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## Math

To Access the Math Book Online:

Click on the "Links" icon.  You will see "Math Book Online."

All 5th graders are invited every Thursday to Math Lab. The students bring their lunches and stay through lunch recess.

Divisibility
Rules

A number is
divisible by 2 if it is an even number.

A number is
divisible by 3 if the sum of its digits is a
multiple of 3.

A number is
divisible by 5 if it ends in a 5 or a 0.

A number is
divisible by 9 if the sum of its digits is a
multiple of 9.

A number is
divisible by 10 if it ends in a 0.

Prime Factorization

Prime factorization
Prime factorization is finding the factors of a number that are all prime. Here's how you do it: Find 2 factors of your number. Then look at your 2 factors and determine if one or both of them is not prime. If it is not a prime factor it. Repeat this process until all your factors are prime. Here's an example:
Find the prime factors of the number 84:

```
84
/  \
42 x  2  (84 is 42 times 2)
/  \
21 x  2     (42 is 21 times 2)
/ \
7 x 3         (21 is 7 times 3)
(7 and 3 are both prime, so we stop!)
```

So the prime factors of 84 are 7 x 3 x 2 x 2.

## Decimals

To understand decimal numbers you must first know about Place Value.

When we write numbers, the position (or "place") of each number is important.

In the number 327:

• the "7" is in the Ones position, meaning just 7 (or 7 "1"s),
• the "2" is in the Tens position meaning 2 tens (or twenty),
• and the "3" is in the Hundreds position, meaning 3 hundreds.
 "Three Hundred Twenty Seven"
 As we move left, each position is 10 times bigger! From Units, to Tens, to Hundreds

... and ...

 As we move right, each position is 10 times smaller. From Hundreds, to Tens, to Units

 But what if we continue past Units?What is 10 times smaller than Units?1/10 ths (Tenths) are!

 But we must first write a decimal point,so we know exactly where the Units position is: "three hundred twenty seven and four tenths"but we usually just say "three hundred twenty seven point four"

## Decimal Point

The decimal point is the most important part of a Decimal Number. It is exactly to the right of the Units position. Without it, we would be lost ... and not know what each position meant.

Now we can continue with smaller and smaller values, from tenths, to hundredths, and so on, like in this example:

## Large and Small

So, our Decimal System lets us write numbers as large or as small as we want, using the decimal point. Numbers can be placed to the left or right of a decimal point, to indicate values greater than one or less than one.

 17.591 The number to the left of the decimal point is a whole number (17 for example) As we move further left, every number place gets 10 times bigger. The first digit on the right means tenths (1/10). As we move further right, every number place gets 10 times smaller (one tenth as big).

## Ways to think about Decimal Numbers ...

### ... as a Whole Number Plus Tenths, Hundredths, etc

You could think of a decimal number as a whole number plus tenths, hundredths, etc:

### Example 1: What is 2.3 ?

• On the left side is "2", that is the whole number part.
• The 3 is in the "tenths" position, meaning "3 tenths", or 3/10
• So, 2.3 is "2 and 3 tenths"

### Example 2: What is 13.76 ?

• On the left side is "13", that is the whole number part.
• There are two digits on the right side, the 7 is in the "tenths" position, and the 6 is the "hundredths" position
• So, 13.76 is "13 and 7 tenths and 6 hundredths"

### ... as a Decimal Fraction

Or, you could think of a decimal number as a Decimal Fraction.

A Decimal Fraction is a fraction where the denominator (the bottom number) is a number such as 10, 100, 1000, etc (in other words a power of ten)

So "2.3" would look like this:
 23 10

And "13.76" would look like this:
 1376 100

### ... as a Whole Number and Decimal Fraction

Or, you could think of a decimal number as a Whole Number plus a Decimal Fraction.

So "2.3" would look like this:
2 and
 3 10

And "13.76" would look like this:
13 and
 76 100

Fractions

Finding Common Denominators

Step 1

See if one of the denominators is a multiple or factor of the other denominator.

Example: 1  +  1       1  +  2

6      3  =   6      6

Step 2

If Step 1 doesn’t work, find a common multiple of the two denominators.

Example:  1  +  1       5  +  2

4     10 =  20    20

Because 20 is a multiple of both 4 and 10

Step 3

If Step 1 doesn’t work, and you can’t easily find a common multiple of the two denominators as in Step 2, multiply the two denominators together for a common denominator.

Example: 1   +  1        7   +   5

5       7  =   35     35

Simplifying Fractions
Simplifying a fraction means to rewrite a fraction as an equivalent fraction with a smaller numerator and denominator.  To do this, you need to find a common factor of the numerator and denominator.  For example:

3
9 can be simplified because both the numerator (3) and
denominator (9) can be divided by 3.  So,

3    ÷   3      1
9   ÷    3   = 3

PERCENTAGES

You can think of a percentage as the numerator of a fraction with 100 as the denominator or a hundredths decimal.  You can write percents as fractions and decimals.  For example:

35
100   =   0.35   =   35%

As long as a fraction has a denominator of 100, it can easily be written as a percent.  If a fraction is not written with a denominator of 100, it needs to be converted into either an equivalent fraction with a denominator of 100, or written as a decimal and then converted to a percent.  For example:

2
5 can easily be written as an equivalent fraction with a denominator of 100.

2    x   20         40
5    x   20   =   100, so this translates to 40%

However,

5
8 cannot easily be written as an equivalent fraction with a denominator of 100.  In this case, we divide 8 by 5 and get 0.625.
This is 625/1000, which equals

62.5
100   =   62.5%

VOLUME AND SURFACE AREA

To find the volume of a rectangular prism, simply multiply the width by the length by the height.

V = w x l x h

To find the surface area, you need to calculate the area of each face of the prism.

3 in.       q    5 in.

2 in

.

You will have:

2 faces that are 2in. x 3 in.  (front and back)

2 faces that are 3 in. x 5 in.  (sides)

2 faces that are 2 in. x 5 in.  (top and bottom)

2 x 2 x 3 = 12 sq. in.

2 x 3 x 5 = 30 sq. in.

2 x 2 x 5 = 20 sq. in.

Total         62 sq. in.

ROUNDING

When rounding to the nearest tenth, look at the number in the hundredths place.  If the number in the hundredths place is 5 or above, round the number in the tenths place up.  If the number in the hundredths place is 4 or less, leave the number in the tenths place the same.

Example:  Round 9.654 to the nearest tenth.

The easiest way to do this is to place 9.654 between two numbers one-tenth apart.

9.600
9.654
9.700

Look at the number in the hundreths place:  9.654
Since the "5" is 5 or above, you will round 9.654 to 9.7.  You are saying that 9.654 is closer to 9.7 than it is to 9.6.