Question

m4|l5 say it with decimals write 4/6 as a decimal. start by filling in the algorithm.

Explanation:

Step1: Recall fraction to decimal conversion

To convert a fraction \(\frac{a}{b}\) to a decimal, we perform the division \(a\div b\). Here, \(a = 4\) and \(b = 6\), so we need to do \(4\div6\).

Step2: Perform the division

When we divide \(4\) by \(6\), we know that \(6\) goes into \(4\) zero times. So we write \(0\) and then add a decimal point. Then we consider \(40\) (since we add a zero after the decimal). \(6\) goes into \(40\) six times (\(6\times6 = 36\)). Subtract \(36\) from \(40\), we get \(4\). Now we have a remainder of \(4\), which is the same as our original dividend. So this division will repeat. So \(4\div6 = 0.666\cdots\) or \(0.\overline{6}\). But first, for the algorithm (the long division setup), the divisor is \(6\) and the dividend is \(4\) (with the decimal setup). So in the long division box, the divisor (outside the bracket) is \(6\) and the dividend (inside the bracket) is \(4\) (with the decimal part to be added as we go). So the first box (divisor) is \(6\) and the dividend part (inside) starts with \(4\).

Answer:

For the long division algorithm (the two boxes: divisor and dividend start), the divisor box (outside the long division symbol) should be \(6\) and the dividend part (inside) starts with \(4\). When performing the division \(4\div6\), the decimal is \(0.\overline{6}\) (or \(0.666\cdots\)). If we are just filling the initial algorithm (the two boxes for divisor and dividend in long division), the divisor is \(6\) and the dividend is \(4\), so the first box (divisor) is \(6\) and the dividend part (inside) is \(4\).

(If the question is just about filling the algorithm boxes: the divisor is \(6\) (the box outside the long division) and the dividend is \(4\) (the box inside the long division start). So the answer for the boxes would be divisor: \(6\), dividend start: \(4\). And the decimal is \(0.\overline{6}\))