*** TEAM TITANS ***
MATH PORTAL
*** TEAM TITANS ***
MATH PORTAL
Definitions & Concepts:
How To:
Sample Problems:
-
A ratio is a comparison of two things, expressed in numbers.
-
Example: For every 1 hour I work, I can mow 4 lawns.
-
-
When expressing a ratio, use the word “to”.
-
Example: 1 to 4. 1 hour of work to 4 lawns mowed.
-
-
There are 3 ways to write a ratio: separate the numbers with the word “to”, separate with a colon, or show as a fraction using the 1st number as the numerator and the 2nd as the denominator.
-
Examples: 1 to 4, 1:4, 1/4
-
-
A value of a ratio is the ratio expressed in its simplest form.
-
Example: the value of the ratio of 8:32, is 1:4.
-
-
Equivalent ratios are two ratios that have the same value.
-
Example: the ratio 8:32 is equivalent to 4:16 because they both have the value of 1:4.
Coming soon...
-
Find the value of a ratio: divide each number in the ratio by the same number. Use the largest divisor possible so you get the lowest possible whole number as a result.
-
Example: 15:25.
-
15 / 5 = 3. 25 / 5 = 5. The value of the ratio is 3:5.
-
-
Determine if 2 ratios are equivalent ratios: find the value of each ratio and see if they are the same.
-
Example: 15:25 and 6:10
-
15 / 5 = 3. 25 / 5 = 5. The value of the ratio 15:25 is 3:5.
-
6 / 2 = 3. 10 / 2 = 5. The value of the ratio 6:10 is 3:5.
-
Since both ratios have the same value, they are equivalent ratios.
-
-
Find equivalent ratios
-
Example: 8:20.
-
To find upscale ratios (meaning equivalent ratios that are larger), multiply both numbers in the ratio by the same number.
-
Example: 8 x 2 = 16. 20 x 2 = 40. An upscale equivalent ratio for 8:20 is 16:40.
-
-
To find downscale ratios (meaning equivalent ratios that are smaller), divide both numbers in the ratio by the same number.
-
Example: 8 / 2 = 4. 20 / 2 = 10. A downscale equivalent ratio for 8:20 is 4:10.
-
-
-
Explain in a full sentence
-
The ratio by itself is meaningless. When answering a problem about a ratio, you need to include the words that a ratio represents.
-
For example: 3 cups of water to 1 cup of juice concentrate
-
-
When explaining how you got your answer, it needs to be in a full sentence and include the important pieces of information from the question.
-
For example: When making juice, Karla used 3 cups of water for every 1 cup of juice concentrate, while Joe used 2 cups of water for every 1 cup of juice concentrate. Using less water will make the juice have a stronger taste, therefore Joe’s juice has a stronger apple taste.
-
-
