Unit One-Number Concepts
This unit is about factors and multiples, prime and composite numbers, prime factors of a whole number, greatest common factor and least common multiple, solving problems that involve these, and fractions, decimals and percents. Don't forget to check out the picture gallery at the end.
Factors, Multiples, Prime Numbers, Composite Numbers, GCFs and LCMs
Definitions
Examples -List 4 factors of 12. Answer: 1, 2, 3, 4. -List 5 multiples of 6. Answer: 12, 18, 24, 30, 36.
-Find the Prime Numbers in this group: 5, 6, 10, 15, 25 and 144. Answer: 5 is the only prime number in the group.
Links
About prime and composite numbers.
http://www.mathsisfun.com/prime-composite-number.html
http://www.aaamath.com/fra63ax2.htm
About factors and multiples.
http://www.mathsisfun.com/numbers/factors-multiples.html
http://www.bbc.co.uk/bitesize/ks2/maths/number/factors_multiples/read/1/
A game about all of them.
http://www.math-play.com/Factors-and-Multiples-Jeopardy/Factors-and-Multiples-Jeopardy.html
Videos
Factors, Multiples, Prime Numbers, Composite Numbers, GCFs and LCMs
Definitions
- FACTOR - Factors are numbers that can be multiplied to form another number.
- For example, two is a multiple of six, because two times three equals six.
- MULTIPLE - Multiples are the products of two numbers being multiplied together.
- For example, six is a multiple of two, because two times three is six.
- PRIME NUMBERS - Prime numbers have only factors of one and itself.
- Seven is a prime number because it's only factors are one and itself. -The only way you can make seven through multiplication is by multiplying one and seven.
- COMPOSITE NUMBERS - Any number greater than one that can be divided by numbers other than one and itself.
- Composite numbers are any numbers that are not prime numbers.
- For example, six can not only be divided evenly by one, but also by three.
- GCF and LCMs
- GCF stands for Greatest Common Factor.
- GCF is the largest number that fits into a set of numbers.
- For example, the GCF of 6 and 9 is 3, since three is the largest number that you can divide into both six and nine.
- LCM stands for Least Common Multiple. It is the smallest number that two numbers can multiply to make. For example, the LCM of 3 and 4 is 12.
- LCM is the smallest number that two numbers can multiply to make
Examples -List 4 factors of 12. Answer: 1, 2, 3, 4. -List 5 multiples of 6. Answer: 12, 18, 24, 30, 36.
-Find the Prime Numbers in this group: 5, 6, 10, 15, 25 and 144. Answer: 5 is the only prime number in the group.
Links
About prime and composite numbers.
http://www.mathsisfun.com/prime-composite-number.html
http://www.aaamath.com/fra63ax2.htm
About factors and multiples.
http://www.mathsisfun.com/numbers/factors-multiples.html
http://www.bbc.co.uk/bitesize/ks2/maths/number/factors_multiples/read/1/
A game about all of them.
http://www.math-play.com/Factors-and-Multiples-Jeopardy/Factors-and-Multiples-Jeopardy.html
Videos
Fractions, Decimals and Percents
Definitions
- FRACTION-A number that is not a whole number.
- DECIMALS-A decimal is a number with a decimal point in it. Like a fraction, it signifies a number that is not whole.
- PERCENTS-A number out of one hundred, used to signify part of a whole. (Like fractions and decimals.)
-To convert a fraction to a decimal, divide it.
Example- 5/10=0.5, because 5 divided by 10 is 0.5.
-To convert a decimal to a fraction, put the number behind the decimal over a ten, hundred, thousand or other number with a whole bunch of zeros according to how many places there are behind the decimal.
Example- 0.5 is 5/10, 0.54 is 54/100 and 0.543 is 543/1000. You can then put the fraction in lowest terms. For information about how to reduce fractions to lowest terms, go to http://www.factmonster.com/ipka/A0933466.html
-To convert a fraction to a percent, turn the fraction into a decimal, then the decimal point gets moved over two places. (It gets divided by one hundred.) This is also how to convert a decimal to a percent-you just take out the first step.
Example- 5/10 turns into 0.5. Move the decimal two sections to the right. Another example is 0.543. This turns into 54.3%.
-To convert a percent to a fraction, put the percent over one hundred, or one thousand if the percent has some decimal places.
Example- 23% turns into 23/100. You can then proceed to turn this fraction into lowest terms.
-When you are adding and subtracting fractions, you must find a common denominator. This means that the bottom number of the fraction must be the same on both fractions. Once you have this, it is easy to add or subtract. Simply add or subtract the numerator.
Example- 2/4 + 3/8. Before you can add these fractions, you have to make both fractions the same. You can give 2/4 the same denominator as 3/8 by multiplying the top and bottom by two. You MUST do the same to the top as you do to the bottom. So 2/4 becomes 4/8. Now add 4 and 3. That is seven, so 2/4 + 3/8 is 7/8.
A Website with Tips and Examples
http://www.jamit.com.au/htmlFolder/FRAC1007.html
-Multiplying and dividing is a bit different. You don't need a common denominator to do that. To multiply a fraction, just multiply the numerators and denominators.
Example- 2/3 x 4/5. 2 x 4 = 8. 3 x 5 = 15. The end result is 8/15.
When dividing fractions, you keep switch flip. The first fraction stays the same, the division sign switches to a multiplication sign, and the last fraction flips upside down. (The reciprocal.) Then you can multiply the fractions like normal.
-Converting fractions from improper to mixed numbers is fairly easy. Lets say you have the fraction 11/7. You want to convert it. Just divide it. Seven goes into eleven once. So you write down one. There is a remainder of four. Write this four over seven. The mixed number is 1 4/7. We have to test this. To convert a mixed number to an improper fraction, multiply the whole number by the denominator and then add the numerator. Put this number over the denominators. So we have 1 x 7 + 4. 1 x 7 = 7. 7 + 4 = 11. Put eleven over seven, and you get 11/7.
A link for a better explanation of decimals and tips on converting decimals to fractions and percents.
http://home.avvanta.com/~math/def2.cgi?t=decimal
Integers and Order of Operations
Definitions
- INTEGER-Any whole number, positive or negative. 1, 2, 3, 4, 5, 6, 7, 8, 9, and 12864836482634864586287368365824567463852639427 are all integers.
- ORDER OF OPERATIONS-BEDMAS. (Brackets, Exponents, Division, Multiplication, Addition, Subtraction.) The order you solve equations in. The equation 2^2 x (3+3) is 3+3 then 2^2 then multiply the two answers together.
A Game to do with Order of Operations
http://www.learnalberta.ca/content/mejhm/index.htmlID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.INTE&lesson=html/object_interactives/order_of_operations/use_it.html
-BEDMAS means that the first thing you solve is the brackets, followed by the exponents, then the division and multiplication, and finally the addition and subtraction.
Printable or Savable Worksheets
http://www.math-drills.com/orderofoperations/ooo_integers_fivesteps_positive_pemdas_all.html
-When dealing with negative integers, always remember that they are less than zero.
Examples- 2 + -3. Since these are both negative numbers, and they are being added, add them together like you would positive numbers then make sure the sign in front is negative. -2 + -3 = -5.
-2 + 3. You can subtract the two from the three, since the two is negative and the three is positive. -2 + 3 = 1.
-2 - -3. The numbers are both negative, and are being subtracted. We can use keep switch flip for this too. It becomes -2 + 3 = 1.
Quick Review of Adding and Subtracting Integers
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i15/bk7_15i1.htm
-Multiplying and Dividing integers is not any more difficult than adding and subtracting integers. When multiplying integers it is important to remember that when you put two of the same signs together, the answer will always be positive.
Example -2 x -2 = 4. Also, 2 x 2 = 4.
-Similar rules apply when dividing. Two of the same signs make positive numbers, while different signs automatically mean negative numbers.
Example- 12 / -6 = -2, and 10 / -5 = -2.