The two lines above are the same length. The top line is split into \(\displaystyle 4\) pieces and the bottom line is split into \(\displaystyle 12\) pieces.

 \(\displaystyle \frac{2}{4}\) and \(\displaystyle \frac{6}{12}\) are equivalent because they occupy the same position on the number line. 

The two lines above are the same length. The top line is split into \(\displaystyle 4\) pieces and the bottom line is split into \(\displaystyle 12\) pieces.

 \(\displaystyle \frac{3}{4}\) and \(\displaystyle \frac{9}{12}\) are equivalent because they occupy the same position on the number line. 

The two lines above are the same length. The top line is split into \(\displaystyle 3\) pieces and the bottom line is split into \(\displaystyle 6\) pieces.

 \(\displaystyle \frac{1}{3}\) and \(\displaystyle \frac{2}{6}\) are equivalent because they occupy the same position on the number line. 

The two lines above are the same length. The top line is split into \(\displaystyle 3\) pieces and the bottom line is split into \(\displaystyle 6\) pieces.

 \(\displaystyle \frac{2}{3}\) and \(\displaystyle \frac{4}{6}\) are equivalent because they occupy the same position on the number line. 

The two lines above are the same length. The top line is split into \(\displaystyle 6\) pieces and the bottom line is split into \(\displaystyle 12\) pieces.

 \(\displaystyle \frac{2}{6}\) and \(\displaystyle \frac{4}{12}\) are equivalent because they occupy the same position on the number line. 

When we round a number to the nearest ten we look to the ones place to tell us if we round up or down.

\(\displaystyle 924\textup,41{\color{Blue} 2}\)

If the number in our ones place is \(\displaystyle 5\) or greater, we round up. If the number in the ones place is \(\displaystyle 4\) or less, we round down. When we round up, the number in the tens place increases by \(\displaystyle 1\) and all the other numbers to the right become \(\displaystyle 0\). When we round down, the number in the tens place stays the same and all the other numbers to the right become \(\displaystyle 0\).

In this case, \(\displaystyle 2\) is less than \(\displaystyle 5\) so our rounded number is \(\displaystyle 924\textup,410\)

When we round a number to the nearest hundred we look to the tens place to tell us if we round up or down.

\(\displaystyle 478\textup,3{\color{Blue} 4}7\)

If the number in our tens place is \(\displaystyle 5\) or greater, we round up. If the number in the tens place is \(\displaystyle 4\) or less, we round down. When we round up, the number in the hundreds place increases by \(\displaystyle 1\) and all the other numbers to the right become \(\displaystyle 0\). When we round down, the number in the hundreds place stays the same and all the other numbers to the right become \(\displaystyle 0\).

In this case, \(\displaystyle 4\) is less than \(\displaystyle 5\) so our rounded number is \(\displaystyle 478\textup,300\)

When we round a number to the nearest ten we look to the ones place to tell us if we round up or down.

\(\displaystyle 42{\color{Blue} 1}\)

If the number in our ones place is \(\displaystyle 5\) or greater, we round up. If the number in the ones place is \(\displaystyle 4\) or less, we round down. When we round up, the number in the tens place increases by \(\displaystyle 1\) and all the other numbers to the right become \(\displaystyle 0\). When we round down, the number in the tens place stays the same and all the other numbers to the right become \(\displaystyle 0\).

In this case, \(\displaystyle 1\) is less than \(\displaystyle 5\) so our rounded number is \(\displaystyle 420\).

When we round a number to the nearest ten thousand we look to the thousands place to tell us if we round up or down.

\(\displaystyle 18{\color{Blue} 8}\textup,152\)

If the number in our thousands place is \(\displaystyle 5\) or greater, we round up. If the number in the thousands place is \(\displaystyle 4\) or less, we round down. When we round up, the number in the ten thousands place increases by \(\displaystyle 1\) and all the other numbers to the right become \(\displaystyle 0\). When we round down, the number in the ten thousands place stays the same and all the other numbers to the right become \(\displaystyle 0\).

In this case, \(\displaystyle 8\) is greater than \(\displaystyle 5\) so our rounded number is \(\displaystyle 190\textup,000\)

When we round a number to the nearest hundred we look to the tens place to tell us if we round up or down.

\(\displaystyle 8\textup,5{\color{Blue} 2}3\)

If the number in our tens place is \(\displaystyle 5\) or greater, we round up. If the number in the tens place is \(\displaystyle 4\) or less, we round down. When we round up, the number in the hundreds place increases by \(\displaystyle 1\) and all the other numbers to the right become \(\displaystyle 0\). When we round down, the number in the hundreds place stays the same and all the other numbers to the right become \(\displaystyle 0\).

In this case, \(\displaystyle 2\) is less than \(\displaystyle 5\) so our rounded number is \(\displaystyle 8\textup,500\)