575. MATHEMATICS: Order of Operations.



     It is very important that you carry out numerical operations in the correct order. This order is used both for positive and negative numbers.

If you do not use the correct order of operations, the answer will often be wrong!

It helps to remember   BIDMAS: 

Brackets are worked first

Indices are next






1. 3X4+5X6=12+30=42  NOT  3X4+5X6=12+5X6=17X6=103;

2. (5-12)X(4+1)= -7X5= -35;

3. (32 – 6)3 = (9-6)3 = 33 = 27.








WHETHER and IF can both introduce indirect questions:

a. He asked IF/WHETHER I knew Paul;

b. The police officer asked IF/WHETHER I had seen the accident.

In a formal style, WHETHER is usually preferred in a two-part question with OR to emphasize a choice:

a. The travel agent asked WHETHER I wanted to go by air OR by sea.

b. The waiter asked WHETHER I wanted chicken OR fish and chip.

Note the use of WHETHER or NOT to emphasize a choice:

a. He asked WHETHER or NOT I wanted to insure my luggage.


After prepositions, only WHETHER is possible:

a. There was a big argument ABOUT WHETHER we should move to a new house (NOT… about IF we should move);

b. I haven’t settled the question OF WHETHER I’ll go back home.


WHETHER, but not IF, is used before to-infinitives:

a. They can’t decide WHETHER TO GET married now or wait (NOT they can’t decide if to get married);

b. He wondered WHETHER TO WAIT for them or go on;

c. He couldn’t remember WHETHER TO TURN right or left.


When a question-word clause is a subject or a complement, WHETHER is normally used:

a. WHETHER WE CAN STAY with my mother is another matter (SUBJECT);



THE QUESTION IS IF …is also possible, but less common:

The question is IF THE MAN CAN BE TRUSTED.







Pinocchio promises the Fairy to be good and to study, as he is growing tired of being a Marionette, and wishes to become a real boy

If Pinocchio cried much longer, the little woman thought he would melt away, so she finally admitted that she was the little Fairy with Azure Hair.

“You rascal of a Marionette! How did you know it was I?” she asked, laughing.

“My love for you told me who you were.”

“Do you remember? You left me when I was a little girl and now you find me a grown woman. I am so old, I could almost be your mother!”

“I am very glad of that, for then I can call you mother instead of sister. For a long time I have wanted a mother, just like other boys. But how did you grow so quickly?”

“That’s a secret!”

“Tell it to me. I also want to grow a little. Look at me! I have never grown higher than a penny’s worth of cheese.”

“But you can’t grow,” answered the Fairy.

“Why not?”

“Because Marionettes never grow. They are born Marionettes, they live Marionettes, and they die Marionettes.”

“Oh, I’m tired of always being a Marionette!” cried Pinocchio disgustedly. “It’s about time for me to grow into a man as everyone else does.”

“And you will if you deserve it–“

“Really? What can I do to deserve it?”

“It’s a very simple matter. Try to act like a well-behaved child.”

“Don’t you think I do?”

“Far from it! Good boys are obedient, and you, on the contrary–“

“And I never obey.”


“Good boys love study and work, but you–“

“And I, on the contrary, am a lazy fellow and a tramp all year round.”

“Good boys always tell the truth.”

“And I always tell lies.”

“Good boys go gladly to school.”

“And I get sick if I go to school. From now on I’ll be different.”

“Do you promise?”

“I promise. I want to become a good boy and be a comfort to my father. Where is my poor father now?”

“I do not know.”

“Will I ever be lucky enough to find him and embrace him once more?”

“I think so. Indeed, I am sure of it.”

At this answer, Pinocchio’s happiness was very great. He grasped the Fairy’s hands and kissed them so hard that it looked as if he had lost his head. Then lifting his face, he looked at her lovingly and asked: “Tell me, little Mother, it isn’t true that you are dead, is it?”

“It doesn’t seem so,” answered the Fairy, smiling.

“If you only knew how I suffered and how I wept when I read `Here lies–‘”

“I know it, and for that I have forgiven you. The depth of your sorrow made me see that you have a kind heart. There is always hope for boys with hearts such as yours, though they may often be very mischievous [badly behaved ]. This is the reason why I have come so far to look for you. From now on, I’ll be your own little mother.”


Oh! How lovely!” cried Pinocchio, jumping with joy.

“You will obey me always and do as I wish?”

“Gladly, very gladly, more than gladly!”

“Beginning tomorrow,” said the Fairy, “you’ll go to school every day.”

Pinocchio’s face fell a little.

“Then you will choose the trade you like best.”

Pinocchio became more serious.

“What are you mumbling [talk indistinctly]to yourself?” asked the Fairy.

“I was just saying,” whined [ talk in a tearful manner] the Marionette in a whisper, “that it seems too late for me to go to school now.”

“No, indeed. Remember it is never too late to learn.”

“But I don’t want either trade or profession.”


“Because work wearies [make tired] me!”

“My dear boy,” said the Fairy, “people who speak as you do usually end their days either in a prison or in a hospital. A man, remember, whether rich or poor, should do something in this world. No one can find happiness without work. Woe [pain] betide [happen] the lazy fellow! Laziness is a serious illness and one must cure it immediately; yes, even from early childhood. If not, it will kill you in the end.”

These words touched Pinocchio’s heart. He lifted his eyes to his Fairy and said seriously: “I’ll work; I’ll study; I’ll do all you tell me. After all, the life of a Marionette has grown very tiresome to me and I want to become a boy, no matter how hard it is. You promise that, do you not?”

“Yes, I promise, and now it is up to you.”



Immagine correlata

According to X  means in “X’s opinion”, “if what X says is true”.

According to Harry, it’s a good film.

The train gets in at 8.27, according to the timetable.

We do not usually give our own opinions with according to. Compare:

According to Ann, her boyfriend his brilliant. 

(=if what Ann says is true=)

In my opinion, Ann ‘s boyfriend is an idiot (NOT According to me,…)

From Michael Swan, Practical English Usage, Oxford