Riya, Teena and John are three friends. They meet after long time. They go to enjoy PIZZA together. While Riya wants capsicum and onion as toppings in her pizza, John wants mushroom and pepperoni and Teena wants to have black olives and capsicum. After much discussion they finally agree to have a combination of all the toppings with equal number of pieces of each type.
Q 1. What is the fraction of mushrooms in all the toppings in this pizza?
Q 2. If there are total 20 pieces of capsicum and fraction of capsicum pieces is 1/5 of total toppings, find the total number of pieces of all the toppings in the pizza.
Q 3. Find the fraction of choice of Riya’s toppings in Pizza.
Q 4. What is the sum of fractions of all the five toppings?
Answers
definition
Euclid's Division Lemma
Let a
and b be any two positive integers. Then there exist unique integers q and r such that
a=bq+r, where 0≤r<b
If b|a, then r=0.
Otherwise, r satisfies the stronger inequality 0≤r<b
example
HCF using Euclid's Divison
If a
and b are positive integers such that a=bq+r, then every common divisor of a and b is a common divisor of b and r, and vice-versa.
Example: Find HCF of 420 and 130.
Since 420>130 we apply the division lemma to 420 and 130 to get ,Since 300 , we apply the division lemma to 130 and 30 to get
130=30×4+10
420=130×3+30
Since 100 , we apply the division lemma to 30 and 10 to get
30=10×3+0
The remainder has now become zero, so our procedure stops. Since the divisor at this step is 10, the HCF of 420 and 130 is 10
.
definition
Fundamental Theorem of Arithmetic
Any integer greater than 1
is either a prime number, or can be written as a unique product of prime numbers
definition
Define and identify examples of terminating decimals
A terminating decimal is a decimal that ends i.e. it has finite number of digits.
For a fraction in decimal form, while performing division after a certain number of steps, we get the remainder zero.
The quotient obtained as decimal is called the terminating decimal.
For eg:-
38=0.375
has 3 digits after decimal point
54=1.25 has 2 digits after decimal point
Hence, 0.375 and 1.25
are terminating decimals.
definition
Non-Terminating Recurring Decimals
While expressing a fraction in the decimal form, when we perform division we get some remainder.
If the division process does not end i.e.
we do not get the remainder equal to zero; then such decimal is known as non-terminating decimal.
In some cases, a digit or a block of digits repeats itself in the decimal part, then the decimal is non-terminating recurring decimal.
For eg:-
1.6666....,0.141414...