If one-half 𝑚 plus one-eighth 𝑛 is equal to eight, what is the value of four 𝑚 plus 𝑛?
We are told in the question that one-half 𝑚 plus one-eighth 𝑛 is equal to eight. And we need to calculate the value of four 𝑚 plus 𝑛. If we consider the second term, one-eighth 𝑛, this has become 𝑛. There are eight-eighths in one whole one. Therefore, eight multiplied by one-eighth is equal to one. This means that multiplying the second term one-eighth 𝑛 by eight would give us one 𝑛 or just 𝑛.
As we are multiplying this term by eight, we need to multiply all of the other terms in the equation by eight. Eight multiplied by a half or a half of eight is equal to four. This means that eight multiplied by a half 𝑚 is equal to four 𝑚. Multiplying the other side of the equation gives us 64, as eight multiplied by eight equals 64.
We now have the expression four 𝑚 plus 𝑛 on the left-hand side of the equation. As this is equal to 64, we can say that if one-half 𝑚 plus one-eighth 𝑛 is equal to eight, then the value of four 𝑚 plus 𝑛 is 64. We can use this method to scale up or down any equation, remembering to multiply every term by the same value. In this case, we multiplied all three terms by eight.