# MSC 12 – Dividing by 4 and 8

We can easily divide a number by 4 by halving the number twice and by 8, by halving thrice.  We shall, however try dividing by 4 and 8 using the one line solution introduced in MSC 6 – Division by Two.

Example 12.1:    586 ÷ 4 =

When dividing a whole number by 4, there are only 4 possible remainders: 0, which means that the number is evenly divisible by 4; and 1, 2 and 3 which are equivalent to 0.25, 0.50 and 0.75 respectively. In this example, the dividend is an even number so the remainder can only be 0 or 2.

1                         1   4                     1   4   6
4) 5 18  6           4) 5 18 26             4) 5 18 26  ( r 2

a) Dividing 5 by 4 gives a quotient of and a remainder of 1 which we place in front of the next digit of the dividend,

b) Dividing the next dividend 18 by 4 results in a quotient of 4 and a remainder of 2, which we then place in front of the next digit

c) Finally, we divide 26 by 4 to give 6 and a remainder of Thus the final quotient is 146 2/4 or 146.5.

Example 12.2:     743  ÷ 4 =

1   8   5
4) 7 323 (r 3

Here the dividend is an odd number, so we expect a remainder of 1 or 3.

1. Dividing 7 by 4 gives 1 remainder
2. 34 divided by 4 gives 8 remainder23 divided by 4 gives 5 remainder
3. The quotient is 185 3/4 or 185.75.

The following are the values of the remainders when dividing by 8.

Remainder                         decimal equivalent
1                                              0.125
2                                              0.25
3                                              0.375
4                                              0.5
5                                              0.625
6                                              0.75
7                                              0.875

Example 12.3:          983÷ 8 =

1   2  2
8) 9 123 (7

Using the one line solution, we have

1. 9 divided by 8 is 1 remainder 1
2. 18 divided 8 is 2 remainder 2
3. 23 divided by 2 is 2 remainder 7

So we arrive at an answer of 122 remainder 7. This is equivalent to 122 7/8 or 122.875

Example 12.4:         6352 ÷ 8 =

7   9  4
8) 63 75 32 (0

Using the one line method, we got the quotient 794. For the careful observer, the dividend, 6,352 is very near 6,400 or exactly 48 less.  6,400÷ 8 = 800 and 48÷ 8 = 6 so 6352 ÷ 8 is simply 800 – 6 = 794.

Exercise 12:

1. )  456 ÷ 4 =
2. )  527 ÷ 4 =
3. )  983 ÷ 4 =
4. )  2,538 ÷ 4 =
5. )  6,789 ÷ 4 =
6. )  745 ÷ 8 =
7. )  1,278 ÷ 8 =
8. )  3,684 ÷ 8 =
9. )  6,454 ÷ 8 =
10. )  10,522 ÷ 8 =

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!

# Bands from MSC

When MSC occupied the old Agrix Supermarket along A. Fule St. it was called the MSC Annex.  The MSC Annex was not only used for classes of the 2-year course and high school students.  It also housed a sound-proofed music studio, complete with instruments, amplifiers, speakers, and band accessories.  Instruments of the MSC High school for its drum and lyre band were also kept in the annex.

During summer, MSC offered lessons to young would-be musicians on guitar, keyboard, and drums.  At the end of each summer, recitals were held to show what the students have learned.

With the supervision of the late Sir Val Tomas (also MSC’s electronics teacher during that time), the MSC Music Studio has produced many successful bands which until now plays very good music here and abroad.  One of the most popular (and successful) “products” of the MSC music studio is the “Layag-laya”, most members of which, namely Alfie Santos, Ronald Andal, Ranegel Latade, and Ron Yabut are from the MSC Band.

The MSC Band also included Althea Maloles, Anjo Latade, Cathy Guevarra, and Celia Domingo.  They are all graduates of MSC and are the first music students of Sir Val.  This band won first place in the Rotarock Battle of the Bands in the first years of the annual Cocofest of San Pablo City, despite being the band with the youngest members.  The band Layag-laya was formed when they graduated from MSC.  Though they are disbanded today, they still perform with other groups, some are abroad, but they remain close friends.

Then there was the Shadow Band, which was later renamed Charcoal Paint Band with MSC High schoolers Jomari Jalandoni, Jayvee Laroza, Oswald Palines, and Anjo Latade, among its members.

The Bionic Band, an all-female band was mainly composed students from MSC High School – Geniena and Ginelle  Dimalanta, and Rachel De la Rama.

Balustre Band with Alvin Cataring, an MSC tech-voc student was another band which was active during those days.  Today, Alvin still sings and is active with his gigs.

# Divisibility Test: 2, 4, and 8

The divisibility rules for 2, 4 and 8 are simple and similar.

A number is divisible by 2 if its last digit is divisible by 2.

Since 10 is divisible by 2, the divisibility of a number by 2 depends only on the unit’s digit. So all even numbers, i.e. those numbers ending in 0, 2, 4, 6 and 8 are divisible by 2.

A number is divisible by 4 if its last 2 digits are divisible by 4.

100 is evenly divisible by 4 so only the last two digits determines the number’s divisibility by 4. First the number must be even to be divisible by 2.  All odd numbers are not.

A number is divisible by 8 if its last 3 digits are divisible by 8.

1000 is evenly divisible by 8, so we only have to determine if the last 3 digits are divisible by 8.

There are several handy methods to simplify the division of the last digits by 4 or 8:

a) Divide the last 2 digits by 4 or the last 3 digits by 8 using the method in MSC 12.

b) Divide the last two digits by 2, if the quotient is an even number, the number is divisible by 4. Divide the last three digits by 2 twice. If the quotient is an even number, the number is divisible by 8.

c) Add the ultimate (last) digit to twice the penultimate (second to the last) digit and if the sum is divisible by 4, the number is divisible by 4. For 8, add twice the hundreds digit and four times the tens digit to the unit’s digit. If the total is divisible by 8, the number is divisible by 8. This method is not recommended but is instructive in understanding divisibility of 3, 9, and 11.

d) Add or subtract from the digits to arrive at numbers obviously divisible by the number tested.

d.1) Add or subtract 4 or 8 from the last digit to make it zero and if the resulting ten’s digit is an even number, the number is divisible by 4.

Examples:   52 + 8 = 60, 52 is divisible by 4; but 74 – 4 = 70, so 70 is not divisible by 4.

d.2) To find out if a number is divisible by 8, add or subtract 8 or 16 from the last three digits to make the last digit zero and see if the number resulting is divisible by four.  Add or subtract 40 or 80 to make the ten’s digit also zero if needed.  If the hundreds digit becomes even, the number is divisible by 8.

392 + 8 = 400; 392 is divisible by 8;             296 – 16 = 280;  280 – 80 = 200;  296 is divisible by 8

324 + 16= 340;  340-40 = 300; 324 is not divisible by 8.

# Announcement – MSC Alumni Homecoming Activities

The MSC Alumni Homecoming Activities have begun with alumni basketball and volleyball ( men and women’s leagues) and will culminate on Saturday, Dec 6, 2014 during the week long 25th MSC Foundation Week Activities, with the the Search for Outstanding MSC Alumni – Awarding Ceremonies, followed by the Alumni Homecoming Ball.

 PROGRAM OF ACTIVITIES Activities December 1, 2014 (Monday) Campus Clean-up Drive December 3, 2014(Wednesday) Ingress of Exhibits December 4, 2014 (Thursday) 8:00-9:00 a.m. Thanksgiving Mass 9:30 a.m. Motorcade 11:00 a.m. Opening of Exhibits Student Recruitment/ Career Orientation Photo Exhibit – MSC milestones Math-Sci Exhibit Eng-Fil-Social Exhibit Arts Exhibit Botanical Garden Booths 1:00 p.m. Scavenger Hunt! Scavenger Hunt! 1st PC assembly & disassembly Visual Graphics 1st digital arts – tarp layout 3:00 p.m. Entrance/ Scholarship Exam/ Orientation to MSC High School MSC High School Got Talent ! Mr. & Ms. MSC December 5, 2014 (Friday) 8:00 a.m.- 4:00 p.m. Math-Sci Exhibit Eng-Fil-Social Exhibit Arts Exhibit Botanical Garden 9:00 a.m. 13th Inter-elem School Quiz Show Inter-class Math Sci Challenge 1:00 p.m. 5th Speed Math Contest Inter-class Speed Math contest 3:00 p.m. 9th Cyberfair web design contest (awarding) Robotics – demonstrations December 6, 2014 (Saturday) 8:00 a.m. Family Day PTA raffle/ games/ boodle fight 3 p.m. Sayawit Search for Outstanding MSC Alumni 6 p.m. Search for Outstanding MSC Alumni – Awarding Ceremony Dinner Alumni Homecoming

We would like to hear from all our MSC Alumni. Please fill up the form below, and click submit.

If you’d like to join the activities, please register using the indicated links:

# MSC High School: consistent Cyberfair winner

Ever since the Philippine Schools Cyberfair competition was launched in 2001, MSC High School has been a consistent winner.  In the International Cyberfair competiton, MSC has also been consistently winning in the largest inter-school web design contest.

Some of the Philippine Schools Cyberfair trophies awarded to MSC through the years.

The International schools CyberFair, which started in 1996 is an award-winning, authentic learning program used by schools and youth organizations around the world. Students conduct research about their local communities and use digital media to publish their findings online. Recognition is given to the best projects in each of eight categories: local leaders, businesses, community organizations, historical landmarks, environment, music, art, and local specialties.

This White House endorsed program encourages youth to become ambassadors for their own local communities by working collaboratively with community members and using technology tools to publish a website or create a video that displays what they have learned. The annual contest has involved more than 5 million students from 45,500 schools across 115 countries—and is considered the longest running international online event of its kind.

Competition judging also takes place online. Students evaluate each others projects using a web-based evaluation tool (rubric) designed by Global SchoolNet. The top forty entries are reviewed by international judges to determine the best educational projects. Winners of International CyberFair are announced each Spring at a event that is global in itself, with hundreds of schools participating via Internet.

The awards received by MSC High School from the International School Cyberfair are the following:

• 2002 – Honorable Mention – Historical Landmarks – San Pablo City (City of Seven Lakes) ..Streets and Historical Landmarks”
• 2004 – Silver – Environmental Awareness – Sampalok Lake… Paradise Lost…Paradise Reborn
• 2005 – Honorable Mention – Local Music and Art – Festivals of Laguna
• 2007 – Honorable Mention – Historical Landmarks – Structures of San Pablo delos Montes
• 2008 – Honorable Mention – Environmental Awareness – Interrelatedness
• 2010 – Silver Awardee – Local Attractions (Natural and Man-made) – Museo ng San Pablo
• 2012 – Honorable Mention – Local Attractions (Natural and Man-made) – Sampalok Lake: Paradise on the Rise… A Dream in Progress

In the Philippine School Cyberfair, here are MSC’s entries:

• 2002 – “San Pablo City (City of Seven Lakes) ..Streets and Historical Landmarks”
• 2003 – “Pasalubong from the city of San Pablo”
• 2004 – “Sampalok Lake… Paradise Lost…Paradise Reborn”
• 2005 – “Festivals of Laguna”
• 2006 –  “Tree of Life”
• –          The Red Trucks and the Firefighters
• –          Local Leaders
• 2007 – Structures of San Pablo delos Montes
• –          A Virtual Tour of San Pablo City Commercial District
• –          Phillipine Sports
• –          Local Artists of San Pablo City
• 2008– Interrelatedness
• –          Explore the Magic of Coconuts
• –          San Pablo City – Seven Lakes
• –          Famous San Pableños
• 2010 – Silver Awardee – Local Attractions (Natural and Man-made) – Museo ng San Pablo
• 2012 – Honorable Mention – Local Attractions (Natural and Man-made) – Sampalok Lake: Paradise on the Rise… A Dream in Progress

MSC is also conducting its own “Cyberfair” thru an annual web design contest for schools in San Pablo City.

Student representatives from different schools are given a seminar on web design and they make a website about their school or community.  Prizes are given to students who make the best websites.

All these efforts surely help put San Pablo City on the Cybermap.

# MSC 11 – Division by 9

Most of us want to avoid the number 9 in almost all calculations. But we can make calculations easier by thinking of 9 as (10 – 1). This fact is particularly useful in division by 9.

Every 10 contains a 9 and a remainder of 1. So every multiple of ten that is less than 90 will have a quotient and remainder equal to its tens digit.

So                           20/9 = 2 r 2

40/9 = 4 r 4

and                        70/9 = 7 r 7.

Extending this observation, we can readily obtain the quotient when small numbers are divided by 9.

Take the case of 34. When divided by 9, the quotient is equal to the tens digit, 3 and the remainder is equal to the sum of the tens and units digits, 3 + 4 or 7.

Similarly,

42/9 =  4 r  (4+2) = 4 r 6

71/9 = 7 r (7+1)  = 7 r 8

26/9 = 2 r (2+6) = 2 r 8

69/9 = 6 r (6+9) = 6 r 15

But wait!  Since the remainder 15 is greater than 9, we can divide 15 by 9 to get 1 r 6.

So 69/9 = 6 r 15  = (6+1) r 6 = 7 r 6.

At this point, we would like to stress that the following results are equivalent:

69/9 = 6 r 15 = 7 r 6 = 8 r -3 but 7 r 6 is the best form.

Example 11.1:                    1321/9

We can write the procedure as:     1 3 2 1 / 9

Step 1. Bring down the first digit (1) to the answer row.

1 3 2 1 / 9
1

Step 2. Add the next digit of the dividend to this number to get the next digit of the quotient: (1+3=4)
1 3 2 1 / 9
1 4

Step 3. Repeat the preceding procedure to get the next digit of the quotient:    (4+2=6)
1 3 2 1 / 9
1 4 6

Step 4. The last sum is the remainder: (6+1=7)                                                   1 3 2 1 / 9
1 4 6 r 7

Example 11.2:             2023/9

2 0 2 3 / 9
2 2 4 r 7

To check: the sum of the digits of the dividend should be equal to the remainder.

2 + 0 + 2 + 3 = 7

Example 11.3:            4352/9

4   3    5    2 / 9
4   7   12  r 14

Here, we see that we have a 12 and a 14 in the quotient. The 1 in the 12 must be carried over to the 7 to yield 482.  There is also one 9 in the remainder 14.

So the final answer is 483 r 5.

We can modify our procedure to avoid double digits in the quotient.

4   3   5    2 / 9
4

Before writing down the 7 (4 + 3), we see that the next addition 7 + 5 will give a two digit result, 12. So we anticipate the carry operation and write down 8 instead of 7.

4   3   5    2 / 9
4   8

We then proceed as before

4   3   5    2 / 9
4   8

8 + 5 = 13. But since we have performed the carry operation in the previous step, we will write down only the last digit 3.

4   3   5    2 / 9
4   8   3

Finally we have the remainder: 3 + 2 = 5

4   3   5    2 / 9
4   8   3 r 5

check:         4 + 3 + 5 + 2 = 14; 1 + 4 = 5

The following are the decimal values of the remainder when dividing by 9.

1 – 1/9 = .1111… = 0.1

2 – 2/9 = .2222… = 0.2

3 – 3/9 = .3333… = 0.3

4 – 4/9 = .4444… = 0.4

5 – 5/9 = .5555… = 0.6

6 – 6/9 = .6666… = 0.7

7 – 7/9 = .7777… = 0.8

8 – 8/9 = .8888… = 0.9

Exercise 11: Divide the following numbers by 9

1. )      134 / 9 =
2. )      215 / 9 =
3. )      2231 / 9 =
4. )      4202 / 9 =
5. )      625 / 9 =
6. )      3030 / 9 =
7. )      7135 / 9 =
8. )      5672 / 9 =
9. )      3692 / 9 =
10. )      46893 / 9 =

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!

# MSC Origins Part V: Transfer to M. Paulino

In a short span of less than two years, the Jesusa Building along A. Flores St. which housed MSC on the second floor (and Monte de Piedad Savings Bank on the first floor) in 1989 became too small for the growing number of MSC students.  In October 1991, MSC transferred to a bigger site along M. Paulino St.

MSC at M. Paulino St.

The site was a residential compound complete with a garage and a small yard at the back.  In the compound was a two-storey edifice known as the Don Juan Alvero building. The three rooms on the second floor were all converted into classrooms and on the first floor were: a computer laboratory, a typing room, the registrar’s office, and a small office for the software department.  There was also a small room for the staff and a canteen at the back of the building.

The transfer to the Alvero building was timed so that classes for the second semester of school year 1991-1992 will be conducted in the new site.

The building was really designed as a home and the students really found a “home” while MSC was there – a “second home”.  All school activities were held there (except for the graduation and sportsfest).  The garage was utilized for several purposes – practice session venue for student activities, “tambayan”, venue for presentations where a stage can be put up, and lastly as parking space.  The “sala” or living room was used as lobby and reception area but it was also utilized for group presentations and even parties!

“MSC – 4 on 4”, MSC’s catch phrase for its 4th year anniversary (December 4, 1993) was celebrated at the Jose Alvero building.  Many activities were held including an evening of cultural presentations, contests, a party and read this – a school fair!  Yes, a school fair in the Alvero compound complete with a jail booth, marriage booth and other gimmicks by the students.

# Converting Fahrenheit to Celsius

To convert Fahrenheit to Celsius, we use the following formula,

C = 5/9 (F – 32) = 10/18 (F – 32)

The trick here is to recognize that 5/9 is the same as 10/18.  Hence after deducting 32, we add a zero (multiply by 10) to the result and successively dividing by 2 and 9 (MSC 11 – Dividing by 9) to effectively divide by 18.

• Step 1.  Subtract 32
• Step 2.  Multiply by 10
• Step 3. Divide by 2
• Step 4. Divide by 9

Let us solve look at some examples.

Example 1:          100 oF = 37.8 oC

• Step 1.  Subtract 32:         100 – 32 = 68
• Step 2.  Multiply by 10:    68 x 10 = 680
• Step 3.  Divide by 2:         680 ÷ 2 = 340
• Step 4.  Divide by 9:         340 ÷ 9 = 37 r. 7  =  37.7…  =  37.8

Example 2:           145oF = 62.8oC

• Step 1.  Subtract 32:          145 – 32 = 113
• Step 2.  Multiply by 10:      113 x 10 = 1130
• Step 3.  Divide by 2:           1130 ÷ 2 = 565
• Step 4.  Divide by 9:           565 ÷ 9 = 62 r. 7  =  62.7…  =  62.8

Easy and simple!

# MSC Welcomes Four New Teachers

MSC welcomes another year of excellence as four new teachers arrived to share their knowledge.

New MSC HS teachers

Jenny Rose Estrellado Gonzales graduated at San Vicente National High School in 2010. During that time, she was a Math Club member, Journalism Club member as cartoonist, an MTAP participant and a consistent top 10 student. In March 28, 2014, she graduated from college in Laguna State Polytechnic University (LSPU) majoring in Mathematics. She was a Manthanein Society member during her college days.

Ms. Jenny Rose Gonzales

Now, she is teaching Mathematics for grades VII to IX, Trigonometry and Statistics in our school. She is a devoted Math teacher and an understanding Grade 7 adviser. She also handles the school’s Math Club.

Jinky Cabubas Artillero is MSC’s Filipino VII, VIII, English IX and X teacher. She handles Grade VIII with patience and also a resourceful teacher. Furthermore, she guides the Journalism Club of our school.

Ms. Jinky Artillero

She graduated in San Pablo City National High School (City High) in 2010 as Salutatorian. Then in Dalubhasaang Lungsod ng San Pablo (DLSP) in March, 2014, she finished BS Education majoring in English. Her high school achievement includes Best in English during her first and second years. In college, she was a Dean’s lister, English Society Club member, production staff of Kulay Play Production and Head ushering committee of Kulay Play Production. She was also an active player of women’s basketball during her second and third years and women’s volleyball during her fourth year.

Krizzalyn Cuasay Barrios, our present zealous teacher of Social VII to X, Filipino IX to X and Music VII and also a supportive adviser of Grade IX.  Moreover, she handles the Glee Club.

Ms. Krizzalyn Barrios

She majored in Social Studies at the Laguna State Polytechnic University (LSPU) and was a Honorific Scholar in her 4th year.  She graduated high school at San Pablo City National High School (City High) in 2010.

Mary Rose Pamplena Cleofe also finished her high school in San Pablo City National High School (City High) class of 2008. She took up BS Education majoring in Science at the Laguna State Polytechnic University (LSPU).  She was a Dean’s lister during her first year and graduated in 2012.

Ms. Mary Rose Cleofe

Today, she handles MSC’s Science and PE VII to X, and school’s Science Club. She is an enthusiastic teacher and a strict yet encouraging adviser of the fourth year students.

We, the MSC students warmly welcome them and look forward to having a wonderful year with them.

(By LC Millares – GR. IX)