Rizwan writes down three numbers a,b and C a: b=1:3 b:c=6:5 (a) (i) Find a:b:c (ii) Express a as a fraction of the total of the three numbers a, b and C Emma writes down three numbers m, n and p n=2m p=5n (b) Find m:p

Let's begin with your questions.(a) Given that:i) ii) We need to find:(i) The ratio (ii) The ratio of to the total of the numbers a, b and c.Sol:(i)First, we're given . This states that for every one "part" of "a", we have three "parts" of "b". Similarly, we're given , stating that for every six "parts" of "b", we have five "parts" of "c".To find the proportion between a, b and c, we can set the value of "b" equal in both ratios. We can uniformly multiply a: b by 6 and b: c by 3, which will maintain our ratios while setting b to be consistent across both:so we get: and So, the final (ii) Now we express " " as a fraction of the total of the three numbers " Following from our results in part i, we have accounted for 6 "parts" of a, 18 "parts" of b, and 15 "parts" of c. Therefore {as} = \frac{a}{a+b+c}= \frac{6}{6 + 18 + 15}= \frac{6}{39} We need to find ${m:p} {2m} {10m} {m} {p = m: p = 1:10} {a:b:c = 6:18:15} {a/(a+b+c) = 6/39} {(m:p=1:10)}$ I hope these derivations were clear and met the goals of your learning guide! Feel free to keep the questions coming to fill the holes in your knowledge!