Use the given pattern to complete each of the diamonds.
A.
B.
C.
D.
Practice makes perfect
To find the missing numbers, let's identify the variables using our variable diamond and substitute the correct numbers into our pattern.
Diamond A
In Diamond A, we are given that C=- 43 and B=-1. Substituting these values into our pattern gives us the following equations.
-4/3 &=A * (-1)
D&= A+(-1)
From the first equation, we can calculate A by isolating it on one side.
In Diamond B, we are given values for A and B, and we want to find C and D.
A= -3/5 and B=-4/5
To do this, we can substitute the numbers in our pattern.
In this case, we are given that D=1 56 and B=- 16. Substituting these values into our pattern gives us the following equations.
C&=A * -1/6
1 56 &= A+ (-1/6)
From the second equation, we can calculate A by isolating it on one side.
Here we are given that C= 116 and D= 12. We want to find the numbers A and B.
1/16=A* B
1/2=A+B
In this case, let's think of different pairs of numbers which multiply to give us 116. Notice that when we add them we want to get 12 which is a fraction. Therefore we need the pair of fractions.
& 116= 12* 18
& 116= 14* 14
Let's check which, if any of these, will match the second condition as well.
& 12+ 18= 58 *
& 14+ 14= 12
The pair A= 14 and B= 14 works for the pattern. Therefore, this is the correct pair of numbers to complete the diamond.
