Ch 4. Essential Math Review

Let's find the mean, median, mode and range of how many medals the U.S. has won over the last six summer Olympics. 94, 101, 101, 104 108, 110

104 + 110 + 101 + 94 + 101 + 108 = 618 618 ÷ 6 = 103 mean: 103 94, 101, 101, 104, 108, 110 101 + 104 = 205 205 / 2 = 102.5 median: 102.5 94, 101, 101, 104, 108, 110 mode: 101 94, 101, 101, 104, 108, 110 110 - 94 = 16 range: 16

On the Ducks' first offensive series, they had plays of 10, 6, 19, 21 and 4 yards before scoring a touchdown. Let's find the median number of yards gained by the Ducks.

4, 6, 10, 19, 21 Since there are five numbers, the middle number would be the third value. The median value of this set of data is 10. On the first offensive series for the Ducks, their median yards gained were 10 yards. median: 10

Sarah went out to watch her favorite band. It's a sold-out show at a 3,600-person club. If 5/9 of the total crowd is there early to hear the show play, and 1/10 of them buy t-shirts. How many shirts were sold?

5 x 1 = 5 9 10 90

The Bears threw the ball to the following jersey numbers in the third quarter: 5, 6, 6, 3 and 4. What is the mode?

5, 6, 6, 3, 4 mode: 6

factors

the parts that make up the whole number example: 24: 1, 2 3, 4, 6, 8, 12, 24 1 x 24 = 24 2 x 12 = 24 3 x 8 = 24 4 x 6 = 24

numerator

the top number in a fraction

square root of 4

2 * 2 = 4 answer: square root of 4 = 2

Find the prime factorization of 117:

(1 + 1 + 7) = 9 9 Divisible by 3 not even Does not end with a 5 or 0 Not divisible by 2 or 5 117 (1 + 1 + 7) = 9 117 / 3 ) = 39 39 divisible by 3 3 + 9 = 12 39 / 3 = 13 prime # answer: the factors of 117 are 3 x 3 x 13

On Saturday, Jessica watched 6 1/4 television shows; on Sunday she watched 4 3/8 more. How many television episodes did Jessica watch?

10 5/8 Explanation: Adding the two you get this. 6 1/4 + 4 3/8 = 6 2/8 + 4 3/8 = 10 5/8.

The Ducks threw the ball to the following receivers: 12, 13, 15, 17, 19 and 20. What is the mode?

12, 13, 15, 17, 19, 20. NO mode

The Bears had plays of 16, 14, 12 and 18 yards on their way to scoring a touchdown. What is the mean?

16 + 14 + 12 + 18 = 60 60 ÷ 4 = 15 mean: 15

1.2 ) 24.6

24.6 /1.2 = 20.5 answer: 20.5

On Monday, Erin wrote 4 2/3 pages of her research paper. On Tuesday, she decided to delete 1 1/5 pages. How many pages are left?

3 7/15 Explanation: Here, you subtract 4 2/3 minus 1 1/5. First, changing to common denominators, you get 4 10/15 - 1 3/15. Now subtracting the whole numbers and then the fractions, you get 3 7/15.

What is 56% written as a decimal?

56 / 100 =0.56 answer: 0.56

The Bears had scored the following points: 6, 7, 3, 0, 7, 3, 7 and 3. What is the mode?

6, 7, 3, 0, 7, 3, 7, 3 mode: 3 and 7

A violin you want to buy costs $4,254. However, it goes on sale for 65 percent off. How much do you end up saving if you buy the violin while it is on sale?

65 / 100 =0.65 4254 x 0.65 = 2765.10 answer: 2765.10

Farran purchased a carton of milk. She drank 1/8 of the carton. How much of the carton of milk does Farran have left?

7/8 Explanation: The question is: 'how much of the carton do you have left?' Since Farran drank 1/8 of a given unit, when 1/8 is taken away (1 - 1/8), 7/8 of that unit remains.

How many answers do I need to get correct if I want a grade of 80 percent on a test with 70 questions?

80 / 100 = 0.8 0.8 * 70 = 56 answer: 56

You're making your own salad dressing for your new, healthier lunch. The recipe calls for 3/8 of a teaspoon of salt and 1/3 of a teaspoon of sugar. How much salt and sugar is that?

Adding Unlike Fractions answer: 17/24

Solve 33.56 - 21.824

subtraction with decimal notation 33.56 - 21.824 11.736 answer: 11.736

Solve: Square root of 121

Explanation: 11 *11 = 121 The square root of 121 is 11.

Solve: Square root of 625

Explanation: 25 *25 = 625 The square root of 625 is 25.

Solve: Square root of 25

Explanation: 5 *5 = 25 The square root of 25 is 5.

Suzie's Snakes and Salamanders Pet Shop has 38 snakes and 22 salamanders. If Suzie sells 9 snakes, what is the ratio of the remaining unsold to sold snakes?

If Suzie sells 9 snakes, then she still has 38 - 9 = 29 snakes left. So the ratio of unsold to sold snakes is 29:9. answer: 29:9

A class with 28 students has 13 boys. What is the ratio of girls to boys?

If there are 13 boys, then there are 28 students - 13 boys = 15 girls. The ratio of girls to boys then is 15:13. answer: 15:13

Jenny has a job that she goes to every day after school. She works at the local cupcake shop. She works for 3 hours every day, 15 hours a week. She bakes 200 cupcakes every day! She earns $10 per hour. How much money will she earn after two weeks?

Jenny has a job that she goes to every day after school. She works at the local cupcake shop. She works for 3 hours every day, 15 hours a week. She bakes 200 cupcakes every day! She earns $10 per hour. How much money will she earn after two weeks? 2 * 15 = 30 30 * 10 = $300 answer: $300

Joe has 8 Dalmatians. Sarah has 3 fewer Dalmatians than Joe. How many Dalmatians do they have together?

Joe has 8 Dalmatians. Sarah has 3 fewer Dalmatians than Joe. How many Dalmatians do they have together? 8 - 3 = 5 Sarah has 5 Dalmatians. 8 + 5 = 13 They have 13 Dalmatians altogether. answer: 13

Joe has four blue pens and three green pens. Sarah gives Joe four blue pens and two green pens. Sarah originally had 10 blue pens and 12 green pens. How many blue pens does Sarah now have?

Joe has four blue pens and three green pens. Sarah gives Joe four blue pens and two green pens. Sarah originally had 10 blue pens and 12 green pens. How many blue pens does Sarah now have? x = 10 - 4 x = 6 answer: 6

mode

the number that occurred the most often.

Sam has 4 RED balloons and 8 PURPLE balloons. Judy has 12 RED balloons and 4 ORANGE balloons. How many RED balloons do Sam and Judy have together?

Sam has 4 RED balloons and 8 PURPLE balloons. Judy has 12 RED balloons and 4 ORANGE balloons. How many RED balloons do Sam and Judy have together? 4 + 12 = 16 answer: 16

Take this word problem: Lucy's rabbit recently had a litter of bunnies and so did Sam's rabbit. Sam's rabbit gave birth to 4 boy and 3 girl bunnies. Lucy's rabbit gave birth to 2 boy and 8 girl bunnies. How many baby rabbits does Lucy have? Which of the following is NOT an important part of this word problem: All of these are equally important to this word problem. Lucy's rabbit gave birth to 2 boy and 8 girl bunnies. Sam's rabbit gave birth to 4 boy and 3 girl bunnies. Lucy's rabbit recently had a litter of bunnies

Sam's rabbit gave birth to 4 boy and 3 girl bunnies. The question is only asking about Lucy's rabbits, so Sam's rabbits are irrelevant. Sam's rabbit and its litter are not important to the problem.

You run a loop around a local park, and it takes 3/4 of an hour. The next time, it only takes 2/3 of an hour. How much time did you cut?

Subtracting Unlike Fractions answer: 1/12

What operations are needed to solve this word problem? Joe has 8 Dalmatians. Sarah has 3 fewer Dalmatians than Joe. How many Dalmatians do they have together?

Subtraction and addition 3 fewer meaning subtraction together meaning addition

Sue is a baker. She bakes all kinds of goodies, like apple pies and cheese pies. Yum! On Mondays, Wednesday and Fridays, Sue bakes apple pies. She bakes cheese pies on Tuesdays and Thursdays. If Sue bakes 50 pies a day, how many more apple pies does Sue bake than cheese pies in a week?

Sue is a baker. She bakes all kinds of goodies, like apple pies and cheese pies. Yum! On Mondays, Wednesday and Fridays, Sue bakes apple pies. She bakes cheese pies on Tuesdays and Thursdays. If Sue bakes 50 pies a day, how many more apple pies does Sue bake than cheese pies in a week? apple pies = a cheese pies = c a= 3 * 50 a= 150 c= 2 * 50 c = 100 150 - 100 = 50 Answer: 50

A burrito artist can make 14 burritos in 5 minutes. How many burritos can she make in one hour?

The proportion here is 14 to 5 (14:5). Setting up your problem, you get 14:5 = B:60. Solving, you get B = 168. You need to multiply the 5 by 12 to get to 60, so you need to multiply the 14 by 12 to get to B. answer: 168

At meetings of the Rough Wood Handlers Organization, every member suffers from 7 splinters. How many splinters will there be when 11 members attend?

The proportion here is 1:7; for every 1 member, there are 7 splinters. So for 11 members, you'll need to multiply the 7 by 11 to get 77 splinters for an equivalent proportion of 11:77. answer: 11:77

If the campers at Camp Grilled Meat prefer hot dogs to hamburgers by a ratio of 4:3, and they need 500 hot dogs, how many hamburgers will they need?

The ratio says for every 4 hot dogs eaten, 3 hamburgers are also eaten. So if 500 hot dogs are eaten (500 / 4 = 125 times the current ratio), then 125 * 3 = 375 hamburgers will also be eaten. answer: 375

Tobias is scared that the banks will close on him, and he's afraid that a fire will come and burn everything he has. So, he keeps his cash savings frozen in a big piece of ice in the freezer. He has $4,300 in frozen cash. His brother, Jude, keeps his cash stuffed inside a teddy bear. Jude has half the amount that Tobias has. How much money does Jude have stuffed in his teddy bear?

Tobias is scared that the banks will close on him, and he's afraid that a fire will come and burn everything he has. So, he keeps his cash savings frozen in a big piece of ice in the freezer. He has $4,300 in frozen cash. His brother, Jude, keeps his cash stuffed inside a teddy bear. Jude has half the amount that Tobias has. How much money does Jude have stuffed in his teddy bear? 1/2 or 0.5 * $4,300 = 2,150 answer: 2,150

Which of the following is an equation to solve this word problem? Joe has four blue pens and three green pens. Sarah gives Joe four blue pens and two green pens. Sarah originally had 10 blue pens and 12 green pens. How many blue pens does Sarah now have? x = 4 + 3 x = 10 - 4 x = 4 + 4 x = 12 - 2 x = 10 + 4

Which of the following is an equation to solve this word problem? Joe has four blue pens and three green pens. Sarah gives Joe four blue pens and two green pens. Sarah originally had 10 blue pens and 12 green pens. How many blue pens does Sarah now have? x = 10 - 4 x = 6 answer: x= 10 - 4

Which of the following is the equation to solve the following word problem? Sam has 4 red balloons and 8 purple balloons. Judy has 12 red balloons and 4 orange balloons. How many red balloons do Sam and Judy have together? x = 8 + 4 x = 4*3 x = 12 + 8 x = 4 + 4 x = 4 + 12

Which of the following is the equation to solve the following word problem? Sam has 4 red balloons and 8 purple balloons. Judy has 12 red balloons and 4 orange balloons. How many red balloons do Sam and Judy have together? 4 + 12 = 16 answer: x = 4 + 12

What is the second step in solving word problems?

Write the equations.

prime factorization

break the number down to its prime factors.

square root

inverse of squaring a number. square root of n^2 = n

proportion

is a pair of ratios that are equal to each other.

word problems

mathematical problems that involve scenarios

Solve 13.9 * 7.12

multiplication with decimal notation 13.9 * 7.12 98.968 answer: 98.968

Solve 23.6 * 8.901

multiplication with decimal notation 23.6 * 8.901 210.0636 answer: 210.0636

percent

per one hundred %

measures of central tendencies

provides us with statistical information about a set of data mean, median , mode, and range

quotient

the answer to the division problem

1 x 2 4 5

1 x 2 = 2 4 5 20 simplify 1 x 2 = 1 4 5 10

denominator

The bottom number in a fraction

prime factor tricks

The tricks to find some of the prime numbers are: 1.) Any even number is divisible by 2.) If you add up the digits in a large number and the sum you get is divisible by 3, the number is also divisible by 3. 3.) A number that ends with a 5 or 0 is divisible by 5.

Mike is in a band, and he wants to eat before their big gig. They get a mega-super-carnivore pizza. Mike is super hungry, so he takes 1/2 of it, which is 4 slices. But after eating just 1 slice, which is 1/4 of what he took, Mike is now full, so he stops eating. How much did Mike eat?

1 x 1 = 1 4 2 8 1 * 1 = 1 4 * 2 = 8 Mike ate one-eighth of the pizza.

What are the three steps to successfully solve any word problem?

1.) visualize the problem. Fully understand the problem so you know what you need to solve and what is going on in the problem. 2.) write equations from the problem that will help you answer the question from the problem. 3.) solve your equations.

the Ducks' kickers had kicked field goals of 10, 14, 17, 19, 21 and 30 yards. Find the range.

10, 14, 17, 19, 21, 30 30 - 10 = 20 range: 20

If a certain shoe has been discounted by 55 percent and the original price is $218, what is the amount you will end up paying for the shoe after the discount?

100 - 55 = 45 45/ 100 = 0.45 45% of 218 0.45 *218 = 98.10 answer: $98.10

What is the first step in solving word problems?

Visualize the problem.

What is 75 percent of 30?

What is 75 percent of 30? 75 / 100 = 0.75 0.75 * 30 = 22.5 answer: 22.5

What percentage is 60 out of 130?

What percentage is 60 out of 130? 60/130 =0.46 answer: 046. or 46%

What percentage is 122 out of 222?

122 / 222 = 0.549... So around 55 percent. answer: 55 percent

Eric completed 1/3 of his homework before dinner and then 2/7 after dinner. How much homework did Eric complete?

13/21 Explanation: This requires adding 1/3 + 2/7. Finding common denominators and then adding, you get 7/21 + 6/21 = 13/21.

At halftime of our game, the Bears quarterback has passes of 3, 8, 9, 12, 12 and 15 yards. Let's find the median pass thrown by the Bears quarterback.

3, 8, 9, 12, 12, 15 Since there are two numbers in the middle, you will average them together. Add the two numbers together, 9 + 12 = 21 = 10.5 2 Then, divide by 2: 21 ÷ 2 = 10.5. The median of this set of data is 10.5. In the first half, the Bears quarterback had a median passing yardage of 10.5 yards. median: 10.5 yards

What is 30 percent of 120?

30 /100 =0.3 0.3 * 120 = 36 answer: 36

Stacy planted 5 1/4 rows of peas in her garden; she then decided to plant 2 1/2 more rows. How many rows of peas did Stacy plant?

7 3/4 Explanation: Adding 5 1/4 and 2 1/2, you can first add your whole numbers: 5 + 2 = 7. Then, add your fractions 1/4 + 1/2. You need a common denominator, so you rewrite: 1/4 + 2/4 = 3/4. Adding the whole numbers and fraction together, you get 7 3/4.

You go out for a ride and cover 7 1/10 miles. You stop for a quick snack. Then, you ride another 11 2/5 miles. How far did you go?

Adding Unlike Mixed Numbers Find the least common denomenator of 10 and 5. 10: 10, 20, 30, 40, 50, 60 5: 5, 10, 15, 20, 25, 30 answer: 18 1/2

The first day, you swim 7 1/2 laps. The next day, you swim 9 1/4 laps. How many total laps did you swim?

Adding Unlike Mixed Numbers answer: 16 3/4

What are the three steps to multiply fractions?

three steps: 1.) multiply the numerators 2.) multiply the denominators 3.) simplify the fractions (if necessary)

bimodal

two modes

Solve: Square root of 64

Explanation: 8 * 8 = 64 The square root of 64 is 8.

Solve: Square root of 81

Explanation: A square is a number multiplied by itself. 9 * 9 = 81 The square root of 81 is 9.

decimal number system

It is a base 10 system, which means that it is based on a 10 number cycle, the numbers 0 - 9

Sam's rabbit recently had a litter of bunnies and so did Lucy's rabbit. Sam's rabbit gave birth to 4 boy and 3 girl bunnies. Lucy's rabbit gave birth to 2 boy and 8 girl bunnies. How many boy rabbits were born altogether?

Sam's rabbit recently had a litter of bunnies and so did Lucy's rabbit. Sam's rabbit gave birth to 4 boy and 3 girl bunnies. Lucy's rabbit gave birth to 2 boy and 8 girl bunnies. How many boy rabbits were born altogether? 4 + 2 = 6 answer: 6 boy bunnies

You decide to take up rock climbing. You're on a practice wall, and you get 4/5 of the way to the top. The next day, you're very sore, and you only get 1/4 of the way. How much less far did you climb?

Subtracting Unlike Fractions answer: 11/20

You complete one triathlon in 14 5/6 hours. But, you train and train, then do another in 9 1/3 hours. That seems like a huge improvement, but how much is it?

Subtracting Unlike Mixed Numbers Find the least common denominator of 6 and 3 6: 6, 12, 18, 24, 30 3: 3, 6, 9, 12, 15 answer: 5 1/2

You've been drinking a 3 5/8 cup smoothie, but you decide to cut that back to 2 1/4. How much less it that?

Subtracting Unlike Mixed Numbers Find the least common denominator of 8 and 4 8: 8, 16, 24, 32 40 4: 4, 8, 12, 16, 20, 24, 28 answer: 1 3/8

factor tree

a diagram that is used to break down a number into its factors until all the numbers left are prime.

decimal point

a dot placed after the number in the one's place and before the number representing the number of sections of the next number.

square

a number multiplied by itself 3^2 3 *3 = 9 3^2 = 9

outlier

a number that is significantly greater or smaller than the rest of the data Example: the Ducks had plays that were 21, 24, 26, 20, 56 and 20 yards. outlier: 56

cube root

a number that when multiplied three times equals a given number

perfect squares

a number that you'd get by squaring a whole number examples: 1 * 1 = 1 2 * 2 = 4 10 * 10 = 100

Solve 1.963 + 2.8 + 0.54 + 13.7

addition with decimal notation 1.963 2.8 0.54 + 13.70 19.003 answer: 19.003

Solve 33.247 + 15.2

addition with decimal notation 33.247 + 15.2 48.447 answer: 48.447

What is 7/8 as a decimal?

answer: 0.875

If you napped for 1 1/6 hours on Monday and 2 1/2 times as long on Tuesday, then how long was Tuesday's nap?

answer: 2 11/12 Explanation: First, convert the mixed numbers to improper fractions. You get 1 1/6 = 7/6 and 2 1/2 = 5/2. Now multiply these two improper fractions together: 7/6 * 5/2 = 35/12. Simplifying, you get 2 11/12 hours.

What is 0.98 as a percentage?

answer: 98 percent

prime Number

any number that is only divisible by itself and 1

mean

average. Add together all of the numbers in your data set. Then divide that sum by the number of addends. add all four of these values together: 16 + 14 + 12 + 18 = 60 divide that sum by 4: 60 ÷ 4 = 15. So, the average number of yards that the Bears gained was 15 yards. The mean is used to show us the true average of a set of data.

Convert 0.2 to a fraction.

decimal to a fraction 0.2 = 1/5 1/5 = 0.2 answer: 1/5

Convert 0.25 to a fraction.

decimal to a fraction 0.25 = 1/4 1/4 = 0.25 answer: 1/4

Convert 0.6 to a fraction.

decimal to a fraction 0.6 = 3/5 3/5 = 0.6 answer: 3/5

What is 0.87 as a percentage?

decimal to a percentage 0.87 (* 100) = 87% answer: 87%

What does the phrase such as 'a number out of another number' or 'a number of another number,' mean?

division So, if you see something like '65 out of 80,' you would write it mathematically as 65 / 80, or 65 divided by 80.

Solve 170.63/1.13

division with decimal notation 170.63 / 1.13 151 answer: 151

square root of 196

factor and just x the same number over and over until you get 196.

square root of 729

factor and just x the same number over and over until your get 729

What is 2/5 as a decimal?

fraction to a decimal 2/5 = 0.4 answer: 0.4

What is 1/4 as a percentage?

fraction to percentage 1/4 = 0.25 (*100) = 25% answer: 25 %

What is 1/5 as a percentage?

fraction to percentage 1/5 = 0.2 (*100) = 20% answer: 20%

What is 3/4 as a percentage?

fraction to percentage 3/4 =0.75 (*100) =75% answer: 75%

ratio

is a comparison between two things. For example, a soccer team may need 5 soccer balls for every 10 players during practice. The ratio of soccer balls to players if 5:10. It could be apples and oranges or drummers and guitarists.

least common denominator

is the smallest shared multiple of the denominators.

radical sign

means 'root.' A symbol to indicate the square root

convert

means to change

What does the phrase such as 'a percentage of something,' mean?

multiplication. So, if you see a problem such as '75 percent of 20,' you should immediately translate that into 75 percent times 20.

What is 34% as a decimal?

percentage to a decimal 34% (/100) = 0.34 answer: 0.34

What is 54% as a decimal?

percentage to a decimal 54 (/100) = 0.54 answer: 0.54

What is 20 percent as a fraction?

percentage to a fraction 20/100=0.2 simplify: 1/5 = 0.2 answer: 1/5

What is 50 percent as a fraction?

percentage to a fraction 50/100 =0.5 simplify: 1/2 = 0.5 answer: 1/2

principle root

positive root

what are the different names for square root?

square root root radical

range

the difference between the highest and lowest values

median

the middle number when listed in order from least to greatest.

divisor

the number you divide by

dividend

the number you divide into the divisor