Question

Start with the equation 4·0=0

to explain why 4·−10
must equal −40
. Drag descriptions and equations to the table to complete the explanation.

Answer 1

Step 1 Given. 4·0=0

Step 2 Substitute. Any number plus its opposite is zero. 4(10+-10)=0

Step 3 Use the distributive property. 4·10+4·-10=0

Step 4 Multiply. 40+4·-10=0

Step 5 Subtract 40 from both sides. 4·-10=0-40

Step 5 Simplify to solve for 4·-10. 4·-10=-40

Answer 2

Step 1 Given. The problem is telling us to start with the equation 4·0=0

Step 2 Substitute. Any number plus its opposite is zero. Since the opposite of 10 is -10, 10+(-10)= 0: 4(10+-10)=0

Step 3 Use the distributive property. In other words multiply 4 by 10 and 4 by -10: 4·10+4·-10=0

Step 4 Multiply. perform the first multiplication of step 3: 4·10=40, so: 40+4·-10=0

Step 5 Subtract 40 from both sides. 40-40+4·-10=0-40; simplify the left side: 0+4·-10=0-40
4·-10=0-40

Step 5 Simplify to solve for 4·-10. Simplify the right side: 4·-10=-40

We can conclude that you should fill your table as follows:
Step 1 Given. 4·0=0
Step 2 Substitute. Any number plus its opposite is zero. 4(10+-10)=0
Step 3 Use the distributive property. 4·10+4·-10=0
Step 4 Multiply. 40+4·-10=0
Step 5 Subtract 40 from both sides. 4·-10=0-40
Step 5 Simplify to solve for 4·-10. 4·-10=-40