Directions: Find three numbers whose product is -64. You may use integers from -10 to 10. You may not use the same absolute value twice. Find all possible combinations.

### Hint

How can you make 64, multiplying just two numbers?

How can the factors of 64 help you find a combination?

### Answer

-2(4)(8)

2(-4)(8)

2(4)(-8)

(-2)(-4)(-8)

2(-4)(8)

2(4)(-8)

(-2)(-4)(-8)

Source: Nathan Charlton and Daniel Martinez

There are more possible solutions if you use 1 & -1. 32(-2)(1), (-32)(2)(1), 32(2)(-1), (-32)(-2)(-1)

Nope, because it has to be between -10 & 10. Forget I said that.

Did this today in class. Made the requirements simpler. Use integers, can’t use the same one twice. Different orders don’t count. More possibilities, more fun!

Aaaand, -64 made my regular kids brains hurt. Going to try -16.

-16 worked great with most of my classes. Only 7 possible outcomes. Making -64 there are 15 outcomes if I remember correctly. This is using ALL integers.

You will only have one answer 2,4,8. You said use absolute value only once. so if the number is positive or negative it still has the same absolute value.

You have the correct thinking for the solution Lonnie, but we are looking for the number combinations that generate that solution. The product of two negative values is positive, which is why you see those in the solution set.

We adapted this question since absolute value isn’t part of our outcomes in our area. We used this as a quick review of the rules for multiplying and dividing integers, and also for order of operations. By opening up the criteria a little bit we were able to create more solutions. -10 to +10. Any operation. No repeated numbers and use at most three numbers. How many ways can we create -64? Was a great short review opening activity.

One more solution: (1)(8)(-8). My class thinks there are 5 solutions.

(-8) and 8 have the same absolute value. This is not a solution as specified in the question.

One more solution: (1)(8)(-8). My class thinks there are 5 possible solutions.

-1*4*8=-64 -4*2*8=-64 -8*2*4=-64 -8*-2*-4=-64

How do you make 64 using 8, 5 and 3?

8 X (5 +3)

but this doesn’t work for the problem above as it clearly says 3 numbers with the product -64

How do you make 64 using 8, 5 and 3 for a year 7 naplan test?

10, 3 and 4. because 10 x 3 plus 10 x 3 can equal sixty and add a four to get 64, you can also do it in different ways.

3 numbers that equal -64 is -10(6)= -60 then you can just add 4