a To find the missing numbers, let's identify the variables using our variable diamond and substitute the correct numbers into our pattern.
Here, we are given that C=- 25 and B=5. Substituting these values into our pattern gives us the following equations.
- 25&=A * 5
D &= A+ 5
From the first equation, we can calculate A by isolating it on one side.
d Here we are given that C= - 20 and D=19. We want to find the numbers A and B.
- 20=A* B
19=A+B
In this case, let's think of different pairs of numbers which multiply to give us - 20. Notice that when we multiply them we want to get a negative number. Therefore, we need a pair with one negative number. Multiplication of positive and negative numbers gives a negative number as a result.
&- 20=-1* 20
&- 20=-2* 10
&- 20=-4* 5
&- 20=- 20* 1
&- 20=- 10* 2
&- 20=- 5* 4
Let's check which, if any of these, will match the second condition as well.
& -1+20=19
&-2+10=8 *
&-4+5=1 *
&-20+1=- 19 *
&-10+2=- 8 *
&- 5+4=- 1 *
The pair A=- 1 and B=20 works for the pattern. Therefore, this is the correct pair of numbers to complete the diamond.
Notice that the pair A=20 and B=- 1 also works for the pattern. In this situation we have two possibilities to complete the diamond.
