Ratios & Proportional Relationships

Understand the ratio and use the concept of proportional language to describe the ratio relationship between two quantities. For example, "The ratio of feathers to scorpions in the zoo's household is 2: 1, because there is one for each of the two feathers." ticket"

The concept of the unit ratio a / b related to the ratio a: b is understood, where b ≠ 0, and the ratio language is used in the context of ratio relationship. For example, "In this formula, there are 3 cups per cup of sugar + 4 cups of sugar and 3/4 cups of flour." "I paid $ 15 for a 15 hamburger, which is 5 dollars per hamburger It is "1

Use ratio and rate inference to solve real world and mathematical problems, for example by inferring geometric tables, tape plots, 2 digit plots or equations

Create the equivalence ratio table, associate the quantity with the measured value of the integer, find the missing value of the table, and plot the value pair in the coordinate plane. Compare proportions using table

We will deal with unit price problems such as bidding and constant speed problems. For example, if you took 7 hours to trim four lawns, how many turfs can you trim at this rate in 35 hours? What is the speed of lawnmowering?

Determining the proportion of the quantity as a percentage of 100 (for example, if 30% of the quantity represents 30/100 times the quantity); the solution involves finding the whole problem by specifying the part and percentage .

Calculate the unit rate associated with the fraction ratio, including length, area, and the ratio of other quantities measured in the same or different units. For example, if you walk 1/2 mile every 1/4 hour, the unit fee is calculated as a multiple of 1/2/1/4 mile per hour. This is equivalent to 2 miles per hour.

To determine if two quantities are proportional, for example, test the equivalence ratio of the table or graph on the coordinate plane and observe whether the graph is a straight line passing through the origin.

The proportional relationship is expressed by an equation. For example, if the total cost t is proportional to the number n of items purchased at the list price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Explain what the point (x, y) on the scale diagram means about the situation. Pay attention to points (0, 0) and (1, r). Where r is the unit ratio.

Use proportional relationships to solve the multistep ratio and percentage problem. Examples: simple interest, tax, price increase and price reduction, tip and commission, fee, change rate, error rate

In identifying ratios, ratios, and proportional relationships, students actively participate in Mathematical Practice Criteria 7 to find and use the structure. In this subject, students use ratio structures to solve ratio problems. The unit they receive is dollars per hour and you are asked to answer questions about unit and time in dollars. A teacher can construct a ratio structure by finding a proportion table, two-digit number, or unit price and instructing the student to solve the problem using it. This task not only allows students to identify the structure, but also applies the structure in the real world.

"Adjust" the ratio using 2 multiplication or division. A common type of problem with ratios involves using ratios to scale up or down two numbers. The ratio of all items that multiplies or divides a ratio by the same numerical value is the same as the original scale. Therefore, to scale the ratio, multiply or divide by the scale factor.

Ratios are around us, just comparing the two numbers each day (eg red fondant vs. Yellow Fondant). Scale is a statement that allows you to find unknown ratios from known ratios. With known ratios, I know these two numbers. With an unknown proportion, you only know one of the numbers. To solve the unknown, set the known ratio on one side and the ratio of unknown ratio on the other side, cross multiplication and solve the obtained equation. This method is always valid as long as it properly identifies known ratios and unknown ratios.

Proportional Analysis Various ratios can be used to identify relationships between the various accounts' sizes in financial statements. For example, you can calculate the company's quick ratio and estimate the ability to pay direct liabilities, or the equity ratio for liabilities, to determine if it is overpayment. These analyzes are usually between income and expenses listed in the income statement and the assets, liabilities and capital accounts listed on the balance sheet.