Final answer:
John disliked 26 songs, as found by using cross-multiplication with the given ratio of 5:2 and the information that he liked 65 songs. Proportional reasoning relies on ratios. A key idea is that every ratio can be written as a fraction, and every fraction can be thought of as a ratio. Example: I make just 2/3 as much as my husband – this is thinking about it as a fraction. Thinking about it as a ratio, I might say – I make $2 for every $3 he makes.
Step-by-step explanation:
The student is asking a mathematics question related to ratios and proportional reasoning. John liked 65 songs, and the ratio of songs he liked to disliked is 5:2. We can use the concept of cross-multiplication to find the number of songs he did not like. If 5 parts represent 65 songs, then 1 part represents 65/5, which is 13 songs. Therefore, if 2 parts represent the number of songs he didn't like, then we multiply 13 by 2, which gives us 26 songs that John didn't like.
Use proportional reasoning with estimation. Proportional reasoning is a great tool to
quickly estimate an answer. You can also use proportional reasoning with estimation to
check the answers to algebra problems.
Example: I know I can drive about 300 miles on a full tank of gas. I plan to visit my
grandmother, a round trip of about 200 miles. How much of a tank will I probably use?
200 is 2/3 of my full range, so I expect to use about 2/3 of a tank.
Example: The formula for converting Fahrenheit temperatures into Celsius temperatures
is ( 32). 9
5 C = F − I converted 70ºF to 7ºC. Did I do that right?
5/9 is about ½, and 32 is about 30, so my answer should be about ½ (70 – 30) = ½ ∙40 =
20 degrees. I must have made a mistake. (The correct answer is about 21º.)