Rates, Unit Rates, and Unit Price   (Using ratios in the context of a problem)

 

Ratio- a fraction, compares 2 numbers 

          3 ways to write - 9/13, 9:13, 9 to 13

 

Rate- A ratio that compares two quantities with different kinds of units

        ex 1) 7 inches of growth in 2 years

                    $1.14 for 3 lbs would be the better buy.

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Solve Proportions

 

Proportion- 2 equal ratios

 

6/9 = 2/3    or  a/b = c/d    b- does not equal zero      d- does not equal zero

 

In a proportion, cross products are equal.

6/9 = 2/3       so cross multiply  6X3 = 2X3

                                                   18 = 18 It is a proportion.

To solve for a proportion:

1) Multiply cross products

2) Divide by the number next to the variable.

 

2/5 = n/25   2 X 25 = 5 X n

                      50 = 5n

                     50/5 = 5n/5

                      10 = n

 

  

5/9 = d/54

9 X d = 5 X 54

9d = 270

9d/9 = 270/9

d = 30

 

 Now take a word problem and set up ratio and then set up proportion and solve.

 

A car travels 174 miles in 3 hours.  How long to travel 290 miles?

 

First set up a ratio.  174/3 (miles over hours)

Next set up a proportion.  174/3 = 290/t.      290/t (miles over hours)

Write the cross multiplication equation. 174 X t = 3 X 290.

Now solve:  174t = 870

                     174t/174 = 870/174

                       t = 5 hours

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Percent of a Number

 

What is 36% of 375?

1) Change % to decimal. Remember % is out of 100, so it is 36/100 or 36 hundreths and written as a decimal is .36.

What is .36 of 375?

2) "of " in math terms means multiply, so 

What is .36 X 375?

3) Solve and don't forget to place decimal!

            375

         X .36

          2250

   135.00 

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