Decimals 2nd part

Decimals 2nd part

By Luis Bello

​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.

Multiple Choice

What is the ratio of sharks to fish?

• 2 to 10

• 2 to 8

• 8 to 2

Multiple Choice

What is ratio of blue to orange

• 3/2

• 3/5

• 2/3

Multiple Choice

Patrick has 2 black, 3 red, and 5   white toy cars. What is the ratio of red toy cars to all the toy cars? 

• 3:5
• 1:3
• 3:11
• 3:10

Multiple Choice

If there are 5 boys and 7 girls, write the ratio of girls to boys.

• 5 to 7
• 7 to 5
• 5 to 12
• 7 to 12

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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Multiple Choice

You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?

• $8 per pound
• $5 per pound
• $35 per pound
• 0.125 pounds per dollar

Multiple Choice

A store sees 120 customers in 8 hours. What is the unit rate (in customers per hour)?

• 16 customers per hour
• 15 customers per hour
• 12 customers per hour
• 20 customers per hour

Multiple Choice

If Justin can type 408 words in 4 minutes, how many words can he type per minute?

• 102 words per minute
• 100 words per minute
• 400 words per minute
• 412 words per minute

​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.

Multiple Choice

What is the mean of these numbers?
4,5,5,2,3,3,2,8

• 40
• 24
• 4
• 256

Multiple Choice

Find the mean:
28, 18, 19, 18, 17

• 20
• 18
• 11
• 19

Multiple Choice

What is the mean for these numbers?
5,5,5,5

• 5
• 20
• 15
• 100

Multiple Choice

What is the mean of these numbers?
4,5,5,2,3,3,2,8

• 40
• 24
• 4
• 256

​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

Multiple Choice

The following M & M colors are in the bowl:
4 yellow, 6 orange, 3 green, 5 blue, 2 brown.
What is the probability of selecting a brown candy?

• 2/18
• 1/9
• 2/20
• 1/10

Multiple Choice

What is the probability of rolling an even number on a dice. The dice is numbered 1-6.

• 3/6
• 1/2
• 1/6
• 5/6

Multiple Choice

What is the probability of getting any letter that is not A?

• 6/8
• 3/4
• 2/8
• 1/4

Multiple Choice

A jar contains 2 pink, 6 red, and 4 blue marbles. If you pick one marble without looking, what is the probability that the marble you pick will be red or blue?

• 5/6
• 1/2
• 1/3
• 1/6

​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

Multiple Choice

2² = _____

• 2
• 6
• 4
• 16

Multiple Choice

√49

• 5
• 3
• 6
• 7

Multiple Choice

15²

• 196
• 289
• 256
• 225

Multiple Choice

Estimate the square root.

• 3
• 4
• 5
• 6

Multiple Choice

Estimate the square root.

• 7
• 8
• 9
• 10

Multiple Choice

In between what two integers is the square root of 44?

• 3 and 4
• 4 and 5
• 5 and 6
• 6 and 7

Multiple Choice

The area of a square is 36 cm².  What is the length of one side?

• 6 cm
• 24 cm
• 9 cm
• 9 cm

Multiple Choice

–√25

• 5
• -5
• ±5
• None

Multiple Choice

The area of a square is 100 cm².  What is the perimeter?

• 25 cm
• 10 cm
• 40 cm
• 50 cm