Cassidy has a bag of 72 red beads and 90 blue beads. She would like use the beads to make bracelets that have the same ratio of red to blue beads as in the bag. If a bracelet has 15 blue beads, how many red beads does it have? *

In a question like this, you are trying to find the Highest Common Denominator, or HCF. This can be done manually, by finding all the factors of 42

(

1

,

2

,

3

,

6

,

7

,

14

,

21

,

42

)

, all the factors of 72

(

1

,

2

,

3

,

4

,

6

,

8

,

9

,

12

,

18

,

24

,

36

,

72

)

, and comparing them to see that their HCF is

6

. Or, it can be done by dividing both numbers,

=

72

42

, simplifying the fraction

=

12

7

, then dividing the starting number with the new simplifiied number, remembering always to divide numerator with numerator and denominator with denominator.

72

12

=

6

or

42

7

=

6

This process works with any two numbers which you want to find the HCF of, and can be simplified into this rule:

If

a

=

any number,

b

=

any number and

c

d

is the simplified fraction of

a

b

,

The HCF

=

a

c

or

=

b

d

I hope that helped!

Step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x