# Ratios and Proportions

Ratios and proportions are fundamental concepts in mathematics that play a crucial role in various real-world applications, from finance to science. Ratios express the quantitative relationship between two or more quantities, often used for comparison or scaling. Proportions extend this idea by stating that two ratios are equal. Understanding ratios and proportions is essential for solving problems involving scaling, mixing ingredients, financial analysis, and many other scenarios where relative quantities are involved. Mastery of these concepts provides a powerful toolset for interpreting and manipulating quantitative relationships with precision and efficiency.

Questions

- What ratio 15/45 expressed in simplest form?
- What must #n# be if the ratio 6:7 is equivalent to 36:#n#?
- Jack’s height is #2/3# of Leslie’s height. Leslie’s height is #3/4# of Lindsay’s height. If Lindsay is 160 cm tall, find Jack’s height and Leslie’s height?
- A baker is going to make 24 blueberry pies. She wants to make sure each pie contains 3.5 cups of blueberries. How many cups of blueberries will she need?
- Roger is planning a picnic, He will invite two times as many boys as girls. If he invites 18 people, how many boys and how many girls will get invitations?
- Kelly has 4x as much money as Joey. After Kelly uses some money to buy a racquet, and Joey uses $30 to buy shorts, Kelly has twice as much money as Joey. If Joey started with $98, how much money does Kelly have? what does the racquet cost?
- In Mr. Xang's French class, there are thirty-eight male students and forty-two female students. How do you express a ratio of female students to male students in simplest form?
- How do you simplify each ratio: 50:30?
- Erica had #3 1/2# yards of fabric and she used #2/3# of the piece. How much fabric she is now left with?
- Annie want to buy a toy, but she has no money? If she saves for 3 weeks she will be $1 short of what it cost to buy the toy, if she saves for 4 weeks she will be $3 above the toy cost. How much is Annie saving every week? what is the cost of the toy?
- Kelly's company is painting a building a unique shade of purple. She needs 12 pints of red paint for every 8 pints of blue paint. Using that ratio, if she uses 65 pints of paint how much blue paint is needed?
- The sum of the altitude and the base radius of a cylinder is #63 cm#. The radius is #4/5# as long as the altitude. Calculate the surface area volume of the cylinder?
- If x and y are in the ratio 3 to 4, and y and z are in the ratio 3 to 4 then what is the ratio of x to z?
- What are the equivalent ratios 4 to 9?
- Maya has 2x as many white beads as black beads. After using 40 white and 5 black to make a necklace she has 3x as many black beads as white. How many black beads she started with?
- One afternoon, Dave cast a 5-foot shadow. At the same time, his house cast a 20-foot shadow. If Dave is 5 feet 9 inches tall, how tall is his house?
- How do you simplify #24 : 36#?
- Arnold can do 65 pushups in 5 minutes. How many pushups can he do in 1 minute?
- How many years are there in 1.4 billion seconds?
- #2.2# pounds of ground turkey costs #$7.59#. What is the price per pound?