Math Concepts 1 Final

What digits would be used to write numbers in the base 7 number system?

0-6

Write the following fraction as a decimal: 3/20

0.15

Write the following fraction as a decimal: 5/7

0.714285 repeating

write the following fraction as a decimal: 7/9

0.77 repeating

Write the following fraction as a decimal: 4/5

0.8

Stuart reads the decimal 0.85 as zero and eighty-five hundredths, but he is confused as to where to place this number on the number line. Explain how he would determine the location of 0.85.

0.85 is 8 tenths and 5 hundredths. First, start by placing 0 and 1 on a number line. from there divide the number line into 10 equal sections. Locate 8 tenths, and from there you can count 5 hundredths from there.

Describe the methods for writing a fraction as a decimal

1) Use long division for fractions with a denominator that is not a power of 10 2) If the denominator is a power if 10, put the numerator down and add the decimal in the right place. Write an equivalent fraction that has the same denominator as the power of ten.

Write the first 18 numbers in base 4.

1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 100, 101, 102... Don't forget to put B4 after every number.

List all of the factors of 32.

1, 2, 4, 8, 16, 32

Subtracting fractions

1. Find a common denominator. 2. Whatever you do to the bottom, you do to the top. (or cross multiply to find the new numerators) 3. Subtract the numerators 5. Keep the denominators the same

Describe the boxes that you'd need to package 42 truffles following B5 rules. How would you represent this packaging using digits?

125 Carton, 25 Flat, 5 long, and 1 unit would be used to represent the B5 system. Out of those, you would find that 42 truffles using the B5 rules would be 1 Flat, 3 Longs, and 2 Units.

Imagine that you packaging truffles for the B6 Candy Factory: how many boxes would you have with 325 truffles?

1301B6

In the base 10 number system, show how you would package 2106 truffles into boxes.

2 Cartons, 1 Flat, 0 Longs, and 6 Units

Write the following decimal number: Forty thousand fifteen and ninety-five hundred thousandths

40,015.00095

how do you find the overall value or quantity represented by a numeral? Find the overall value of 675,398 as an example.

6(100,000)+7(10,000)+5(1,000)+3(100)+9(10)+8(1)

Partial sums algorithm:

612 +269 11 70 800= 881

Write the following decimal number: Eight million seven thousand fifty-three and two hundred nineteen thousandths.

8,007,053.219

Explain the rule used to test whether a number is divisible by 6.

A number is divisible by 6 if it is divisible by 2 and 3

Explain the rule used to test whether a number is divisible by 9.

A number is divisible by 9 if the sum of the digits is divisible by 9

Define a prime number

A prime number is a number that is only divisible by 1 and its self.

Ben explained how he computed the following sum: 48+59. "I started with 48 and added 2 to get 50. Then I added 59 to 50 to get 109. the I subtracted 2 at the end to get 107." What addition strategy did Ben use?

Compensation

State whether the following number is prime, composite, or neither: 46

Composite

State whether the following number is prime, composite, or neither: 51

Composite

FOIL uses which property?

Distributive

Common denominator method

Find a common denominator in both fractions at find out which is greater

Explain order of operations used in problem solving.

First solve parenthesis then exponents in the problem. The next step is to solve multiplication and division left to right whatever comes first. Then do the same for addition and subtraction.

Smallest to largest

First, find the fractions that are smaller than one half and bigger than one half and put them on different sides. On the side with the smaller fractions, multiply using the cross product and put the fractions into order. Do the same thing for the fractions on the other side.

Show or explain how a first grader might solve 6+7 using a "doubles" strategy.

Having 6+7, you would split 7 into 6+1. You would then add 6+6 to get 12 and there you would add the 1 to get a final answer of 13.

Show or explain how a first grader might solve 9+6 using "make ten" strategy.

Having 9+6, you would split 6 into 1+5. From there you would add 9+1 to get ten. There the student would know that 10+5=15

Explain why 0.16 plus 0.5 is not 0.21

In the number 0.16, the number 1 is int the tenths place and the number 6 is in the hundredths place. When adding decimals, we add the place values to the face values. In the number 0.5, the 5 is in the tenths place. So when adding these numbers, you would add 0.5 and 0.1 together and then you would add .06 to the end.

Is the following number rational or irrational?: 0.25255255525555255555...

Irrational

State whether the following number is prime, composite, or neither: 1

Neither

State whether the following number is prime, composite, or neither: 2

Prime

Is the following number rational or irrational?: 14/20

Rational

Is the following number rational or irrational?: 5.243

Rational

How do you determine if a number is rational or irrational?

Rational numbers can repeat or terminates and can be written as a fraction. Irrational numbers never terminate or repeat

In the numeral, 5516, there are two 5's. In terms of what they represent, how are they different and how are they the same?

Sim: They Bothe represent 5 of something. Diff: The first 5 is in the thousands place and the second 5 is in the hundreds place.

Stacked short division:

Start at the bottom, if the number is divisible by 2, divide it by 2. From there, check to see if the number is divisible by 2 again and if its not, divide it by 3. Do this process with all prime numbers until the answer is 1. once you get 1, write the prim factorization using powers if told to do so.

Place values

Tens, Ones. Tenths, Hundredths, Thousandths, Ten Thousandths, hundred thousandths, Millionths,

LCM

The highest prime factor of both numbers multiplied

GCF

The numbers that both numbers have in common multiplied with each other

multiplying fractions

Turn the fractions into mixed numbers if necessary. Cross cancel the fractions to simplest form and then multiply across. simplify the fraction.

Write the following in words: 2,072,000,129.021

Two billion seventy-two million one hundred twenty-nine and twenty-one thousandths

Write the following decimals in words: 0.000136

Zero and one hundred thirty-six millionths

Terminating decimal

a decimal whose digits end

Adding fractions

find a common denominator then add the numerator

Dividing fractions

keep change flip. do the same thing that you did for multiplying fractions after that.

Cross-product shortcut

multiply the denominator of the first number to the numerator of the second number and put it on top. Then multiply the bottom number of the second number to the top number of the first on and put that on top. see which number is bigger and put your sign of the respected number

What does ordering decimals by place value mean?

when you order a decimal by its place value, you first make the number have the same place value. After making the numbers have the same place value, you look at the decimal as a whole number and order it by either smallest to largest or from largest to smallest.

Join problems

you join or add the numbers

Separate problems

you separate or subtract the numbers