Formulas for Area and Perimeter

• Perimeter of a rectangle is P=2l x 2w
• Area of a rectangle A=l x w
• Perimeter of a square P= 4s
• Area of a square A= s x s

Division Steps back to the top

• Dad (Dad says, “How many times does _________ go into ____________?”
• Mom (Mom says, “Don’t forget to multiply!”)
• Sister (Sister tells us to subtract)
• Brother (Brother says, “Bring down!”)
• Sometimes our COUSIN visits and he/she tells us to compare

Equations back to the top

Solving equations and expressions can be easy, but you need to be sure to follow the rules.

What’s an equation? Well an equation is a mathematical statement containing an equals sign to show that two expressions are equal.

For example 7x-3=6x and x=3. Let’s check if this statement is true.

• 1. Replace x with 3: 7(3)-3=6(3). Don’t forget equations don’t use x to represent multiplication. When you see 6x or 6(3) that means that you need to multiply those two numbers together.
• 2. Solve the problem:
• 7(3)-3=6(3)
• 21-3=18

• 18=18 The statement is true!

Changing Mixed Numbers into Improper Fractions back to the top

M.A.D.

What is M.A.D.? Well it’s a formula to convert a MIXED NUMBER to an IMPROPER FRACTION.
·What is a MIXED NUMBER? It’s a whole number mixed with a fraction, thus a mixed number.   2 3/4
·What is an IMPROPER FRACTION? It’s when the numerator of a fraction is larger than the denominator. 11/4 = 2 ¾
M is the first step in changing a mixed number to an improper fraction. M stands for multiplying. You need to multiply the whole number by the denominator. So, multiply 2 (the whole number) by the denominator, which is 4. 2 x 4=8.
A is the second step. The A stands for addition. Now you need to add the product of the whole number and denominator by the numerator. 8 + 3 = 11
D stands for denominator. Look back at the denominator of the original problem and take that denominator (2 ¾) and PUT the denominator under the sum of the A step 11/4.
 M Step 1: 2 ¾ = 2 x 4= 8
 A Step 2: 8 +3= 11
 D Step 3: 11/4 

Changing an Improper Fraction into a Mixed Number

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This formula isn’t as easy to remember- D NR D , but it can be fun once you memorize the steps. 11/4

D this time is for DIVISION. Take the numerator 11 and divide it by 4.

NR N stands for numerator and R stands for remainder. Once you divide 4 into 11 you get 2 with a remainder of 3. The remainder 3 becomes the numerator while the 2 becomes a whole number 2 and 3/?.

D The last D stands for denominator. Look at the denominator in the original problem 11/4ths. The four is going to remain the denominator. So the final answer if 2 3/4.

Changing a proper fraction into its simplest form

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In order to turn a proper fraction into its simplest form you must find the greatest common factor. For example if we have the fraction 5/15 we first need to reduce this fraction by finding a number that both the numerator and denominator can be divided by. It can be divided by one, but it won’t reduce the fraction. It cannot be divided by 2, 3, or 4, but it CAN be divided by 5.

5 ÷ 5 = 1 and 5 ÷ 15 = 3 so 5/15 = 1/3

Another example: 7/10 = 7/10 there is not a number that both the numerator and denominator can be divided by therefore 7/10 is in it’s simplest form.

Subtracting and Adding Fractions with Unlike Denominators back to the top

To subtract or add fractions with unlike denominators, we must make the denominators the same.

• Step 1 3/4 + or - 3/12 find a common denominator.
• Step 2 Write down the factors of each denominator and find the lowest common factor. 4, 8, 12, 16, 20 and 12, 24, 36, 48, 60. We find that 12 is the lowest common denominator.
• Step 3 To change the denominators to 12 we must do the following: for the fraction 3/4 we must multiply both the denominator and numerator by 3 to get the new denominator of 12. 3x3=9 and 3x4=12 gives us the new fraction of 9/12 For the fraction 3/12 we do not have to change it because the denominator of 12.
• Step 4 Adding the fractions. 9/12 + 3/12=12/12 or 1 or 9/12 - 3/12 = 6/12 or 1/2.

Prime Numbers back to the top
A prime number is an integer whose value is larger than one and whose only whole number factors are 1 and itself. For example, the number 17 is a prime number since the only whole number factors of 17 are 1 and 17. The following is a list of the first 100 prime numbers. (0 and 1 are neither prime or composite)
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101.........

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