Algebra Honors ( Periods 4 & 7)

Ratios & Proportions 2-6
A ratio is a comparison of two things.

Comparisons:

Say you are a dog walker and you want the ratio of large dogs to small dogs to remain at 8 small dogs to 2 large dogs for your business.

3 ways to write a ratio:

8 small dogs to 2 large dogs or
8 small dogs : 2 large dogs or
8 small dogs /2 large dogs

 You can also reverse the order and put the large dogs first.

Just as with fractions, since a ratio functions like a fraction, you ALWAYS SIMPLIFY the ratio:

4 small dogs to 1 large dog or
4 small dogs : 1 large dog or
4 small dogs /21 large dog

Proportions:

A proportion is 2 EQUAL ratios.

You can use CROSS PRODUCTS or SIMPLIFYING to determine if two ratios are equivalent.

 Means:

The means in a proportion are the two middle terms if written with a : or the denominator of the 1st term and the numerator of the 2nd term.

Extremes:

The extremes in a proportion are the two outside terms if written with a : or the numerator of the 1st term and the denominator of the 2nd term.

CROSS PRODUCTS PROPERTY:

The product of the MEANS is always equal to the product of the EXTREMES

Rate:

A ratio with 2 DIFFERENT units of measure like miles per gallon

Unit Rate:

A rate with a denominator of 1 unit that is found by dividing the numerator by the denominator of a rate

Scale Rate:

A rate that is used to make a model bigger or smaller of an actual sized item that is usually too big to draw or use…Example: a building sketch or a map.

Remember: It’s all about the labels! After setting up the proportion, you have your choice of 3 methods:

1)  equivalent fraction method (doesn’t always work- the numbers must be compatible)

3/5 = y/15   y = 9 because 5(3) = 15 must multiply 3(3) to get numerator in second fraction

2)  balancing equation method  (always works) multiply by the multiplicative inverse

3/5 = y/15  multiply both sides by 15 ( the multiplicative inverse of 1/15

3)  cross products method (this is the only time that name is accurate) Multiply the “corners” making an X. Same example but this time you would set up the cross product equation or

 5y = 3(15). Don’t be too quick to multiply 3(15).  Divide by 5 first. It may simplify.   so   y = 9