Category Archives: MATH-Inic

Conversion: Feet and inches to Meters

Filipinos (and most Americans) are more accustomed to using Feet and Inches in measuring their heights.But the Philippines is officially on the metric system, so we are often required to give our heights in meters or centimeters. It is not difficult to approximate if we remember the following:

  • 100 centimeters = 1 meter
  • I foot = 30 centimeters (cm)
  • 1 inch = 2.5 cm
  • 4 inches = 10 cm

So how do we compute 4’ 8”? How about 5′ 6″?  6′ 11?

Hence, we compute 4′ 8″ as four feet ( 4 x 30cm ) and eight inches ( or 2 x 4 inches, or 2 x 10cm )

  • 4′ 8″
    = 4’ + (2 x 4)” = (4 x 30) + (2 x 10)
    = 120 + 20 = 140 cm = 1.4 m
  • 5’ 6”
    = 5’ + 4” + 2” = (5 x 30) + (1 x 10) + (2 x 2.5)
    = 150 + 10 + 5 = 165 cm = 1.65 m
  • 6’11”
    =  6’ + (2×4”) + (3 x1”) = (6 x 30) + (2 x 10) + (3 x 2.5)
    = 180 +20 + 7.5 = 207.5m

Note that under this conversion 6’ 8” is 2.0 m

We used 2,5 cm = 1 inch instead of the exact 2.54 cm = 1 inch. To make our conversion more accurate we can add 0.5 cm for every  foot

So more accurately, we estimate as follows:

  • 4’ 8”
    = 4’ + (2 x 4)” (4 x 30) + 4 x 0.5+ (2 x 10)
    = 120 + 2 + 20 = 142 cm = 1.42 m
  • 5’ 6”
    = 5’ + 4” + 2” = (5 x 30) + (5 x 0.5)+ (1 x 10) + (2 x 2.5)
    = 150 + 2.5 + 10 + 5 = 167.5 cm = 1.675 m
  • 6’ 11”
    =  6’ + (2×4”) + (3 x1”) = (6 x 30) + (6 x 0.5)+(2 x 10) + (3 x 2.5)
    = 180 + 3+20 + 7.5 = 210.5cm

A easier and more accurate way to compute the last example is to treat 6′ 11″ as 7 feet less 1 inch

  • 7′  minus 1″
    = (7’ x 30) + (7 x 0.5) – 2.5
    = 210 + 3.5 – 2.5 = 211 cm = 2.11m

Feet and inches to meters made easy!

 

MSC 16 – Multiplying Complementary Numbers

Complementary numbers are numbers with the same initial digits and the sum of the last digits equal to 10.

The technique in multiplying complementary numbers is similar to that of squaring numbers ending in 5 (By one more than the one before) except that the right hand part is not 25 but the product of the last digits

Example 16.1:    Find 46 x 44

             =  4 x 5 | 6 x 4

             = 20 | 24

              = 2,024

P16: Let t = the common ten’s digit; a, b = the units digit such that a + b = 10

(10t + a)(10t + b)

= (10t)(10t) + 10ta + 10tb + ab

= 100t2 + 10t(a + b) + ab

= 100t2 + 10t(10) + ab

= 100(t2 + t)+ ab

= 100 t(t + 1)+ ab

 

Example 16.2:    Find 39 x 31

= 3 x 4 | 9 x 1

= 12|09 Note that the right part has two digits, 09 not 9.

= 1,209

Again, this can be applied to decimals and fractions as long as they have the same whole number part and their decimal and fractional parts total to 1.

Example 16.3:    8.3 x 8.7 = 8 x 9 | .3 x .7 = 72.21

Example 16.4:    4  2/7 x 4  5/7 = 4 x 5 | 2/7 x  5/7 = 20 10/49

Example 16.5:    699 x 601

Since 99 + 01 = 100, we can also apply complimentary rule

699 x 601 = 6 x 7 | 99 x 01 = 42| 0099 = 420,099

 Exercise 16:

  1. ) 24 x 26 =
  2. ) 73 x77 =
  3. ) 81 x 89 =
  4. ) 998 x 992 =
  5. ) 4.3 x 4.7 =
  6. ) 7.4 x 7.6 =
  7. ) 3 3/7 x 3 4/7 =
  8. ) 4 1/6 x 4 5/6 =
  9. ) 2 4/9 x 2 5/9 =
  10. ) 297 x 203 =

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!

 

MATH-Inic conducts FREE Mental Math Training for Teachers

MATH-Inic Philippines started the series of Mental Math Training seminars for teachers on November 16, 2014.

A total of 23 teachers, mostly from the San Francisco District attended the training at the green school campus of VYP-MSC Institute of Technology at Sitio IX, San Gabriel, San Pablo City.

MATH-Inic President, Virgilio “Sir Ike” Prudente personally conducted the training on mental math techniques and methods to make teaching math easier and fun.

Here are some comments from the trainees:


“Thank you so much. We learned a lot from you. The knowledge you shared with us is of big help if we can share this one also to our students.”


“Thank you very much Mr. Prudente for sharing us some of the techniques in solving math equations. This will be of great help not only for us teachers but especially for our learners.


May God continue to bless you so that you can continue blessing others too.”


“Thank you po sa lahat ng techniques, malaking tulong poi to hindi lang sa akin higit sa lahat para sa aming mga bata.”


“Thank you po sa lahat ng nai-share n’yo. Natutuwa po ako sa mga techniques na kahit po ako ay malaki ang natutunan.


The next training session is scheduled on November 23, 2014 and starts at 8:00 am and ends at 12:00 noon.  This is free and certificates of attendance are given to all participants.

To register, visit or contact us at:

VYP – MSC Institute of Technology
Sitio IX, San Gabriel, San Pablo City
Telephone number: 562-6006
Cellphone numbers:
0917 853 5069
0922 854 3244
0939 939 9702

Conversion: Yards to Meters

One yard is 3 feet or 36 inches, while one meter is 39.37 inches. This makes one yard to be about 0.9155 meters. But for practical use, we can approximate and use the rate 1 yard = 0.9 meters.

We can easily do that if we apply MSC-8 multiplying by 9.

In this case we can use the fact that 0.9 is 1 – 0.1.   Let us see some examples:

  • 10 yard = 10 -1 = 9 meters
  • 20 yards = 20 -2 = 18 meters
  • 35 yards = 35 – 3.5 = 31.5 meters
  • 67.5 yards = 67.5 – 6.75 = 60.75 meters

yards to meters

              yards to meters

From a previous section we learned that 1 yard = 36 inches = 36 x 2.54 = 91.44 cm. Therefore 1 yard is exactly is 0.9144 meters . Using 1 yard = 0.9 meter is about 98.4 % accurate

 

MSC 15: Squaring Numbers Ending in 5

Squaring is multiplying a number by itself.

It is very easy to square two-digit numbers ending in five by using the Vedic Math sutra or word formula By one more than the one before.

The square of a two-digit number ending in 5 is composed of 2 parts.

  • The first or left hand part is obtained by multiplying the ten’s digit “By one more than the one before” or by the next number.
  • The second part is always 5 x 5 or 25.

Example 15.1:     Find 652

  • The first part is the ten’s digit 6 multiplied by the next number 7, (By one more than the one before) so  6 x 7 =  42.
  • The second part is always 25 ( 5 x 5) .
  • 652= 42|25 or 4,225

Even larger numbers can be squared.

Example 15.2:     Find 9952

          9952  =  99 x 100|25

          9952  = 990,025

Proof P15: Let t = the ten’s digit; 10t + 5 = two digit number ending in 5(10t + 5)2 = (10t)2 + 2(10t)(5) + 52= 100t2  + 100t + 25= 100(t2 + t) + 25= 100(t)(t + 1)+ 25

We can extend the technique to decimals and fractions.

Example 15.3:     3.52 = 3 x 4 | .5 x .5  = 12.25

Example 15.4:     (7 ½)2 = 7 x 8 | ½  x ½  =  56 1/4

Exercise 15:     Find the square of the following numbers

  1. )   45
  2. )   95
  3. )   195
  4. )   10,005
  5. )   10.5
  6. )   7.5
  7. )   6 ½
  8. )   9 ½
  9. )   100.5
  10. )   0.025

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!

Conversion: Meters to Feet

Since 1 yard  =  3 feet, we can use the conversion factor 1 meter  =  3.3 feet.  We can simplify this computation using  one of our favorite shortcuts, multiplying by 11. Remember that multiplying by 1.1 is simply multiplying by 11, and dividing by 10.

We can convert meters into feet  in two ways, both involving only mental calculations:

  1. Multiply the meter measure by 3 then by 1.1.
  • 7 meters = 7 x 3 x 1.1 = 21 x 1.1 = 23.1 feet
  • 23 meters = 23 x 3 x 1.1 = 69 x 1.1 = 75.9 feet
  • 30 meters = 30 x 3 x 1.1 = 90 x 1.1 = 99.0 feet

2.  Multiply the meter measure by 1.1 then by 3

  • 7 meters = 7 x 1.1 x 3 = 7.7 x 3 = 23.1 feet
  • 23 meters = 23 x 1.1 x 3 = 25.3 x 3 = 75.9 feet
  • 30 meters = 30 x 1.1 x 3 = 33 c 3 = 99 feet

Many will find the first method, easier to use.

For rough calculations, we can just multiply the meter measure by 10 and then divide by 3

  • 7 meters = 70 ÷ 3 = 23 1/3 feet
  • 23 meters = 230 ÷ 3 = 76 2/3 feet
  • 30 meters = 300 ÷ 3 = 100 feet

As seen in last example, the result is only 1% different from the previous method.

In this last example we used the conversion rate of 1 foot = .30 m whereas the exact conversion is 1 foot = 0.3048 meters. This is 98.4% accurate which is good enough for estimates.

This is another example how we can creative apply the 25 Math Short Cuts (and combinations thereof) in our everyday computing problems

MSC 14 – Dividing by 25, 250, 125

Remember that 25 is 100 divided by 4, so dividing by 25 is the same as dividing by 100 and multiplying by 4:

  1. move the decimal point two places to the left then
  2. multiply by 4 ( or double twice)

Of course, the multiplication can be done first, but using the recommended procedure has the advantage of providing us the magnitude of the answer first.

Example 14.1:    Find 700 ÷ 25 = (7 x 100) ÷ 25 = 7 x (100 ÷ 25) = 7 x 4 = 28

This example shows the basis of our shortcut. There are 4  25s  in every 100, so there are 7 x 4 or 28  25s in 7 hundreds.

 Example 14.2:    Find 3,400÷ 25

1.   Move the decimal point two places to the left to get 34.00.
2.   Double it to get 68.
3.   Double it again to get 136.

Example 14.3:    Find 3562÷ 250

1.   250 is 1/4 of 1000 or 10so we move the decimal point three places to the left giving us 3.562.
2.   Multiplying it by 4 gives us 14.248.

To divide a number by 125,

  1. Move the decimal point three places to the left then
  2. Multiply it by 8 (or double thrice)

 Example 14.4:    Find 20,400÷ 125

Moving the decimal point three places to the left gives 20.4

20.4 x 8 = 40.8 x 4 = 81.6 x 2 = 163.2

Example 14.5:    Find 758 ÷ 12.5

1.   This time 12.5 is 1/8 of 100 so we have to shift the decimal point two places to the left making it 7.58.
2.   Multiplying it by 8 gives us 60.64

Exercise 14:

  1. ) 1050 ÷ 25 =
  2. ) 6025÷ 25 =
  3. ) 8375 ÷ 25 =
  4. ) 12,400 ÷ 250 =
  5. ) 71000÷ 125 =
  6. ) 5,125÷ 125 =
  7. ) 3,475÷ 250 =
  8. ) 830÷ 12.5 =
  9. ) 2475÷ 2.5 =
  10. ) 5264÷ 0.25 =

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!

Photo Courtesy of WikiHow

Converting Meters to Yards

One meter is approximately equal to 1.1 yards.

For practical purposes we can use this conversion factor. Here we can apply MSC 4 – Multiplying by 11 to quickly convert meters to yards.

200 meters = 220 yards (1 furlong)

400 meters = 440 yards (1 quarter mile)

23 meters = 25.3 yards

324 meters = 356.4 yards

1 yard is exactly 36 inches x 2.54 centimeters/inch = 91.44 centimeters. 1.1 yards is 91.44cm.x 1.1=100.58 cm. or 1.0058 meters. The conversion 1 meter = 1.1 yard is more than 99% accurate.