Equivalent Ratios and Tape Diagrams

Front

What is an equivalent ratio?

Back

An equivalent ratio is a ratio that expresses the same relationship between two quantities, even if the numbers used are different. For example, the ratios 1:2 and 2:4 are equivalent.

Front

How do you use a tape diagram to represent ratios?

Back

A tape diagram visually represents ratios by using rectangles divided into parts that correspond to the quantities in the ratio. Each part represents a unit, making it easier to see the relationship between the quantities.

Front

If the ratio of blue to red Jolly Ranchers is 3 to 4, how can you find the total number of Jolly Ranchers?

Back

To find the total number of Jolly Ranchers, add the parts of the ratio together. In this case, 3 (blue) + 4 (red) = 7 parts. If you know the total number of Jolly Ranchers, divide that number by 7 to find the value of one part.

Front

What is the first step in solving a problem involving ratios?

Back

The first step is to identify the ratio and the quantities involved. Then, determine if you need to find a missing quantity or express the ratio in a different form.

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How do you convert a ratio to a fraction?

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To convert a ratio to a fraction, write the first quantity as the numerator and the second quantity as the denominator. For example, the ratio 3:4 can be written as the fraction 3/4.

Front

What is the simplest form of a ratio?

Back

The simplest form of a ratio is when the numbers are reduced to their smallest whole number values while maintaining the same relationship. For example, the ratio 6:8 simplifies to 3:4.

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How can you find a missing quantity in a ratio problem?

Back

To find a missing quantity, set up a proportion using the known quantities and the ratio. Cross-multiply and solve for the unknown.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions state that two ratios are equal. For example, if a:b = c:d, then a/b = c/d.

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How do you scale a ratio up or down?

Back

To scale a ratio up, multiply both parts of the ratio by the same number. To scale it down, divide both parts by the same number.

Front

In the context of recipes, how do you adjust ingredient quantities based on ratios?

Back

To adjust ingredient quantities, use the ratio of the original recipe to the desired quantity. Multiply or divide the ingredient amounts accordingly.