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M.Phil. Preparatory Flashcards > Arithmetics > Flashcards

Arithmetics Flashcards

1
Q

No matter what how two numbers are arranged their addition is always the same

A

Commutative property of addition

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2
Q

When zero is added to a number x the answer is always equals to x, what property is this?

A

Additive property of addition

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3
Q

Irrespective of their arrangments, three numbers will always give the same sum. What is this addition property called?

A

Associative property of addition

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4
Q

Are the properties (associative, commutative, and additive) also true for subtraction?

A

No

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5
Q

What is subtrahend and minuend in subtraction?

A

Subtrahend: smaller number
Minuend: Larger number

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6
Q

What is the value of a number x if it’s power is 0?

A

1

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7
Q

What is the number called which is a whole number with square root X also as a whole number?

A

Perfect square

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8
Q

In division if the divisior does not gets into any of the numbers in the dividend, what shall be done?

A

It will only go into 0 in that case. Do this by placing a 0 as quotient.

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9
Q

What is the operation rule for numbers?

A

PEDMAS

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10
Q

What is the special case of appearance for DMAS?

A

From left to right according to appearnce

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11
Q

What will you do when there is no parenthesis involved in an operation and you have all the operators given?

A

Follow “DMAS” look for order of appearance for each case.

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12
Q

What is the inside out rule of operations with brackets?

A

If there are brackets within brackets then the innermost brackets need to be solved first and the coming out to the others.

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13
Q

Is the square root sign also a grouping symbol like round or braces bracket?

A

Yes

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14
Q

What is the area of triangle?

A

A = (a*b)/2

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15
Q

What is the formula and theoram for calculating the perimeter of a right triangle hypothenus?

A

Pythagorean theoram

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16
Q

Can we put zero in the numerator?

A

No, n/0 is undefined

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17
Q

Recall the formula for converting mixed numbers into improper fraction!

A

N.p/q = N.q+p/q

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18
Q

What is the rule of finding parts of a fraction in a fraction?

A

If a/b of d/c then to find the fractions within a fraction a.d/b.c

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19
Q

Give one scenario of using the multiplication of fraction in daily life?

A

For instance, you’ve 12 fruits and 1/2 of it is orange. This me you’ve 50% orange (6).

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20
Q

What are equivalent fractions and how do fractions qualify for it?

A

They have same values. Their cross products should be the same for this condition to be true.

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21
Q

How would you find equivalents of a fraction?

A

Multiply the numerator and denominator with same numbers (remember c/c).

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22
Q

Why is fraction simplified with common factor?

A

It’s a whole number which divides the num and denon without remainder.

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23
Q

In what condition is reducing fractions to the lowest terms not possible?

A

When the common factor is 1

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24
Q

What is a number called, which does not have a factor other than 1?

A

Prime number (>1)

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25
Q

In prime factorization, what is the strategy of division?

A

Divide from the least (>1) to the largest, stop when you hit a prime number (note: this number is also added to the list of prime factorization).

26
Q

What are composite numbers?

A

Which have a factor >1 e.g: 4,8, and 12 etc.

27
Q

What is the 5-step procedure of finding GCF?

A
  1. find prime factors
  2. Find common factors
  3. If there is no common factor then take 1.
  4. Find the smallest exponents of those common factors.
  5. GCF is the product of the common factors found in step 2 and exponents in 4.
28
Q

How can cancelling help with multiplication of bigger numbers in fractions?

A

Simplifies the fraction, making it easier to do the operation.

29
Q

Is it necessary to have same fractions with common factor to be cancelled?

A

No any common factor across the fraction can be used for cancellation.

30
Q

What are the rules of adding/subtracting like and unlike fractions?

A

a/c+b/c = a+b/c and a/b+b/c = ac+bb/bc

31
Q

What method would you use to simplify fraction addition like pre cancellation in multiplication?

A

1=a/a or 1=b/b etc method

32
Q

Least or highest, which exponents should be selected for GCF, LCM?

A

GCF lowest and LCM highest

33
Q

In what type of fraction does GCF help?

A

Division

34
Q

In what type of fraction does LCM help?

A

Addition

35
Q

How would you find the largest fraction in fractions?

A

Find LCD, the one with the highest numerator is the largest

36
Q

If the quotients of more than one fraction are equal what is done?

A

Only take the fractional parts, no need to convert into improper fraction.

37
Q

If you get a question that asks to find how many times something goes into anything, what operation would you perform?

A

Division

38
Q

What’s a proper and improper fraction?

A

Proper: num is less than the denon and improper num is either greater than denon or equal to it.

39
Q

Explain how would you add mixed numbers and what rule should be followed?

A

Align them and find their LCD after that check if the resulting fraction is in the proper form or not, if not then carry the whole number part and leave the fractional part.

40
Q

When is it easier to use mixed number addition instead of improper fraction?

A

When the improper fractions are incredibly large.

41
Q

Explain the procedure of mixed number addition.

A

first align the mixed numbers, next find their LCD. Check if the final value is in the proper fraction form, if not then carry a 1 from the whole number and leave the fractional part untouched.

42
Q

What should you do when the mixed number has 0 fractional parts?

A

Represent the fractional part with 0 as the num and the convineint number as the denon. x0/c

43
Q

What is the procedure for mixed number subtraction.

A

Align find convineint number.

44
Q

What should be remembered while doing mixed number addition or subtraction?

A

Carrying and borrowing is done with the subtraend part. In case of subtraction only when fractional subtraction is not possible.

45
Q

When are you supposed to do carrying in round-off?

A

When the digit at the decimal has round off greater than 9 such as 10, hence the 1 is added to the left number in sequence.

46
Q

What is your strategy for subtraction?

A

If there’s a zero then find the closest digit to it. Carry from this digit to the next.

47
Q

What do you learn from the division and multiplication with 10^n?

A

Decimal point moves to the right with multiplication and vice versa with division.

48
Q

True or false? You can also bring down a non-significant zero from the dividend in decimal division as per your need?

A

Yes it’s true!

49
Q

What should you do when the ratios are in measurable quantities?

A

They must be in the same unit, not different.

50
Q

What important trick should you remember for fractional multiplication and division?

A

When dividing, bring fraction in whole number form and then at the end multiple it with the 10^n. Same steps for multiplication but the end is vice versa.

51
Q

What rule should you remember while performing a similar triangle proportion?

A

1:2 or 2:1, the answer will be the same even after the ratios are reveresed!

52
Q

When you turn two fractional numbers to a whole number, should you move the decimal point after division?

A

No keep it the same (context: both have been converted with same degree).

53
Q

What’s an absolute value?

A

It’s a non-zero number.

54
Q

What’s the rule when two values being added are of different signs?

A

Sign of sum will be the value with the highest abs. value. and abs value will be larger - smaller

55
Q

What’s the rule when the signs are same(-ve) in addition

A

Sign is the common sign of summand and abs value will be the sum of the individual values. E.g: -A + (-B) = -(A+B)

56
Q

What important conventional rule do you remember regarding finding difference between two unequal values?

A

Always do Larger - smaller and the sign should be positive.

57
Q

Can we put zero in denonminator?

A

No, it’s undefined.

58
Q

What is the rule for signed numbers with fractions?

A

If the fractions have same sign they will be positive, however, if the signs are opposite, then it will be negative. it(quotient)

59
Q

What is the rule of signed numbers for exponents and powers?

A

If negative number has even power, then apply positive power whereas vice-versa for odd power.

60
Q

What important thing to remember in expression evaluation?

A

multiply divide (reve. reciprocal) and subtract with similar numbers.

61
Q

What important rule should you remember while conducting fraction cancellation in expression simplification?

A

When finding equalities or simplifying expressions involving fractions, always cancel out fractions with their reciprocal values like 2/3 with -3/2 etc.

M.Phil. Preparatory Flashcards (3 decks)

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