
5/10 20 15
2 / 2 4 3
2/ 1 2 3
2 / 1 1 3
Then multiply the factors.
5x2x2x2x1x1x3=120
Second divide the denominator by denominator then multiply to
the numerator.
1/10, 12/120, 1/20, 6/120, 3/15, 24/120
Third add all the numerators.
12+6+24=42
The final answer is 42/120.
REMEMBER:
To add dissimilar fraction, first make the fractions
similar by finding the least common denominator, and
then follow the steps in adding similar fractions.
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8/14/2019 documents in math.docx
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TOPIC: Addition of similar fractions
Example:
5/3 and 4/3First add the numerator by numerator and then copy the
denominator.
5/3+4/3=9/6
Second divide the numerator and denominator.
9%6=1 3/2
The final answer is 1 3/2
1 will become whole number. Multiply the denominator by the
whole number then numerator minus denominator. Copy the
denominator.
12/10 + 15/10=27/10
27%10=2 7/10
The final answer is 2 7/10
REMEMBER:
To add similar fractions, add the numerators and have thesum over the common denominator. Do the same with
mixed numbers. Add the similar fractions and then find
the sum of the whole numbers.
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8/14/2019 documents in math.docx
15/27
TOPIC: Ordering fractions
Example:
Ken have 1/5 of orange, Leonard have 3/8 of mango and Derrickhave 5/10 strawberry.
First we arrange it to ascending order, ascending order is from
least to greatest fraction.
1/5 of orange, 3/8 of mango, and 5/10 of strawberry
Second we arrange it to descending order, descending order is
from greatest to least fraction.
5/10 of strawberry, 3/8 of mango and /5 of orange
REMEMBER:
In ordering fraction, always considered that the bigger the
numerator the bigger the number of equivalent parts of the
whole will be.
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8/14/2019 documents in math.docx
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TOPIC: Comparing fractions
REMEMBER:
We can compare fractions and mixed numbers using
different methods as:Cross multiplicationGet the product of the first numerator and the second
denominator write under the first fraction.Get the product of the first denominator and the second
numerator write under the second fraction. Compare the
results.Find the LCD of the given fractions and then convert them
to similar fractions.To determine whether a given fraction is close to 0, or 1,
use the number lines to visualize the fractions.The bigger or greater the fraction, the nearer or closer it is
to 0.
If the numerator is greater than of the denominator, the
fraction is greater than and close to 1.If the numerator is less than of the denominator, the
fraction is less than and close to If the numerator is 1, the fraction is small and close to 0.
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8/14/2019 documents in math.docx
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TOPIC: Fraction in lowest term
Example:
9/159 is divisible by 3
9%3=3
15 is divisible by 3
15%3=5
The answer is 3/5
6/12
6 is divisible by 6
6%6=1
12 is divisible by 6
12%6=2
The answer is 1/2
REMEMBER:To find the lowest terms of a fraction, find the GCF of
the two terms of the fraction. Then divide both terms by
the GCF.
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8/14/2019 documents in math.docx
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TOPIC: Equivalent fractions
Example:
You can have some equivalent fraction by multiplying thenumerator and denominator by the same number .
2/3
2x2=4
3x2=6
The answer is 4/6
You can find other equivalent fractions by dividing thenumerator and denominator by the same number.
5/10
5%5=1
10%5=2
The answer is 1/2
REMEMBER:
Fractions are equivalent when they name or refer to
the same fractional part of a whole.
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8/14/2019 documents in math.docx
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TOPIC: Renaming fractions as decimals:
Example:
5%1.00=0.20The fraction of the decimal is 1/5=0.20
0.20 is terminating because the remainder is zero.
4%8.00=2.00
The fraction of the decimal is 4/8 =2.00
2.00 is terminating because the remainder is zero.
REMEMBER:
In changing a decimal number to a fraction, read the
decimal number, write it in fraction form and then reduce
the fraction to its lowest term.
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8/14/2019 documents in math.docx
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TOPIC: Greatest Common factor (GCF)
Example:
Get the GCF of 4and 64and 6 to get the GCF we will use continues division
2/4 6
/ 2 3 when the two number is prime and composite stop dividing it so the
answer is 2
Get the GCF of 3 and 9
3/3 9
/ 1 3 the number is now prime and composite so the GCF is
3
REMEMBER:
The greatest common factor (GCF) of 2 or more given
numbers is the largest number that can divide the
numbers.
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8/14/2019 documents in math.docx
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TOPIC: Prime factor of a given number
Example:
Factors of 2424=4x6 factors of 4 2x2
Factors of 6 3x2
REMEMBER:
A whole number greater than 1 is composite if it has
more than two different factors.Composite numbers can be expressed as a product of
prime factors in different ways ending with the same set
of factors.
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8/14/2019 documents in math.docx
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Example:
636 divisible by 6
636%6=16
6%6=1 6x1=6 66=0
6%3= cannot be bring 6 it will become 36
6%36=6 6x6=36 3636=0
636 is divisible by 6
936 divisible by 3
936%3=312
9%3=3 3x3=9 99=0
3%3=1 3x1=3 33=0
6%3=2 3x2=6 66=0
936 is divisible by 3
484%4=121
4%4=1 4x1=4 44=0
8%4=2 4x2=8 88=0
4%4=1 4x1=4 44=0
484 is divisible by 4
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8/14/2019 documents in math.docx
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TOPIC: Prime and Composite
Example:
What are the factors of 3636=6x6, 3 x12, 4x9, 2x18
the factors of 36 are 6,3,4,2 thats we call composite
What is the factor of 5
5=5x1
Thatswe call prime because the factor is 1 and itself
REMEMBER
BER:The whole Number that Have more than one factor
pair aside from 1 and the number itself are called
composite numbers.
The whole numbers that have only one factor pair,
that is, 1 and the number itself, are called prime
numbers.
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8/14/2019 documents in math.docx
24/27
Rafael Palma Elementary School
North district
2ndGrading
Prepared by:
JEREMY ASHLY A. PASION
IV-I (Einstein)
Submit to:
Mrs. FLODELINA I. ROS
Date submit
Rating:
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8/14/2019 documents in math.docx
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TOPIC: Division of Decimal
REMEMBER:
In dividing a whole number by a decimal, multiply the
divisor by 10,100 or 1000 to make it a whole number.Multiply the dividend by the same power of 10 that you
used in your divisor and then divide just like dividing
whole numbers.
When dividing mixed decimals by mixed decimal, move
the decimal point in the divisor as many places to the
right as necessary to make it a whole number. Move the
decimal point in the dividend as many places to the right
as in the divisor.When dividing decimals by .1,.01,.001mentaly,just move
the decimal point one place to the left, two places to the
left and three places to the to the left respectively, inyour quotient.
Where the dividend is smaller or less than the divisor,
put a decimal point in the dividend, annex the necessary
zeros and then divide as in dividing a whole numbers.
If you notice that the numerals in the quotient are
continuously repeating put ellipsis (.)indicating that
the numerals repeat unendingly.
When the numerals in the quotient are not repeated, just
continue dividing as a whole numbers.
Place the decimal point in the quotient directly above the
decimal point in the dividend.
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8/14/2019 documents in math.docx
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Examples:
Erick has 5 pieces of apples the weight of all apples is 1.4
kilograms. How many kilograms does each apple have?
5%1.4=2
5x2=10
14-10=4
Four add zero became 40
40%5=8
The final answer is 28 kilograms
Jenny is buying 4 ballpen each cost is php 8.2.how much the
cost of all ballpen?
4%8.2=2
Multiply the answer by the divisor then bring down two and add
zero.
4x2=8 8-8=0
20%4=5 5x4=20 20-20=0 the final answer is php 25.00
TOPIC: Divisibility Rules
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8/14/2019 documents in math.docx
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REMEMBER:
E product from t
A number is divisible by:2-if the number ends in even numbers (0, 2, 4, 6, 8)
3-if the sum of its digits is divisible by 3
Example: 561=5+6+1=12:12 is divisible by 3
4-if the number has 2 last digits divisible by 4
Example: 252; 52 is divisible by 4 so 252 is divisible by 4
5-if the number ends in 0 or 5
6-if the number is even and the sum of its digits is divisible
by 3, the number is divisible by 6.Example: 498; 4+9+8=21; 21 is divisible by 3 so 498 is
divisible by 6
7-multiply the last digit by 2, subtract the product from the
remaining digits, and if the difference is divisible by 7 the
number is divisible by 7 repeat the process if the number is
big.
Example: 24 822 - 2x2=4 - 2 482-4=2 487
2 4788x2=1624716 =231
2311x2=2232 =21
Since 21 is divisible by 7, therefore 24 822 is divisible by 7.
8If the number has the last 3 digits divisible by 8
Example: 1 432,432 % 8= 54; 1 432 is divisible by 8
9If the sum of the digits is divisible by 9Example: 2 + 8 + 9+