# Fractions & Decimals for 3rd Graders

NCTM math standards to include learning goals & objectives, a lesson plan to include

differentiation of instruction to address the diverse needs of students and

problem solving strategies plus

informal and formal assessments that align with objectives in addition to

concrete manipulative to help develop fraction sense and also

authentic, formative and summative assessment strategies for a 3rd grade class

1. What is a Fraction?

2. Name the three kinds of fraction

3. What is Improper Fraction?

4. What is Mixed Number?

5. How to changed improper fractions into mixed or whole number?

6. How to convert fractions?

7. How to reduce fractions?

8. Comparing fractions

9. How to add or subtract fractions?

10. Finding the least common denominator.

11. Adding mixed numbers.

12. Multiplying and dividing fractions

13. Introduction to Decimals

14. Adding and dividing decimals

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Study plan for 3rd grader in Fraction and Decimal

What is a Fraction?

A fraction is a part of a whole.

The two numbers that compose a fraction are called the: numerator/denominator

For the fraction 3/8, the numerator is 3, and the denominator is 8. The easy way to remember which is which is to associate the word denominator with the word down. (1) The numerator indicates the number of parts you are considering, the denominator indicates the number of equal parts contained in the whole. (1) You can represent any fraction graphically by shading the number of parts of being considered (numerator) out of the whole (denominator). (1)

Example:

Pizza is cut into 8 equal slices, you ate 3 of them. The fraction 3/8 tells you what part of the pizza you ate.

Three Kinds of Fraction

Proper Fractions

In proper fraction, the top number is less than the bottom number:

1/2 ; 2/3; 4/9; 8/13

The value of a proper fraction is less than 1.

Example: If you eat 3 slices of pizza that is cut into 8 slices. Each slice is 1/8 of the pizza.

You have eaten 3/8 of the pizza.

Improper Fractions

In an improper fraction, the top number is greater than or equal to the bottom number:

3/2 ; 5/3 ; 14/9; 12/12

The value of an improper fraction is 1 or more. (1)

When the top and bottom numbers are the same, the value of the fraction is 1. (1)

For example, all of these fractions are equal to 1: 2/2 ; 3/3 ; 4/4 ; 5/5 , etc.

Any whole number can be written as an improper fraction by writing that number as the top number of a fraction whose bottom number is 1, for example, 4/1= 4.

Mixed Numbers

When a fraction is written to the right of a whole number, the whole number and fraction together constitute a mixed number:

3 Â½, 4 2/3, 12 Â¾ , 24 Â¾

The value of a mixed number is greater than 1: It is the sum of the whole number plus the fraction.

Changing Improper Fractions into Mixed or Whole Numbers

1. Divide bottom number into top number. (1)

2. If there is remainder, change it into a fraction by writing it as the top number over the bottom number of the improper fraction. (1)

Example: Change 13/2 into a mixed number.

3. Divide the bottom number ( 2) into top number (13) to get the whole number portion ( 6) of them mixed number

4. Write the remainder of the division (1) over the original bottom number ( 2)

5. Write the two number together:

6. Check: Change the mixed number back into an improper fraction. If you get the original improper fraction, your answer is correct.

Include a chapter on Converting Fractions

A fraction means "divide." The top number of the fraction is divided by the bottom number.(1)

For example, Â¾ means " 3 divided by 4," or may be written as 3 Ã· 4 . (1) The value of Â¾ is the same as the quotient you get when you do the division. Thus, Â¾ = 0.75, this is the decimal value of the fraction. Â¾ of a dollar is the same thing as 0.75, which can also be written as $0.75, the decimal value of Â¾. (1)

Reducing the Fraction

Reducing a fraction is writing the fraction in it lowest term with smaller numbers. (1) For instance, 50/ 100 in the reduced form is Â½ of a dollar. (1) 50/100 reduces to Â½. When you reduce a fraction, you do not change its value. (1) When you do arithmetic with fractions, always reduce your answers to lowest term.

To reduce a fraction:

1. Find a whole number that divides evenly into top numbers and the bottom number.

2. Divide the number into both the top and bottom numbers and replace them with the quotients

3. Repeat the process until you cannot find a number that divides evenly into the top and bottom numbers.

It's faster to reduce when you find the largest number that divides evenly into both numbers of the fraction.

Example: reduce 8/ 24 to lowest terms

Comparing Fractions

Which fractions is larger, 3/8 or 3/ 5?

Do not be fooled into thinking that 3/8 is larger just because it has the larger bottom number. (1) There are several ways to compare two fractions:

Change both fractions to decimals. Divide the top number by the bottom number.

3/5 = 0.6 ; 3/8 = 0.375

Because 0.6 is greater than 0.375. the corresponding fractions have the same relationship: 3/5 is greater than 3/8.

Raise both fractions to higher terms

If both fractions have the same denominator, then you can compare their top numbers

3/5 = 24/ 40 ; 3/8= 15/40

Because 24 is greater than 15, the corresponding fractions have the same relationship: 3/5 is greater than 3/ 8

Adding and Subtracting Fractions

If you add two fractions which have the same bottom number (denominator), just add the top numbers (numerator) together and write the total over the bottom number. (1)

Example: 2/9 + 4/9 = 2+4/ 9 = 6/9, which reduced to 2 /3

Example 1

5/8 + 7/8 = 5+7/8 = 12/8

Finding the Least Common Denominator

To add fractions with different bottom numbers, raise some or all the fractions to higher terms so they all have same bottom number, called common denominator. (1) Then add the numerators, keeping all denominators the same. (1)

The original bottom numbers divide evenly into the common denominator. (1) If it is the smallest number that they all divide evenly into, then it is called the least common denominator ( LCD) . (1)

Here are some tips for finding LCD:

- See if all the bottom numbers divide evenly into the largest bottom number

- Check out multiplication table of the largest bottom number until you find a number that all the other bottom numbers divide into evenly. (1)

Tip: the fastest way to find a common denominator is to multiply the two denominators together. Example: For 1/ 4 and 3/ 8 you can use 4 X 8 = 32 as your common denominator.

Example: 2/3 + 4/5

1. Find the LCD by multiplying the bottom numbers:

2. Raise each fraction to 15th , the LCD: 3 X 5 = 15

3. 2/ 3 = 10/ 15

4/5 = 12/ 15

22/ 15

Adding Mixed Numbers:

1. Add the fractional parts of the mixed numbers.

2. If the sum is an improper fraction, change it to a mixed number.

3. Add the whole number parts of the original mixed numbers

4. Add the results of steps 2 and 3.

5. Example: 2 3/5 + 1 4/5

6. Add the fractional parts of the mixed numbers:

7. Change the improper fraction into a mixed number:

8. Add the whole number parts of the original mixed numbers"

9. Add the results of steps 2 and 3: 3/5 + 4/5 = 7/ 5

7/ 5 = 1 2/5

2 + 1 = 3

1 2/5 + 3 = 4 2/5

Subtracting Fractions

As with addition, if the fractions you are subtracting have the same bottom numbers, just subtract the second top number from the first top number and write the difference over the bottom number.

Example: 4/9 - 3/9 = 4 - 3/ 9 = 1/9

Multiplying and Dividing Fractions

Multiplication by a proper fraction is same as finding a part of something. (1) Suppose if you have a pizza cut into 4 slices. Each slice is Â¼ of the pizza. If you eat Â½ of a slice, then you eaten Â½ of Â¼ of a pizza or Â½ X Â¼ of the pizza ( of means multiply), which is the same as 1/8 of the whole pizza.

Multiplying Fractions by Fractions

1. Multiply top numbers together to get the top number of the answer.

2. Multiply bottom numbers together to get the bottom number of the answer.

Example: Â½ X Â¼

1. Multiply the top numbers:

2. Multiply the bottom numbers:

3. Example : 1/3 X 3/5 X 7/ 4

4. Multiply the top number:

5. Multiply the bottom numbers:

6. Reduce

7. _1 X 3X 7 = 21

3 X 5 X 4 60

21 Ã· 3 = 7

60 Ã· 3 20

Introduction to Decimals

Decimals are fractions that you use every day when you deal with measurements or money. (1) For instance, $10.35 is a decimal that represents 10 dollars and 35 cents. (1) The decimal point separates the dollars from the cents. (1) Because there are 100 cents in one dollars, 1 cent is 1/100 of a dollar. $0.01 or 10 cent is 10/100 of a dollar or $0.10; 25 cent is 25/100 of a dollar or $ 0.25; and so forth. (1)

If there are digits on both sides of a decimal point, like 5.65, the number is called a mixed decimal; its value is greater than1.

Decimal Names

Each decimal digit to the right of the decimal point has a special name. Here are the first four:

0.1234

0.1 = 1 tenth = 1/10

0.02 = 2 hundredths = 2/100

0.003 = 3 thousandths = 3/1000

0.0004 = 4 ten thousandths = 4/10000

So the decimal names are ordered by multiples of 10: 10ths, 100ths, 1000ths, 10000ths, 100,000ths, 1000,000ths, etc.

Adding zeros to the end of the decimal does NOT change its value.

For example, 5.1250

5.12500

5.125000

5.1250000

5.12500000

5.1250000000, and so forth

Changing Decimals to Fractions

1. Write the digits of the decimal as the top number of a fraction

2. Write the decimal's name as the bottom number of the fraction

Change 0.018 to a fraction

3. Write 18 as the top of the fraction:

Since there are three places to the right of the decimal, it's thousandths

4. Write 1000 as the bottom number:

5. Reduce by dividing 2 into the top and bottom numbers:

Changing Fractions to Decimals

1. Set up a long division problem to divide the bottom number (the divisor) into the top number (the dividend) , but don't divide yet! (1)

2. Put a decimal point and a few zeros on the right of the divisor. (1)

2. Bring the decimal point straight up into the area for the answer ( the quotient) (1)

3. Divide

Comparing Decimals

Decimals are compared by lining them together with the decimal point. (1) They are easy to compare when they have the same number of digits after the decimal point. (1)

Compare 0.08 and 0.1

1. Since 0.08 has two decimal digits, tack on zero onto the end of 0.1, making it 0.10

2. To compare 0.10 and 0.08, just compare 10 and 8. Ten is larger than 8, so 0.1 is larger than 0.08. (1)

Rounding Decimals to the Nearest Whole Number

To round a decimal to the nearest whole number, look at the decimal digit to the right of the whole number, the tenth digits, and follow these guidelines:

If the digit is less than 5, round down by dropping the decimal point and all the decimal digits. (1) The whole number portion remains the same. (1)

If the digit is 5 or more, round up to the next larger whole number. (1)

25.3999 rounds down to 25 because 3 is less than 5.

23.5 rounds up to 24 because the tenths digit is 5.

2.613 rounds up to 3 because 6 is greater than 5.

Adding and Subtracting Decimals

Adding Decimals

Adding decimals is difference from adding whole numbers; the difference is the decimal point. (1) The location or position of the decimal point determines the accuracy of the final answer. (1) In order to add decimal correctly, follow these three simple rules:

1. Line the numbers up in a column so their decimal points are aligned.

2. Tack zeros onto the ends of shorter decimals to keep the digits lined up evenly

3. Move the decimal point directly down into the answer area and add as usual.

4.2 ----ïƒ 4.200

0.34 --ïƒ 0.34

5.871 ---ïƒ 5.871

18 -ïƒ 18.000

+__________________

28.411

Multiplying Decimals

To multiply decimals:

1. Ignore the decimal points and multiply as you would whole numbers. (1)

2. Count the number of decimal digits ( the digits to the right of the decimal point) in both of the numbers you multiplied (1)

3. Beginning at the right side of the product ( the answer), count left that number of digits, and put the decimal point to the left of the last digit you counted. (1)

4. Multiply 157 times 24:

157

X 24

______

628

314

_____

3768

Because there are three decimal digits in 1.57 and 2.4, count off 3 places from the right in 3768 and place the decimal point to the left of the third digit you counted 3.768 (1)

Dividing Decimals

To divide a decimal by a whole number, bring the decimal point straight up into the answer ( the quotient ) , and then divide as you would normally divide whole numbers. (1)

Reference:

1. Practical Math Success. 4th Edition. Learning Express.

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