**Ratio and Rate Problems**

We will use real world examples to solve ratio and rate problems. To solve ratio and rate problems you can use equivalent ratios with multiplication and division:

**Example 1:** A survey found that 12 out of every 15 people in the United States prefer eating at a restaurant over cooking at home. If 400 people selected eating at a restaurant on the survey, how many people took the survey?

Step 1 simplify 12/15 using GCF.

Find GCF: Factors of 12 :**1**,2,**3**,4,6 and 12

Factors of 15:**1**,**3**,5, and 15

Common factors of 12 and 15: **1** and **3** . Although all bold numbers are common factors of 12 and 15, **3 is the greatest common factor. We divide the numerator and denominator by 3.**

**Step 2 use an equivalent ratio to solve this problem:**

We need to put the number of people who selected eating at a $1 restaurant in the numerator and x as the unknown factor. We multiply the numerator by 100 to get 400. Since we multiplied the numerator by 100 we also need to multiply the denominator by 100. Therefore, 500 people took the survey.

Example 2:

A tutor charges $30 for 2 hours.How much does she charge for 5 hours?

Step 1 We can set up an equivalent ratio to find the unit rate:

Step 2 If she charges $15 per hour, we need to multiply $15 x 5= $75

So for 5 hours, the tutor will charge you $75

**Found On the Web:**

**Ratio, Rate and Proportion Video**

**Activity:**

**Ratio, Proportion, and Percent Activity**

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Created by Wanda Collins May 10, 2015 at 1:56pm. Last updated by Wanda Collins May 10, 2015.

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Question: Why is this a mathematical limerick?

( (12 + 144 + 20 + 3 Sqrt[4]) / 7 ) + 5*11 = 9^{2} + 0 .

Answer:

A dozen, a gross, and a score,

plus three times the square root of four, divided by seven, plus five times eleven, is nine squared and not a bit more.

---Jon Saxton (math textbook author)

**Presentation Suggestions:**

Challenge students to invent their own math limerick!

**The Math Behind the Fact:**

It is fun to mix mathematics with poetry.

**Resources:**

Su, Francis E., et al. "Math Limerick." Math Fun Facts.

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