Category Archives: MATH-Inic

MSC 13 – Multiplying by 25, 250, 125

Remember that 25 is 100/4. This means we can multiply the number by 100, and then divide by 4.

To multiply by 25, move the decimal point of the multiplicand two places to the right and divide the resulting number by 4.

Example 13.1:    Find 64 x 25

  1. Since the multiplicand is a whole number, add two zeroes at the end to make it 6400.
  2. Divide 6400 by 2 giving 3200
  3. Divide 3200 by 2 to get the final answer, 1600

Example 13.2:    Find 9.3 x 25

  1. Move the decimal point two places to the right to make it 930
  2. Divide by using the one line method to get 5.

 Example 13.3:    How much is $250 in pesos if the exchange rate is P45.15 = $1

  1. Since 250 is one-fourth of 1000, move the decimal point three places to the right to get 45,150.
  2. Divide 45,150 by 4 to get P11,287.50

 Example 13.4:    How much is the selling price of a pair of running shoes originally priced at P4,795 if it is offered at 75% discount?

A 75% discount means the selling price is just 25% or 1/4 of the original price, so the selling price is just 4,795 divided by 4 or P 1,198.75.

How about multiplying by 125?

Remember 125 is simply 1000/8.

To multiply by 125, move the decimal point three places to the left and divide the result by 8.

Example 13.5:

2 x 4 x 5 x 8 x 25 x 125 =

(2 x 5) x (4 x 25) x (8 x 125)

= 10 x 100 x 1000 = 1,000,000

Example 13.6:    384 x 125 = 384,000/8 = 48,000

Exercise 13:

  1.    36 x 25 =
  2.    78 x 25 =
  3.    67 x 25 =
  4.    256 x 125 =
  5.    55 x 125 =
  6.    123 x 250 =
  7.    466 x 2.5 =
  8.    3599 x 25% =
  9.    2468 x 2.5% =
  10.    2552 x 1.25% =

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!

Issue 12 – MSC Alumni Activities; Dividing by 4 and 8

25 Math Short Cuts NewletterNov 3, 2014         Issue 12

Issue 12 – MSC Alumni Activities; Dividing by 4 and 8

Announcement – MSC Alumni Homecoming Activities

We would like to hear from you! Fill out the forms

  • to update our Alumni directory
  • to submit nominations for MSC Outstanding Alumni
  • to join the Alumni Shirt Design Contest
  • to join the Alumni Men’s Basketball League
  • to join the Alumni Men and Women’s Volleyball League

Read More. . .


In this issue


To ensure you receive our newsletter in your inbox, please add newsletter@msc.edu.ph to your email address book or safe sender list. Just click here to subscribe, or just send an email with “Subscribe” on the subject line to newsletter@msc.edu.ph .


MSC Scouts Investiture and Camping

MSC held its Scout Investiture last September 26, 2014 with students ready to take their responsibility to the next level. Their fellow Girl Scouts and Boy Scouts, parents and godparents attended the commencement ceremony.

Campfire

Girl Scout Campfire

Read more….

 


MSC Origins Part VII: Ghosts at M. Paulino

Almost everyone have ghost stories to tell, especially those about old buildings and houses. There is something about old houses that makes them perfect for terrifying stories, imaginary or otherwise. Maybe it is because an old building would have been the site of many events and happenings in the past. An old building would have stood as a “silent witness” to many stories about the people who lived there or visited the place.

Ghosts at M. Paulino

Ghosts at M. Paulino

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Alumni Update: Teachers from MSC

MSC has always led the way and broke new ground involving many things, but what’s good about it is that we are always willing to share our knowledge with everybody. MSC has always been generous with whatever new technology or equipment it has so that others can also benefit from it.

This way of thinking have been instilled in its students, hence many graduates are willing to impart their knowledge through the teaching. We gathered a list of educators who were graduates of MSC and it was no surprise to find a lot!

Read more


How To Compute Lumber Measurement

The amount of lumber is expressed in terms of Board Feet. A Board Foot is a piece of lumber 1 foot (12 inches) long, 1 foot wide and 1 inch thick which is equal to 144 cubic inches. If all dimensions are expressed in inches, the amount in board feet is equal to:
(l x w x t)/ 144.

Measuring lumber in board feet, L x W x thickness.

Measuring lumber in board feet, L x W x thickness.

 Read more….


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.

ron paulo yabut of Layag laya band

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.

Read more


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.

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.

Read more


Previous Issues

In the Next Issue

  • 25 years of MSC ( more stories )
  • MSC 13
  • MSC – First School to have a generator
  • Batches of OMC and CTC Graduates

Every week, for 25 weeks up to December 4, 2014 when we celebrate our 25th Foundation day, this newsletter will feature one math short cut. We will progress from the simplest to the simple. Believe you can do it! Just proceed one step ( short cut ) at a time, and be pleasantly surprised to discover none of the math short cuts are difficult! Forward this newsletter to your friends, relatives, and young kids.

To ensure you receive our newsletter in your inbox, please add newsletter@msc.edu.ph to your email address book or safe sender list. Forward this mail to your friends and invite them to subscribe to the 25 Math Short Cuts Newsletter today!

How To Compute Lumber Measurement

The amount of lumber is expressed in terms of Board Feet.  A Board Foot is a piece of lumber 1 foot (12 inches) long, 1 foot wide and 1 inch thick which is equal to 144 cubic inches.  If all dimensions are expressed in inches, the amount in board feet is equal to:
(l x w x t)/ 144.

Measuring lumber in board feet, L x W x thickness.

Measuring lumber in board feet, L x W x thickness.

In the Philippines, it is customary to express width and thickness in inches while we use feet to express length.  So a 2 x 3 x 10 means 2 inches thick by 3 inches wide and 10 feet long piece of lumber  computed as (t x w x l)/12.

Example 1a:     How many board feet is 2” x 3” x 10’ ?

          ( 2 x 3 x 10) / 12 = 60/12 = 5 bd. ft.

To simplify calculations, factors making up 12 should be cancelled as early as possible instead of multiplying out the thickness by the width and then by the length before dividing it by 12

Example 1b:      How many board feet is 2” x 3” x 10’?

2 x 3 x 2 x 5= 5 bd. ft.

Example 2:     2” x 6” x 8’  =  2” x 6” x 8’  =  8 bd. ft.

Example 3:      2” x 5” x 12’  =  2” x 5” x 12’  =  10 bd. ft.

Example 4:      1 ½” x 2” x 8  =  1 ½” x 2” x 4 x 2  =  2 bd. ft.

Example 5:      1 ½” x 2” x 10  =  1 ½” x 2” x 2 x 5  =  5/2 bd. ft.

1 ½” x 2” x 2 is only 6 so we still have to divide by 2

Example 6:      2” x 2” x 10‘  =  2” x 2” x 10‘  =  10/3  =  3.33 bd. ft.

2 x 2 is only 4 so we still have to divide by 3

We can include the number of pieces in the calculations.

Example 7:      3 pcs – 2” x 2” x 14’  =  3 pcs – 2” x 2” x 14’  =  14 bd. ft.

Example 8.  4 pcs – 1 ½” x 2” x 10= 4 pcs – 1 ½” x 2” x 10 = 10 bd. ft.

With this method you won’t ever have to use a calculator in computing lumber.

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 )!

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.

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.

Dividing-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 )!

 

Converting Fahrenheit to Celsius

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

                C = 5/9 (F – 32) = 10/18 (F – 32)

h

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 10 – Multiplying by 5, 50, 5%, etc

Five is 10 divided by 2. To multiply by 5, we can

  1. multiply first by 10 then divide the product by 2 or
  2. divide the multiplicand by 2 first and then add a zero at the end of the quotient.

This shortcut requires only the skill of dividing by 2.

Except when half of the multiplicand is readily computed, we recommend that the first procedure be followed because adjusting the decimal point first gives the magnitude of the product, i. e.,  hundreds or thousands.

As discussed in Short cut # 6, dividing by means getting half of the number

Half of 10 is 5.

Half of 20 is 10.

Half of 50 is 25.

Half of 64 is half of 60 plus half of 4 or 34.

Half of 72 is half of 60 plus half of 12 or 36.

Half of 96 is half of 80 plus half of 16 or 48.

Half of 7 ishalf of 6 plus half of 1 or 3.5

Example 10.1: 36 x 5 =

Half of 36ishalf of20 plus half of16 which is 18. This becomes 180 when a zero is affixed at the end.

Example 10.2: 245 x 5 =

When a zero is affixed at the end, the number becomes 2,450.  We can recite the answer as we mentally compute

a)      half of 2 thousand is “1 thousand”,
b)      half of 4 hundred is  “2 hundred”
c)       And half of 50 is “25”.

Example 10.3: 455 x 5 =

455 became 4,550 after multiplying by ten. We can think of it as 4000 + 400 + 150

a)      Half of 4000 is “Two Thousand”
b)      Half of 400 is “two Hundred”
c)      Half of 150 is “seventy-five

Example 10.4: 3,758 x 5 =

Here all digits are odd except the last digit.

After adding a zero at the end, the number becomes 37 thousand, 5 hundred and 80. We can think of it as 36,000 + 1,400 + 180 as in the previous example to get a quick 18,000 + 700 + 90 answer. Here we will try to divide  it by 2 using the one-line method used in MSC 6.

31715180 ÷ 2 = 18, 790

a)       3 divided 2 is 1 with a remainder of 1 which will become the first digit of the next dividend.

b)      7 becomes 17 which when divided by 2 will give 8 with a remainder of 1. We can now start to say our answer aloud as “ eighteen thousand,”

c)       5 now becomes 15 and when divided by 2 gives 7, remainder 1, so we continue as “seven hundred and”

d)      The last two digits of the dividend then becomes180  which when divided by 2 is “ninety”.

Example10.5: 462 x 50 =

Fifty is half of 100 so we

a)      Add two zeroes at the end of 462 so it will become 46,200.

b)      Half of that is Twenty three thousand one hundred.

Example 10.6: 5% 0f 864=

5% is half of 10% so we

a)      move the decimal point one place to the right so that it will become 86.4

b)      divide it by 2 to get 43.2

 

Exercise 10: compute for the following products:

  1. )   864 x 5 =
  2. )   748 x 5 =
  3. )   356 x 5 =
  4. )   475 x 5 =
  5. )   2,357 x 5 =
  6. )   685 x 50 =
  7. )   873 x 50 =
  8. )   347 x 500 =
  9. )   5% of 739 =
  10. )   5% of 95.5 =

 

 

 

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