documents in math.docx

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.


3/27

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.


4/27

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


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


6/27

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.


7/27

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.


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.


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.


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.


11/27

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.


12/27

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.


13/27

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.


14/27

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.


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.


16/27

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.


17/27

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%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.


18/27

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.


19/27

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.


20/27

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.


21/27

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.


22/27

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


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


484%4=121

4%4=1 4x1=4 44=0

8%4=2 4x2=8 88=0

4%4=1 4x1=4 44=0



23/27

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.


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:


25/27

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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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


27/27

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+

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documents in math.docx