What’s 1 times 2 and 2 / 1 plus 1/2 and 1

Plus 2

What is 2 times the square root of 3?

How can the multiplication table be used to solve division​ problems?

A.

Find the column for the first​ factor, if possible. Then find the row corresponding to the second factor. The quotient is the entry diagonally up and to the right of the corresponding entry.

B.

Find the row for the​ quotient, if possible. Within this​ row, find the entry corresponding to either factor. The other factor is the number of the corresponding column.

C.

Find the column for either​ factor, if possible. Within this​ column, move down n​ rows, where n is the other factor. The resulting entry is the quotient.

D.

Find the row for either​ factor, if possible. Within this​ row, find the entry corresponding to the other factor. The quotient is the number of the corresponding column.

2. Consider the odd number 35 shown in the multiplication table. Consider all the numbers that surround it. Note that they are all even. Does this happen for all odd numbers in the​ table? Explain why or why not.

A.

No. A product of two numbers is odd if at least one factor is odd.​ Therefore, the surrounding​ row(s) and​ column(s) will contain products of odd and even​ numbers, which are odd and even.

B.

No. An odd number has the form

2kplus+​1,

where k is a whole number.​ Therefore, the entry to the right will equal

2kplus+1plus+​b,

where b is the number of the corresponding​ row, and

1plus+b

can be even or odd.

C.

Yes. The only way for a product of two numbers to be odd is if both factors are odd.​ Therefore, the surrounding​ row(s) and​ column(s) will contain products of even​ numbers, which are even.

D.

Yes. An odd number has the form

2kplus+​1,

where k is a whole number.​ Therefore, the entry to the right will equal

2kplus+1plus+​b,

where b is the number of the corresponding​ column, and

1plus+b

must always be an even number.