Mathematics Grades $6-7$ Term $2/2024-2025$

Homework $($HW$)$

Read all problems carefully and answer the questions accurately.

Any positive number can be fed into a number crunching machine which produces one of two results:

If the numberfed in is even, the macchine divides the number by $2.$

If the numberfed in is odd the machine ${?}^1{?}^1$

What to do:

$1.$

Findathe result when the following numbers are fed into the machine:

$b.\frac{26}{15}$

$\frac{\text{W}\text{h}\text{a}\text{t}\text{w}\text{a}\text{s}\text{t}\text{h}\text{e}in\text{o}\text{u}\text{t}\text{t}\text{o}\text{t}\text{h}\text{e}\text{m}\text{a}\text{c}\text{t}\text{r}\text{i}\text{n}\text{e}if\text{t}\text{h}\text{e}\text{o}\text{u}\text{t}\text{o}\text{u}\text{t}is\text{:}}{b.\frac{8}{13}}$

It is possible to feed the output from the machine back into the input, and continue to do so until the output reaches zero.

For example, with an initial input of $11,$ the following would occur:

$111052210$

We see that $6$ steps are required to reach zero

Give the number of steps required to reach zero if you start with: $7,24$ and $32$