Decimals 2nd part

​Previously:

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5.1 Decimals

5.2 Decimal Operations

5.3 Decimals and Fractions

5.4 Solve Equations with Decimals

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Today:

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5.5 Averages and Probability

5.6 Ratios and Rate

5.7 Simplify and Use Square Roots

​Ratios

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a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3).

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​When you apply for a mortgage, the loan officer will compare your total debt to your total income to decide if you qualify for the loan.

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This comparison is called the debt-to-income ratio.

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A ratio compares two quantities that are measured with the same unit. If we compare aa and bb, the ratio is written as a to b, a/b, or a:b.

Rate​

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rate is the ratio between two related quantities in different units.^[1] If the denominator of the ratio is expressed as a single unit of one of these quantities,

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One common type of rate is "per unit of time", such as speed, heart rate and flux. Ratios that have a non-time denominator include exchange rates, literacy rates, and electric field (in volts per meter).

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​Frequently we want to compare two different types of measurements, such as miles to gallons.

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To make this comparison, we use a rate.

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Examples of rates are 120miles in 2 hours, 160 words in 4 minutes, and $5 dollars per 64 ounces.

​Bob drove his car 525miles in 9 hours. Write this rate as a fraction.

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So 525 miles in 9 hours is equivalent to 175 miles/3 hours.

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​5.5 Averages and Probability

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​The mean is often called the arithmetic average.

​Suppose Ethan’s first three test scores were 85, 88, and 94.

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To find the mean score, he would add them and divide by 3.

(85+88+94)/3

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His mean test score is 8989 points.

​Calculate the average of all the 5 heights measurements.

​Probability: Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true

​5.7 Simplify and Use Square Roots

​ A square root of a number x is a number y such that y² = x; in other words, a number y whose square (the result of multiplying the number by itself).

​For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16