How can the multiplication table be used to solve divisionâ problems?
A.
Find the column for the firstâ 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 theâ quotient, if possible. Within thisâ row, find the entry corresponding to either factor. The other factor is the number of the corresponding column.
C.
Find the column for eitherâ factor, if possible. Within thisâ column, move down nâ rows, where n is the other factor. The resulting entry is the quotient.
D.
Find the row for eitherâ factor, if possible. Within thisâ 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 theâ table? Explain why or why not.
A.
No. A product of two numbers is odd if at least one factor is odd.â Therefore, the surroundingâ row(s) andâ column(s) will contain products of odd and evenâ numbers, which are odd and even.
B.
No. An odd number has the form
2kplus+â1,
where k is a whole number.â Therefore, the entry to the right will equal
2kplus+1plus+âb,
where b is the number of the correspondingâ 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.â Therefore, the surroundingâ row(s) andâ column(s) will contain products of evenâ numbers, which are even.
D.
Yes. An odd number has the form
2kplus+â1,
where k is a whole number.â Therefore, the entry to the right will equal
2kplus+1plus+âb,
where b is the number of the correspondingâ column, and
1plus+b
must always be an even number.
