Question

1Higher Order Thinking Karen found apattern on the multiplication table.What pattern did she find?Explain why it is true.

Answer 1

PATTERNS IN MULTIPLYING BY 3’S

Multiples of 3 have a pattern of 3, 6, 9, 2,5, 8, 1, 4 in the ones place

The digits in the multiple of 3 add up to give a multiple of 3 (12=1+2=3,18=1+8=9)

All even multiples of 3 are also a multiple of 6

`\begin{gathered} 3*2=6,6*1=6 \\ 3*4=12,6*2=12 \\ 3*6=18,6*3=18 \\ 3*8=24,6*4=24 \end{gathered}`

PATTERNS IN MULTIPLYING BY 6’S

Multiples of 6 have a pattern of 6, 2, 8, 4, 0 in the ones place.

When a multiple of 2 and 3 overlap, you get a multiple of 6.

All multiples of 6 are even numbers.(6,12,18,24)

All multiples of 6 are 6 away from each other.

Multiples of 6 are every other multiple of 3.

The upper value on the multiplication table is multiplied by two to get the multiples of 6 below

`\begin{gathered} 3*2=6,(3*2)*1=6*1=6 \\ 3*4=12,(3*2)*2=6*2=12 \\ 3*6=18,(3*2)*3=6*3=18 \\ 3*8=24,(3*2)*4=6*4=24 \end{gathered}`

The general formula for the multiples of 3 is given below as

`3+3(n-1)`

To get for the multiple of 6, we will multiply the formula above by 2

`\begin{gathered} 2(3+3(n-1)) \\ =6+6(n-1) \end{gathered}`