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Sunday, 4 December 2011


Biasanya operasi tolak diajar mengikut turutan daripada tolak tanpa mengumpul semula kepada tolak dengan mengumpul semula. Sebelum mempelajari operasi tolak dengan mengumpul semula, murid perlu mahir kemahiran yang berikut: 
  • fakta asas bagi tolak
  •  menolak nombor yang sama nilai tempatnya
  •  nilai tempat bagi angka 
  • menulis nombor dalam bentuk tambah menggikut nilai tempat dan seterusnya menulis nombor berkenaan dalam bentuk yang lain.

Fakta Asas

Fakta asas tolak ialah ayat matematik bagi penolakan nombor 1 digit daripada nombor 1 digit atau 2 digit dan hasilnya nombor satu digit. Terdapat dua kaedah untuk memperkenalkan fakta asas tolak iaitu mengekalkan bilangan unsur yang dikeluarkan dan mengekalkan bilangan unsur dalam set asal.

Konsep Tolak

Konsep penolakan dapat difahami melalui beberapa pendekatan iaitu pengasingan atau mengabil jalan keluar, perbandingan, pelengkap dan penyekatan. Pengasingan atau mengambil jalan keluar -  daripada satu set objek, satu subset dikeluarkan.
       Terdapat 8 buah buku di atas meja. Sebanyak 4 buku dimasukkan ke dalam beg. Berapa buah buku lagikah yang tinggal di atas meja tersebut?

Perbandingan - dua set objek berasingan diberi. Set objek pertama disusun semula dan dipadankandengan set objek kedua. Set objek yang tidak ada pasangan dikenali sebagai baki atau beza.


       Terdapat 8 biji gula-gula dan 5 potong kek. Berapakah bilangan gula-gula melebihi bilangan kek?

Pelengkap – bermula dengan satu set objek, kemudian fikirkan berapa lagi perlu ditambah untuk melengkapkan set keseluruhan.


       Saya ada 6 ekor kuda di dalam sebuah kandang yang boleh memuatkan 10 ekor kuda. Berapa ekor kudakah yang boleh saya masukkan lagi ke dalam kandang itu?

Penyekatan – dalam konsep ini, ahli sesuatu set objek perlu diubahsuai kedudukannya untuk menepati sesuatu syarat.


       Terdapat 7 buah kereta di sebuah tempat letak kereta. 2 buah kereta berwarna biru dan dan yang lain berwarna merah. Berapa buah keretakah yang berwarna merah?

Operasi Tolak

Operasi tolak biasanya diajar selepas operasi tambah. Operasi tambah melibatkan penggabungan atau penyatuan dua set objek, sedangkan operasi tolak pula berhubung dengan pengasingan atau pengurangan sesuatu set objek kepada set-set kecil. Dengan kata lain operasi tolak merupakan proses menterbalikkan operasi tambah.  Kemahiran yang diajar pada peringkat ini adalah menulis ayat matematik, melengkapkan ayat matematik, menolak secara spontan fakta asas tolak, menulis hitungan tolak dalam bentuk lazim dan penyelesaian masalah berkaitan penolakan.

Monday, 21 November 2011

Kenapa Salah?

Kebanyakan murid masih lagi gagal menolak dengan mengumpul semula. Mengapa?
Bila dikaji....rata-rata murid-murid ini: 

  1. tidak faham konsep tolak yang mana nombor besar tolak nombor yang kecil
  2. Murid tidak mempunyai pengetahuan dan idea bagaimana untuk menolak yang memerlukan proses pinjaman daripada rumah yang terhampir.
  3. Murid tidak memahami menolak nombor 2 digit dengan 1 digit secara congak 

Monday, 14 November 2011

Pembilang EQ

Pembilang EQ (Rujuk Rajah 1) untuk mencari hasil tolak dengan mengumpul semula

Tuesday, 1 November 2011

How to Subtract in Excel Using a Subtraction Formula in Excel By Ted French, About.com Guide

Subtracting Numbers in Excel

Related tutorial: Subtract Dates in Excel.
To subtract two or more numbers in Excel you need to create a formula.
Two important points to remember about Excel formulas:
  1. Formulas in Excel always begin with the equal sign
    ( = ).
  2. The equal sign is always typed into the cell where you want the answer to appear.

Use Cell References in Formulas

Even though you can use numbers directly in a formula, it is much better to use the cell references of the numbers you want to subtract.
If you use the cell references rather than the actual data, later, if you need to change the data in either cell, the results of the formula will update automatically without you having to rewrite the formula. 

Setting Up the Subtraction Formula

As an example, let's create a formula in cell E3 that will subtract the contents of cell E2 from cell E1.
For help with these instructions, see the image above.
Our formula:
= E1 - E2
Our data:
  • type the number 20 in cell E1 and press the ENTER key on the keyboard.
  • type the number 10 in cell E2 and press the ENTER key on the keyboard.

Formula Steps

To subtract 10 from 20 and have the answer appear in cell E3:
  1. Click on cell E3 with the mouse pointer to make it the active cell.
  2. Type the equal sign ( = ) in cell E3 to begin the formula.
  3. Click on cell E1 with the mouse pointer to add that cell reference to the formula after the equal sign.
  4. Type a minus sign ( - ) in cell E3 after the cell reference E1.
  5. Click on cell E2 with the mouse pointer to add that cell reference to the formula after the minus sign.
  6. Press the ENTER key on the keyboard.
  7. The answer 10 should be present in cell E3.
  8. Even though you see the answer in cell E3, if you click on that cell you will see our formula in the formula bar above the work area.
  9. To test the value of using cell references in a formula, change the number in cell E2 from 10 to 5 and press the ENTER key on the keyboard.
  10. The answer in cell E3 should automatically update to 15 to reflect the change in data in cell E2.
To expand your formula to include additional operations - such as addition, multiplication, or more subtractions - just continue to add the correct mathematical operator followed by the cell reference containing your data.
Note: Before you mix different mathematical operations, be sure you understand the order of operations that Excel follows when evaluating a formula.

Did You Know?

The plus and minus signs (+ and ) are mathematical symbols used to represent the notions of positive and negative as well as the operations of addition and subtraction. Their use has been extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning "more" and "less", respectively.

Though the signs now seem as familiar as the alphabet or the Hindu-Arabic numerals, they are not of great antiquity. The Egyptian hieroglyphic sign for addition, for example, resembled a pair of legs walking in the direction in which the text was written (Egyptian could be written either from right to left or left to right), with the reverse sign indicating subtraction:[citation needed]
D54 or D55
In Europe in the early 15th century the letters "P" and "M" were generally used. The symbols (P with stroke for piu, i.e., plus, and M with stroke for meno, i.e., minus) appeared for the first time in Luca Pacioli’s mathematics compendium, Summa de arithmetica, geometria, proportioni et proportionalità, first printed and published in Venice in 1494. The + is a simplification of the Latin "et" (comparable to the ampersand &).[citation needed] The may be derived from a tilde written over m when used to indicate subtraction; or it may come from a shorthand version of the letter m itself.[citation needed] In his 1489 treatise Johannes Widmann referred to the symbols − and + as minus and mer (Modern German mehr; "more"): "das − ist, das ist minus, und das + ist das mer".
A book published by Henricus Grammateus in 1518 makes another early use of + and − for addition and subtraction.
Robert Recorde, the designer of the equals sign, introduced plus and minus to Britain in 1557 in The Whetstone of Witte:[citation needed] "There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made – and betokeneth lesse."

Minus sign

The minus sign has three main uses in mathematics:
  1. The subtraction operator: A binary operator to indicate the operation of subtraction, as in 5 − 3 = 2. Subtraction is the inverse of addition.
  2. Directly in front of a number and when it is not a subtraction operator it means a negative number. For instance −5 is minus 5.
  3. A unary operator that acts as an instruction to replace the operand by its opposite. For example, if x is 3, then −x is −3, but if x is −3, then −x is 3. Similarly, −(−2) is equal to 2.
All three uses can be referred to as "minus" in everyday speech. In modern US usage, −5 (for example) is normally pronounced "negative five" rather than "minus five". "minus" may be used by speakers born before 1950, and is still popular in some contexts, but "negative" is usually taught as the only correct reading. In most other parts of the English-speaking world, "minus five" is more common. Textbooks in America encourage −x to be read as "the opposite of x" or even "the additive inverse of x" to avoid giving the impression that −x is necessarily negative.
In some contexts, different glyphs are used for these meanings; for instance in the computer language APL a raised minus sign is used in negative numbers (as in 2 − 5 gives 3), but such usage is rare.
In mathematics and most programming languages, the rules for the order of operations mean that −52 is equal to −25. Powers bind more strongly than multiplication or division which binds more strongly than addition or subtraction. While strictly speaking, the unary minus is not subtraction, it is given the same place as subtraction. However in some programming languages and Excel in particular, unary operators bind strongest, so in these −5^2 is 25 but 0−5^2 is −25.

Other uses

In chemistry, the minus sign (rather than an en dash) is used for a single covalent bond between two atoms, in skeletal formula.
Subscripted plus and minus signs are used as diacritics in the International Phonetic Alphabet to indicate advanced or retracted articulations of speech sounds.
The minus sign is also used as tone letter in the orthographies of Dan, Krumen, Karaboro, Mwan, Wan, Yaouré, , Nyabwa and Godié. The Unicode character used for the tone letter (U+02D7) is different from the mathematical minus sign.