Mathematics Tips & Tricks: Division

How you know when a number can be evenly divided by the certain numbers? By evenly means that the quotient has no remainder or you get an exact whole number.

Here’s a quick way to know when a number can be evenly divided by these certain numbers:

A number can be evenly divided by:

• 10 if the number ends in 0

Examples:

1) 500 / 10 = 50

2) 2750 / 10 = 275

3) 5240 / 10 = 520

• 9 when the digits are added together and the total is evenly divisible by 9

Examples:

1) 522 ==> 5+2+2 = 9 ; Since 9 is divisible by 9  (or a multiple of 9), then 522 can be evenly divided by 9.

522 / 9  = 58

2) 84213 ==> 8+4+2+1+3 = 18: Since 18 is divisible by 9 ( or a multiple of 9), then 84213 can be evenly divided by 9.

84213 / 9 = 9357

3) 50045 ==> 5+0+0+4+5 =  14: Since 14 is not divisible by 9, then 50045 cannot be evenly divided by 9.

• 8 if the last three digits are evenly divisible by 8 or are 000

Examples:

1) 71024 ==> the last 3 digits 024 are evenly divisible by 8 so 71024 can be evenly divided by 8.

71024 / 8 = 8878

2) 5027000 ==> the last 3 digits are 000, then 5027000 can be evenly divided by 8.

5027000 / 8 = 628375

3) 2000 ==> the last digits are 000, the 2000 can be evenly divided by 8.

2000 / 8 = 250

• 6 if it is an even number and when the digits are added together the answer is evenly divisible by 3

Examples:

1)  2532 ==> Is it even number? Yes! ; 2+5+3+2 = 12 : Since 12 is a multiple of 3, then 2532 can be evenly divided by 6.

2532 / 6 = 422

2)  984 ==> Is it even number? Yes! : Is 9+8+4 = 21 a multiple of 3? Yes!  (3x7 = 21)

984 / 6 = 164

• 5 if it ends in a 0 or 5

This is easy. Any number with 0 or 5 at the end can be evenly divided by 5.

Examples:

1) 510 ==> 510 / 5 = 102

2) 5355 ==> 5355 / 5 = 1071

3) 20035 ==> 20035 / 5 = 4007

• 4 if it ends in 00 or a two digit number that is evenly divisible by 4

Examples:

1)  4800 ==> 4800 / 4 = 1200

2) 724 ==> the last digits 24 is a multiple (4x6=24) of 4 so 724 can be evenly divided by 4.

724 / 4 = 181

3) 6816 ==> 16 is a multiple of 4 (4x4=16) then 6816 can be evenly divided by 4.

6816 / 4 = 1704

• 3 when the digits are added together and the result is evenly divisible by the number 3

Examples:

1) 56451 ==> 5+6+4+5+1 = 21: Is 21 divisible by 3? Yes! Then 56451 can be evenly divided by 3.

56451 / 3 = 18817

2) 300342 ==> 3+0+0+3+4+2 = 12: Is 12 divisible by 3? Yes! Then 300342 can be evenly divisible by 3.

300342 / 3  = 100114

3) 522 ==> 5+2+2 = 9; Since 9 is divisible by 3, then 522 can be evenly divided by 3.

522 / 3 = 174

• 2 if it ends in 0, 2, 4, 6, or 8

Like 5, this is very easy to understand. Any number with 0, 2, 4, 6 & 8 at the end, can be evenly divided by 2.

Examples:

1) 2010 ==>  2010 / 2 = 1005

2) 278 ==> 278 / 2 = 139

3) 62456 ==> 62456 / 2 = 31228

Mathematics Tips & Tricks

Nasa isa pang tip at trick para mapadali ang pagsagot sa mga Math problems:

Multiplying 5 times any number (Pag-multiply ng 5 sa anumang bilang)

When multiplying the number 5 by an even number, there is a quick way to find the answer.

For example, 5 x 4 =

• Step 1: Take the number being multiplied by 5 and cut it in half, this makes the number 4 become the number 2.
• Step 2: Add a zero to the number to find the answer. In this case, the answer is 20.

5 x 4 = 20

A. Pagmu-multiply ng 5 sa anumang bilang na EVEN ( o biilang na 0, 2, 4, 6, at 8 ang nasa hulihan nito) 

Halimbawa:

5 x 4

Step 1: Hatiian ang bilang na imu-multiply sa 5 at hatiin ito sa dalawa (2).

Sa ating halimbawa, ang numerong ito ay 4.  Hatiin natin ito sa 2.... 4/2 = 2

Step 2: Pagkatapos makuha ang sagot sa Step 1, lagyan ito ng zero (0).

20 ...Ito bale ang sagot.

i=tsek... 5 x 4 = 20

Mga Halimbawa

a.  5 x 536 ===> 536/2 = 268 ... lagyan ng 0 .....2,680 ....5 x 536 = 2,680

b.  5 x 7128 ===> 7128/2 = 3564...lagyan ng 0 ...35,640 ... 5 x 7128 = 35,640

c. 5 x 854 ==> 854/2 = 427...lagyan ng 0 ....4,270.... 5 x 854 = 4,270

d. 5 x 63510 ==> 63510/2 = 31755...lagyan ng 0 .....317,550 ....5 x 63510 = 317,550

Tsekin ang mga sagot sa itaas gamit ang iyong calculator.

When multiplying an odd number times 5, the formula is a bit different.

For instance, consider 5 x 3.

• Step 1: Subtract one from the number being multiplied by 5, in this instance the number 3 becomes the number 2.
• Step 2: Now halve the number 2, which makes it the number 1. Make 5 the last digit. The number produced is 15, which is the answer.

5 x 3 = 15

B. Pagmu-mulitply ng 5 sa isang ODD na bilang ( o bilang na 1, 3, 5, 7 at 9 ang nasa hulihan nito)

Halimbawa

5 x 3

Step 1:  Kunin ang imu-multiply sa 5 at ibawas ang isa (1) mula rito.

3 - 1 = 2

Step 2: Hatiin ang sagot sa Step 1 at ilagay ang 5 sa huli

2/2 = 1 .... ilagay ang 5 sa huli  ===>  15 .... ito ang sagot

Tsekin... 5 x 3 = 15

Mga Halimbawa.

a.  5 x 113 ===> 113-1 = 112/2 = 56...lagyan ng 5 ==> 565 .... 5 x 113 = 565

b. 5 x 7251 ==> 7251 - 1 = 7250/2 = 3625...lagyan ng 5 ==> 36,255 ... 5 x 7251 = 36,255

c. 5 x 349 ==> 349-1 = 348/2 = 174 ...lagyan ng 5 ==> 1,745.... 5 x 349 = 1,745

d. 5 x 20143 ==> 20143-1 = 20142/2 = 10071...lagyan ng 5 ==> 100,715 .... 5 x 20143 = 100,715

Tsekin ang mga sagot sa ibaba, gamit ang inyong calculator.