Ratio problem solving

• What is the key to answering questions involving ratios along with fractions and/or percentages?

  Ratios can also be turned into fractions (or vice versa).
• How can you express the ratio of stay members to students in a school with a ratio of 3:37?

  The stay members represent $\frac{3}{40}$ of the people in the school.
• What fraction of the people in the school are students if the ratio of stay members to students is 3:37?


  The students represent $\frac{37}{40}$ of the people in the school.

  
• Do you need to know the total number of people in the school to determine the fractions of stay members and students?

  No, you don't need to know the total number of people in the school.

  
• How can multiplication be used in relation to fractions or percentages?

  You can use multiplication to find fractions or percentages of something.
• If $\frac{3}{40}$ of the people in the school are stay members and $\frac{2}{3}$ of them wore Christmas jumpers, what fraction of the total people wore jumpers?


  $\frac{1}{20}$ of the people in the school wore Christmas jumpers.

  
• What percentage of the people in the school were members of stay wearing Christmas jumpers if $\frac{1}{20} =$$0.05$?


  5% of the people in the school were members of stay wearing Christmas jumpers.
• If $\frac{37}{40}$ of the people in the school are students and 88% of them wore Christmas jumpers, what is the percentage of students wearing jumpers?


  81.4% of the people in the school were students wearing Christmas jumpers.

  
• What is the total percentage of people in the school wearing Christmas jumpers if 5% are stay members and 81.4% are students?

  86.4% of the people in the school were wearing Christmas jumpers.
• What is a method to avoid dealing with abstract fractions and percentages in ratio questions?

  You can pick a number for the total number of things in the question.

  
• If you assume there are 1000 people in the school, how many members of stay and students would there be based on the ratio 3:37?

  There would be 75 members of stay and 925 students.

  
• What is the final step after calculating the number of items in a ratio question?

  You need to turn your answer back into the form (fraction, ratio, or percentage) that the question asks for.

  
• What is a potential problem with the 'pick a number' method in ratio questions?


  You might pick a number that doesn't divide nicely with the ratios, fractions, and percentages.

  
• What is an important exam tip when answering ratio questions?

  Read the question carefully to understand which bits refer to what.
• What are the steps to find the percentage of jumbo sized crisps in a shop with two flavors and sizes?

  1. Find the fractions of each type of crisp based on the given ratios.
  2. Calculate the percentage of regular sized crisps.
  3. Subtract the percentage of regular sized crisps from 100% to find the percentage of jumbo sized crisps.

  
• How do you combine two separate ratios to form a 3-part ratio?

  You can use a common element in both ratios to link them together.
• If the ratio of cows to sheep is 2:3 and the ratio of sheep to pigs is 6:7, how do you find the combined ratio?

  Use sheep as the link and adjust the ratios to have the same number of sheep.
• How do you determine the number of each animal on a farm with a total of 85 animals given the combined ratio of cows, sheep, and pigs?

  Share the total number of animals in the ratio 4:6:7 after determining the total parts.

  
• What is the first step in answering a 'changed ratio' question?

  Determine how many of each type there was to start with.
• If there were originally 16 lemon sweets in a bag and Natasha adds blackcurrant sweets to change the ratio to 2:5, how do you find the number of blackcurrant sweets added?

  Calculate how many blackcurrant sweets are now in the bag and subtract the original amount.

  
• How do you handle a situation where the number of items in a ratio question remains the same while the ratio changes?

  Identify which amounts have remained the same and adjust the other part of the ratio accordingly.

  
• What are the steps to determine the total number of socks in Jamie's drawer given the ratios of black, striped, and white socks?

  1. Use the ratios to link the black and striped socks.
  2. Scale the ratios to have the same number of striped socks.
  3. Calculate the total number of socks based on the combined ratio.

  
• If there are originally 12 llamas and the ratio of llamas to quokkas is 3:7, how do you find the original number of quokkas?

  Calculate the number of quokkas based on the ratio using the number of llamas.
• After new quokkas arrive, how do you determine the number of quokkas that arrived at the sanctuary?

  Subtract the original number of quokkas from the new total based on the changed ratio.
• What are the steps to solve a problem involving multiple ratios and a total number of items?

  1. Identify the ratios and the common elements.
  2. Scale the ratios to have the same number for the common element.
  3. Combine the ratios into a single ratio.
  4. Use the total number of items to find the individual amounts.