When you compare two numbers by division, you are using a ratio. Ratios can be written 3 to 5, 3:5, or -5-. Ratios, like fractions, also can be written in simplest form.

Ratios can represent probabilities, also called odds. This is a ratio that compares the number of ways a certain outcome occurs to the number of outcomes. For example, if you flip a coin 100 times, what are the odds that it will come up heads? There are two possible outcomes, heads or tails, so the odds of coming up heads are 50:100. Another way to say this is that 50 out of 100 times the coin will come up heads. In its simplest form, the ratio is 1:2.

Example 1 A chemical solution contains 40 g of salt and 64 g of baking soda.What is the ratio of salt to baking soda as a fraction in simplest form?

Step 1 Write the ratio as a fraction. salt = -baking soda 64

Step 2 Express the fraction in simplest form.

The ratio of salt to baking soda in the sample is 5:8.

Example 2 Sean rolls a 6-sided die 6 times.What are the odds that the side with a 3 will show?

Step 1 Write the ratio as a fraction.

number ofsideswitha3 _ — numberofsides 6

Step 2 Multiply by the number of attempts. 1 6

— x 6 attempts _ — attempts _ 1 attempt 1 attempt out of 6 will show a 3.

Practice Problem Two metal rods measure 100 cm and 144 cm in length.What is the ratio of their lengths in simplest form?

Use Decimals

A fraction with a denominator that is a power of ten can be written as a decimal. For example, 0.27 means --. The decimal point separates the ones place from the tenths place.

Any fraction can be written as a decimal using division. For example, the fraction -can be written as a decimal by dividing 5 by 8. Written as a decimal, it is 0.625.

Add or Subtract Decimals When adding and subtracting decimals, line up the decimal points before carrying out the operation.

Example 1 Find the sum of 47.68 and 7.80.

Step 1 Line up the decimal places when you write the numbers.

Step 2 Add the decimals. 47.68 + 7.80

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