MATH 157

How does Associative Property make math problems easier?

it tells us that when we add three numbers, it doesn't matter whether we add the first two and then the third, or whether we add the first number to the sum of the second and the third-either way we will always get the same answer.

What problems did Base 10 fix?

In the beginning we would right numbers as symbols, ex. IV, VVV, and so on. If we wanted to do numbers like 1,000 it went on to create more symbols. Well that was hard and it was when the base 10 came around. This is when we replaced symbols with digits like 1,2,3,4,5,6,7,8,9,10, and more. The key reason it helped is that rather then using new symbols to represent larger and larger number. To put it simply it uses place value.

Define and identify irrational numbers

Irrational numbers are those that cannot be written as a fraction.

How do you solve inverse proportions

ex. 5 people each can do 40 envelopes in 1 hour, how many people can finish 10 envelopes in 1 hour equations: k=y*x, y=k/x K = 5 * 40, K=200 5(10)=200p/40 50 = 200p/40 50*40 =200k 2000 = 200k 2000/200 = 200p/200 P=10

How do you write decimal numbers in scientific notation and vice versa.

ex. 987 = 9.87 * 10^2 ex. 2.4 * 10^-3 = .0024 two things that are important to remember, when turning a whole number into scientific notation, that the whole number cannot be bigger then 10. when that happens you turn the number into a decimal, hence 987 = 9.87 When the base ten has a positive exponent the decimal is moved to the right. If the base 10 has a negative exponent the decimal is moved to the left.

Define Associative Property

states that the addition or multiplication of a set of numbers gives the same output regardless of how they are grouped.

What are composite numbers.

the counting numbers other then 1 that are not prime. Can be divisible by any number and itself.

How does Commutative Property make math problems easier?

this says that no matter what the number A and B are, A + B is equal to B + A in other words, A + B = B + A

How do you solve direct proportions

ex. 5 people each can do 40 envelopes in 1 hour, how many envelopes can 10 people finish in 1 hour. equations: y =kx, k= y/x 40(10) = e * 5 400 = 5e 400/5 = 5e/5 e = 80

Polya's Four Steps to Problem Solving

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Explain and use divisibilty tests for 2,3,4,5,(6,8),9,10

2- any number that is even ex. 2,4,6,8,10... 3- if the sum of a digits number is divisible by 3 then its divisible by 3 4- if the last 2 numbers are divisible by 4 then its all divisible by 4 5- if the number ends with 0 or 5 its divisible by 5 6- if the number is divisible by 2 and 3 its divisible by 6 8- if the last 3 numbers are divisible by 8 then the whole number is divisible by 8 9-if the sum of the digits is divisible by 9 then its all divisible by 9 10- if the number ends with a 0 it is divisible by 10

How to write numbers including decimals, expanded and note form

305.24 = 3 * 10^3 + 5 * 10 + 2 * 10^-1 + 4 * 10^-2 Threehundred and five and twenty four

What are different forms used to express a percent?

100% of 400 = 400 10% of 400 = 40 5% of 400 = 20

Explain how a mixed number may be expressed as an improper fraction and vice-versa

4 2/3 = 14/3, to change a improper fraction into a mixed number you must first multiply the whole number into the denominator. You then add the numerator to your sum and then you got your numerator. You keep the denominator the same.

Why is division by zero not defined?

7/0 is undefined because if you translate in into multiplication it equals 0*?=7, meanwhile 0/7=1 because if you put it into a multiplication problem it is 7*?=0

Define a fraction

A number that represents part of a whole, part of a set, or a quotient in the form a/b which can be read as "a divided by b"

Define ratio

A ratio is a mathematical way to describe certain qualities of quantities that are mixed, combined, or related

What will A and B each represent in A/B

A represent the numerator while B represents the denominator. Also you have A parts, each of size 1/B, of unit amount.

Define Percent

Percent is defined as "of each hundred" or "out of a hundred"

Define Prime Factorization

The counting numbers other then 1 that are only divisible by 1 and itself.

Define Commutative Property

When you add two numbers together, it doesn't really matter in which order you add them. Similarly when you multiply two numbers together, you're going to get the same results whether you say 2 times 3 or 3 times 2.

Base 10 System

a place value system in which each digit is 10 times greater than the digit to the right of it.

how do you do complete calculations with decimal numbers in scientific notation.

ex. Multiply (6.1 * 10^13) * (9.2 * 10^8) = 56.12 * 10^21 = 5.612 * 10^22 = 56120000000000000000000 step one : multiply the decimals together, keep the base 10, and add the exponent. step two : if the number on the left is bigger then a 10 change it to be less then ten. if you have to move the decimal to the left add one to the exponent, if you move it to the right subtract one step

how do you compare different expression of a percent increase/ decrease

ex. if sales tax is 6% and the sales price is $35 what is the original price. 100% + 6% = 106% = 1.06 1.06(35) = $37.10 what if the original price was $35 1.06(X) = 35 1.06x = 35 1.06x/1.06 = 35/1.06 x = 133.02

What are two ways to calculate percent increase/decrease

ex. ken went from 3.5 to 2.5 first way is to calculate Change/original 3.5 - 2.5 = 1/3.5 = 0.2857 = 28.6% this shows the actual decrease. second way is to calculate new/original 2.5/3.5 = .714 = 71.4% now you may be thinking, this is wrong because the answer is supposed to be 28.6%. well you are correct, so after you find your sum you do this 100% - 71.4% = 28.6%

Fraction - what must be known first

if you have A/B that means you have equal parts, where each part is 1/B

3 Concepts a child must demonstrate to show understanding of counting

one concept is that each child should understand that counting numbers is a list, it is very straightforward and you cant mix any numbers around. The second concept is that they need to understand one-to-one corresopondence, and third they should know cardinality.

Define and identify rational numbers

rational numbers are those that can be expressed as a fraction or a negative fraction ex. 1/3 = 0.33333

How to identify values

to identify values you first need to know where they are places, thus the place value.

Explain characteristics of Base 10

uses numbers instead of symbols, Focuses on place values,

Understand the interpretation of non-negative numbers that M x N, is the number of units in M equal groups of size N

when we read M * N it means the number of units (or objects) in M equal groups if there are N units in 1 group. we define multiplication as equal groups. the value of M * N is called the product. M is the multiplier and N is the multiplicand.