4.f Remainder Theory

Question 1

What is the remainder of this?

Answer 1

0

As the numerator is a multiple of 2, and 2 is the denominator

Question 2

If the numerator is a _________ of the denominator, the division will leave no remainder

Answer 2

If the numerator is a MULTIPLE of the denominator, the division will leave no remainder

Question 3

What is the remainder of this?

Answer 3

0

As the numerator is a multiple of 2

Question 4

What is the remainder of this?

Answer 4

0

The numerator is essentially 12 x 12 x 12 (144 times), but as 12 is a multiple of 3, it can also be expressed as 3 x 4, and therefore the remainder must be 0.

Question 5

When the product of x, y and z is divided by either x, y or z, what is the remainder?

Answer 5

0

As the numerator is a multiple of the denominator

Question 6

What if the numerator is not a multiple of the denominator?

Answer 6

A remainder will be left

Question 7

What is the result of this fraction?

Answer 7

19 is not a multiple of 7, so a remainder will result

= 2 + 5/7

So, 5 is the remainder
“7 divides into 19 twice, leaving a remainder of 5”

Question 8

Label each variable/ fraction in this:

Answer 8

23 = numerator (or dividend)
5 = denominator (or divisor)

4 = quotient
3 = remainder

Question 9

What is this formula?

Answer 9

Just a classic formula expressing a simple division with a remainder

Question 10

How can the division formula be rewritten?

Answer 10

Question 11

In a fraction, what is the range of all possible remainders?

Answer 11

if n is the divisor (denominator)

the range of the remainder is from 0 to n-1

Question 12

What are all possible remainders for: n/5 ?

Answer 12

0/5 1/5 2/5 3/5 4/5

Hence, satisfying the range of 0 to n-1
(where n is the denominator)

Question 13

A remainder must always be a _______________ and less than the ____________

Answer 13

A remainder must always be a NON-NEGATIVE INTEGER and less than the DIVISOR

Question 14

If an integer leaves a remainder of 11, when divided by 13, what must that number be?

Answer 14

11, and any number that is 11 greater than a multiple of 13

Question 15

If positive integer N divided by d leaves a remainder of r, what are the possible values of N?

Answer 15

N = r, r + d, r + 2d, r + 3d,

Question 16

If N is divided by 16 and leaves a remainder of 3, what values could N be?

Answer 16

3, 3 + 16, 3 + 32, 3 + 48

Question 17

What is the fastest way to find values that satisfy two remainder statements?

Answer 17

If positive integer N divided by j leaves a remainder of a, and when divided by k leaves a remainder of b:

1) Find the smallest possible value of N
2) Add the LCM of j and k onto this number as often as necessary

Question 18

If N divided by 16 leaves a remainder of 3, and N divided by 12 leaves a remainder of 7, which are the first 3 terms that satisfy both statements?

Answer 18

1) Find the first value that satisfies both statements

2) find the LCM of 12 and 16, and add this on for every term you need

Question 19

What are the ways in which you can express 32/5 ?

Answer 19

Mixed number form:
32/5 = 6 + 2/5

Decimal form:
6.40

Question 20

If a division between two integers yields a decimal (eg. 9.48), what would the remainder be?

Answer 20

We can’t know!!

x/y = 6.64, the actual remainder could (technically) be anything

Question 21

What would the remainder of 9.48 be?

Answer 21

9.48, you can’t know what the remainder is!!!!

Could be:
48 (9 + 48/100)
24 (9 + 24/50)
12 (9 + 12/25)

So, you can’t know!

Question 22

Can you multiply remainders together?

Answer 22

Yes!

But remember to correct for excess remainders at the end..

eg. 1/5 * 2/5 =

Question 23

How woulc you tackle this?

Answer 23

Divide first, then take the remainders and multiply them,

4 x 0 x 4 = 0

So, the overall remainder is 0

Question 24

How would you tackle this?

Answer 24

Same as multiplying! You can also just subtract or add!