Video: Comparing by Using Unit Rates

Scarlett uses 2 tablespoons of sugar for every 3 glasses of lemonade, while Natalie uses 3 tablespoons of sugar for every 6 glasses of lemonade. Who makes the sweeter lemonade?

02:31

Video Transcript

Scarlett uses two tablespoons of sugar for every three glasses of lemonade, while Natalie uses three tablespoons of sugar for every six glasses of lemonade. Who makes the sweeter lemonade?

We can begin this question by writing down a ratio of sugar to lemonade for both of the girls. Scarlett used two tablespoons for every three glasses of lemonade. Therefore, her ratio is two to three. Natalie used three tablespoons of sugar for every six glasses of lemonade. So, her ratio is three to six. One way of comparing two or more ratios is to write them in the form one to đť‘›. This is known as the unit ratio. When finding an equivalent ratio, we must divide or multiply both sides by the same value. Two divided by two is equal to one. And three divided by two is equal to 1.5. This means that, for every one tablespoon of sugar that Scarlett uses, she will fill 1.5 glasses of lemonade.

Repeating this process for Natalie, we divide both sides of her ratio by three. The ratio three to six simplifies to one to two. This means that, for every one tablespoon of sugar that Natalie uses, she is able to fill two glasses of lemonade. We’re asked to work out who makes the sweeter lemonade. This will be the person who has less glasses per tablespoon of sugar. As Scarlett is only able to make one and a half glasses of lemonade for one tablespoon of sugar, she makes the sweeter lemonade.

Had we noticed that Natalie had double the number of glasses originally than Scarlett, we could’ve used an alternative method for this question. Multiplying both sides of Scarlett’s ratio by two gives us a new ratio, four to six. As Scarlett used four tablespoons of sugar for six glasses of lemonade whereas Natalie only used three tablespoons, once again, we have proven that Scarlett made the sweeter lemonade.

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