Free preview Module 1: Ratios and unit rates

Topic A: Representing and reasoning about ratios

▶ Intro to ratios

The video explains ratios, which show the relationship between two quantities. Using apples and oranges as an example, it demonstrates how to calculate and reduce ratios (6:9 to 2:3) and how to reverse the ratio (9:6 to 3:2).

⏱ 3:58 💾 4.8 MB License: cc-by-nc-sa Streaming via CDN

📄 Ratio review

A ratio compares two different quantities.

For example, those two quantities could be monkeys and bananas:

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Notice that there are $\blueD4$ monkeys and $\goldD5$ bananas.

Here are a few different ways we can describe the ratio of monkeys to bananas:

There are $\blueD4$ monkeys for every $\goldD5$ bananas.
The ratio of monkeys to bananas is $\blueD4$ to $\goldD5$.
The ratio of monkeys to bananas is $\blueD4 : \goldD5$.

Order matters in ratios. Here are a few different ways to describe the ratio of bananas to monkeys:

There are $\goldD5$ bananas for every $\blueD4$ monkeys .
The ratio of bananas to monkeys is $\goldD5$ to $\blueD4$.
The ratio of bananas to monkeys is $\goldD5 : \blueD4$.

##Let's practice!

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▶ Basic ratios

In this video, the instructor explains ratios using three examples: amusement park ride lines, Katie's book collection, and a picture of apples and bananas. Ratios compare two quantities and can be written as "a to b" or "a:b." The video demonstrates how to find and interpret ratios in various situations.

⏱ 2:53 💾 3.0 MB License: cc-by-nc-sa Streaming via CDN

▶ Part:whole ratios

In this video, we explore ratios using apples and oranges. We find the simplified ratio of apples to total fruit (2:5) and learn to represent ratios as fractions (2/5). The fraction indicates that 2/5 of the fruit are apples. Key definitions include ratio, simplified ratio, and fraction notation.

⏱ 3:22 💾 3.3 MB License: cc-by-nc-sa Streaming via CDN

▶ Equivalent ratios

One way to identify equivalent ratios is to determine if you can multiply or divide the corresponding parts of the ratio by the same amount. To do this, look at the two ratios and see if there is a common factor that you can use to scale one ratio to the other. If you can scale one ratio to the other by multiplying or dividing every part of the ratio by the same number, then the two ratios are equivalent.

⏱ 4:43 💾 5.1 MB License: cc-by-nc-sa Streaming via CDN

▶ Equivalent ratios: recipe

Adjusting a cake recipe for different guest numbers involves understanding ratios. Halving ingredients for a smaller cake maintains the same ratio, like eggs to flour (4:3). Ratios ensure consistent taste and quality, regardless of cake size.

⏱ 4:51 💾 6.1 MB License: cc-by-nc-sa Streaming via CDN

▶ Equivalent ratio word problems

This video teaches solving ratio word problems, using examples like Yoda Soda for guests, fish ratios in a tank, ice cream sundae ingredients, and dog color ratios at a park. Mastering these techniques helps students tackle real-world math challenges.

⏱ 6:02 💾 6.4 MB License: cc-by-nc-sa Streaming via CDN

▶ Understanding equivalent ratios

Sal discusses what it means for two ratios to be equivalent.Comparing ratios is essential for determining equivalent relationships between quantities. By analyzing and simplifying ratios, we can identify if they have the same proportion, helping us make decisions in real-life situations like mixing paint colors or comparing food recipes.

⏱ 5:45 💾 8.8 MB License: cc-by-nc-sa Streaming via CDN

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