Math Unit 2 Study guide - Southwest Middle School



Adding& Subtracting decimal numbers

Step 1: Write down the numbers, one under the other, line up decimals

Step 2: Put in zeros so the numbers have the same length

Step 3: Then add/ subtract normally, remembering to put the decimal point in the answer

Practice:

|Multiplying decimals numbers |

|Step 1: Write down the numbers. |

|Step 2: Count your dp’s for each number |

|Step 3: Multiply the numbers as if they were whole numbers. |

|Step 4: Move your decimal point in the answer from right to |

|left. |

Prime Numbers (Prime Factorization)

A prime number can be divided evenly only by 1, or itself. The prime numbers between 2 and 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. Prime Factorization is a number written as the product of its prime factors. Ex. 10 = 2 * 5 or 24 = 23 * 3 or 24 = 2*2*2*3.

GCF

The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers:

1) Find the factors of each number by: listing all the factors, prime factorization, upside-down cake or ladder, or T-Chart.

2) If the only common factor is 1; the GCF is 1 and the numbers are called relatively prime.

Practice:

1) Find the GCF of this pair of numbers 14 and 49.

2) What is the GCF of 15 and 75?

a) 5 b) 3 c) 15 d) 1

3) What is the GCF of 14 and 24?

a) 2 b) 3 c) 7 d) 6

LCM

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. For example, to find the LCM of 3 and 4 you will list the multiples of 3, then list the multiples of 4, and identify the least multiple they have in common.

Practice

| 1) What is the LCM of 30 and 45? |

|a) 5 b) 90 c) 120 d) 150 |

| |

|2) What is the LCM of 12 and 80? |

|a) 80 b) 12 c) 4 d) 160 |

| |

|3)Find the LCM of 26 and 20. |

| |

|4) Find the LCM of 15, 30, and 20. |

| |

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Distributive Property

Distributive property is used to rewrite a simple addition problem using a common factor.

Dividing Fractions

|Step 1: SAME (copy the 1st fraction how it is) |

|Step 2: CHANGE (division symbol to multiplication) |

|Step 3: FLIP ( the second fraction) |

|Step 4: Multiply the fractions ACROSS |

|Step 5: Simply your answer |

| |

|When dealing with mixed numbers, before you apply steps |

|1-5 CONVERT your MIXED # to IMPROPER FRACTION. |

Long division :D M S B

Long division is an algorithm that repeats the basic steps of

1) Divide;

2) Multiply & Subtract;

3) Bring down the next digit.

|1. Divide. |2. Multiply & subtract. |3. Drop down the next digit. |

| | | |

| | | |

|t  o |t  o |t   o |

| | | |

| | | |

| | | |

|2   |2   |2 9 |

| | | |

|2  |2  |2  |

|) |) |) |

|5 8  |5 8  |5 8  |

| | | |

|  | | |

|Two goes into 5 two times, or 5 tens ÷ 2|-  |-  |

|= 2 whole tens -- but there is a |4 |4 ↓ |

|remainder! | | |

| | | |

| | | |

| |1 |1 8 |

| | | |

| |To find it, multiply 2 × 2 = 4, write |Next, drop down the 8 of the ones next to the |

| |that 4 under the five, and subtract to |leftover 1 ten. You combine the remainder ten with|

| |find the remainder of 1 ten. |8 ones, and get 18. |

Practice:

|1. |3  |2. |3  |

| |)  | |)  |

| |1 2 8  | |9 5  |

| | | | |

|  | | | |

| | | | |

|  | | | |

|3. |6  |4. |4  |

| |)  | |)  |

| |4 2 6 7  | |2 8 4 5  |

| | | | |

-----------------------

1) 100- 65.27 =

2) 40+ 21.32 =

3) 112.83 - 37.94 =

4) 112.83 + 37.94 =

Dividing decimal numbers

Step 1: If the divisor is not a whole number, move the decimal place to the right to make it a whole number. Then move the decimal place in the dividend the same number of places to the right

Step 2: Divide as usual. Add zeros to the right of the dividend and keep dividing until you get a 0 remainder, or until a repeating pattern shows up.

Step 3: Put the decimal point in the quotient/answer directly above where the decimal point now is in the dividend.

Step 4: Check your answer against your estimate to see if it's reasonable.

Practice:

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3.1 × 5.06 =

Examples:

Factor out expression:

6 (10 + 4) = 6 * 14

= 84

6 (10 + 4) = 6*10 + 6 * 4

= 60 + 24

= 84

Rewrite expression using distributive property:

Use distributive property to rewrite expression

a. 5

Factor out the expression

When you multiply a number times a sum, you can:

1) Find the sum first and then multiply, or

2) Multiply by each number in the sum and then add

Practice:

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