 A ratio compares two things.  It can compare part to part, a part to the whole, or the whole to a part.  The word “to” compares the two terms in a ratio.

 You can write a ratio three different ways.  In words: 4 to 3  Using a colon: 4:3  Like a fraction 4/3 In this ratio we are comparing the number of pink squares to the number of blue squares.

RATIO If a recipe says, “For every cup of rice, add 2 cups of water” that’s a ratio. In school, if there is 1 teacher to every 5 students, that’s a ratio, too. A ratio is a handy way to express the relationship between numbers.

If you've spent any time in the kitchen, then you already know quite a bit about ratios. A rice recipe calls for 2 cups of water to 1 cup rice. The ratio of water to rice is 2 to 1.

What is the ratio of oil to vinegar in a salad dressing recipe that calls for 2 tablespoons oil to 1 tablespoon vinegar? Separate your numbers by the word "to."

The ratio of oil to vinegar in the salad dressing is 2 to 1. We can also write this with a colon as 2:1.

A biscuit recipe calls for 7 cups flour and 1 cup shortening. What is the ratio of flour to shortening? Write the ratio with a colon. Don't add any spaces between the numbers and the colon.

ANSWER 7:1

Ratios can also be written as fractions. A tortilla recipe calls for 4 cups flour and 1 cup water. The ratio of flour to water would be 4 to 1, or 4:1. As a fraction we write this as 4/1.

A stew recipe calls for 5 cups of carrots and 2 cups of onions. A stew recipe calls for 5 cups carrots and 2 cups onions. Write the ratio of carrots to onions as a fraction

ANSWER 5/2 is the same as 5:2 and 5 to 2.

A recipe for orange juice calls for 3 cups water and 1 cup orange juice concentrate. A recipe for orange juice calls for 3 cups water and 1 cup orange juice concentrate. Write the ratio of water to concentrate as a fraction.

Good job. 3 to 1 is the same as 3/1.

What if we want to double the amount of orange juice we make?  The original recipe calls for 3 cups water and 1 cup orange juice concentrate.  The ratio of water to concentrate is 3:1.  To double the recipe, we multiply both terms (in ratios we call the numbers "terms") in the 3:1 ratio by 2 (because we’re making twice as much).  This is called an equivalent ratio. Two ratios that equal the same thing.

The new ratio is 6:2.

If we triple the recipe, what is the ratio of water to concentrate? Write the ratio as a fraction.

ANSWER 9/3

What if we want to make 5 times the original amount of orange juice? The original recipe calls for 3 cups water and 1 cup orange juice concentrate. The ratio of water to concentrate is 3:1.

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No matter how much orange juice we make, we still need 3 cups of water for every 1 quart of concentrate So the ratio of 12 cups of water to 4 cups concentrate in the quadrupled recipe is the same as the ratio of concentrate to water in the original recipe.

In other words, the relationship between the two terms in the ratio 3:1 is the same as that in 12:4. Just do the math! 3 is three times as much as 1, and 12 is three times as much as 4. Since 3:1 and 12:4 have the same relationship, these two ratios are equal.

When two ratios are equal, we say they are in proportion. In other words, a proportion is a mathematical statement that two ratios are equal. Equivalent ratio = proportion

We write proportions like this: 3 to 1 equals 12 to 4 3:1 = 12:4 3/1 = 12/4

A recipe for chili calls for 5 oz beans and 2 oz beef. The ratio of beans to beef is 5:2. You want to quadruple the recipe to fill a big pot for a party.

Write the original beans to beef ratio and the quadrupled recipe ratio as a proportion. Don’t forget to write your answer with colons and the equal sign.

ANSWER 5:2 = 20:8

To figure out the new ratio you multiply both terms in the original recipe ratio 5:2 by 4. Another way to write the same proportion is 20:8 = 5:2.

Which of the following is not a proportion? A) 1:6 = 24:4 B) 3:4 = 15:20 C) 7:6 = 14:12

ANSWER A In true proportions, both terms in one ratio must be multiplied (or divided) by the same number to get the terms of the second ratio. If you do the math, you’ll see that 1:6 = 24:4 is not a proportion. 1 x 24 = 24 but 6 x 24 = not 4!

In Mrs. Jones’ class there are 20 students. There are 12 boys and 8 girls. 7 students have brown hair, 10 have blonde hair and 3 have red hair. What is the ratio of students with blond hair to those that have red hair?

ANSWER 10:3

Martha has 10 dresses. 3 are red and the rest are blue. How many red dresses to blue dresses does she have?

3:7

Tom has 13 video games. 5 are action games, 2 are adventure and the rest are sports. How many sports games to action games does Tom have?

6:5

In problems involving proportions, there will always be a ratio statement.

An automobile travels 176 miles on 8 gallons of gasoline. How far can it go on a tankful of gasoline if the tank holds 14 gallons?

176 miles 8 gallons

14 gallons

miles

X or any letter because it’s the variable

176 miles = x miles 8 gallons 14 gallons Math Note: Notice in the previous example that the numerators of the proportions have the same units, miles, and the denominators have the same units, gallons.

176 = x 8 14

176 = m m = 176 x 14 8m = 2464

8m = 2464m= 308 miles 8

On 14 gallons, the automobile can travel a distance of 308 miles.

Read the problem.

Identify the ratio statement. There will ALWAYS be one.

Set up the proportion Be sure to keep the identical units in the numerators and denominators of the fractions in the proportion.

Solve for x or the variable.

Let’s try another If it takes 16 yards of material to make 3 costumes of a certain size, how much material will be needed to make 8 costumes of that same size?

What’ s the next step Find the ratio statement. The ratio statement is:

Be sure to keep the identical units in the numerators and denominators of the fractions in the proportion. yards yardscostumes

Setting the proportion Identical units 16 yards = x yards 3 costumes 8 costumes

Next step cross multiply 16 yards = y yards 3 costumes 8 costumes 3y = 16 x 8 3y = 1283 Y =

Remember: Pounds across from pounds square feet across from feet.

3075 square feet

$5600

$5070

21 gallons

13 or 13.5 tablespoons