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Fractions And Mixed Numbers

Fractions

Question:
What are fractions?

Answer:
Fractions name parts of a whole or parts of a set of objects.
Every fraction has a numerator (the number above the fraction bar) and a denominator (the number below the fraction bar).
The denominator tells you how many are in the whole set.
The numerator tells how many parts you are talking about.

Equivalent Fractions

Question:
What are equivalent fractions?

Answer:
Equivalent fractions name the same amount. You can use equivalent fractions to add, subtract, compare, and order fractions.

Question:
How do we find equivalent fractions?

Answer:
To find equivalent fractions you can multiply or divide the numerator and the denominator by the same number.
This DOES NOT change the value of the fraction, because you are really just multiplying or dividing by one since any number over itself as a fraction is equal to one.

Simplest Form

Question:
What is simplest form?

Answer:
A fraction is in simplest form when its numerator and denominator have no common factor other than one.

Mixed Numbers & Improper Fractions

Question:
What are mixed numbers?

Answer:
Mixed numbers have a part that is a whole number and a part that is a fraction.

Example:
4 2/8

Question:
What are improper fractions?

Answer:
Improper fractions are fractions where the numerator is greater than the denominator.

Example: 11/10

Question:
How do we write mixed numbers as improper fractions?
Example: 4 2/5

Answer:
Step 1: Multiply the whole number part by the denominator.
4 x 5 = 20
Step 2: Add the numerator to the product.
20 + 2 = 22
Step 3: Rewrite the mixed number as an improper fraction with the new number. The denominator stays the same.
22/5

Question:
How do we write improper fractions as mixed numbers?
Example: 13/6

Answer:
Step 1: Step 1. Divide the numerator by the denominator.
Step 2: Write the remainder as a fraction with the original denominator.
1/6
Step 3: The quotient becomes the whole number in the mixed number.
2 1/6

Comparing/Ordering Fractions & Mixed Numbers

Question:
How do we compare/order fractions with unlike denominators?

Answer:
To compare/order fractions with unlike denominators you:
Step 1: Create equivalent fractions with the same denominator.
Step 2: Compare the numerators.

Example:
Alani runs 3/10 mile and Vi-Vi runes 3/4 mile. Who runs farther?
**Hint: Ask yourself what number could be a common denominator of 10 & 4?

Step 1:
3/10 x 2/2 = 6/20
3/4 x 5/5 = 15/20
Step 2: Compare the numerators.
6 < 15 s0 3/10 < 3/4. Vi-vi ran further.

Example:
Order From Least To Greatest:
2/3 3/4 1/6

Step 1:
2/3 x 4/4 = 8/12
3/4 x 3/3 = 9/12
1/6 x 2/2 = 2/12
Step 2: Compare the numerators.
2 < 8 < 9
REMEMBER TO WRITE THE ORIGINAL FRACTIONS
1/6; 2/3; 3/4

Question:
How do we compare/order mixed numbers?

Answer:
To compare mixed numbers, compare the whole number parts. If the whole number parts are the same, then compare the fractional parts.

Example:
Order From Least To Greatest:
2 3/5 2 1/2 3 1/4

Since 3 > 2 3 1/4 is the biggest mixed number.
To compare 2 3/5 and 2 1/2 find equivalent fractions.

Step 1:
3/5 x 2/2 = 6/10
1/2 x 5/5 = 5/10
Step 2: Remember to compare the numerators.
6 > 5
REMEMBER TO WRITE THE ORIFGINAL MIXED NUMBERS.
2 1/2; 2 3/5; 3 1/4

Adding & Subtracting Fractions With Unlike Denominators


Question:
What is a Least Common Denominator? (LCD)

Answer:
When fractions have the same denominator you can say they have a common denominator.

When you add/subtract fractions, it helps the find the smallest common denominator or LCD of the two fractions.


Question:
How do we add/subtract fractions with unlike denominators?

Answer:
Step 1: Find the LCD of the denominators.
Step 2: Create equivalent fractions.
Step 3: Add/Subtract
Step 4: Simplify

Example:
Add:
1/6 + 3/4
Step 1:
The LCD of 4 and 6 is 12.
Step 2:
1/6 x 2/2 = 2/12
3/4 x 3/3 = 9/12
Step 3:
2/12 + 9/12 = 11/12

Example:
Subtract:
5/6 – 3/10
Step 1:
The LCD of 6 and 10 is 30.
Step 2:
5/6 x 5/5 = 25/30
3/10 x 3/3 = 9 30
Step 3:
25/30 – 9/30 = 14/30
Step 4:
14/30 ÷ 2/2 = 7/15

Mulitplying & Dividing Fractions

Question:
How do we multiply fractions?

Answer:
Step 1: Multiply the numerator.
Step 2: Multiply the denominator.
Step 3: Simplify

Example:
7/ 8 ●2/3
Step 1: 7 x 2 = 14
Step 2: 8 x 3 = 24
Answer: 14/24
Step 3:
14/24 ÷ 2/2 = 7 12

Question:
What is a reciprocal?

Answer:
To find the reciprocal of a fraction “flip” the fraction, with the numerator taking the denominator’s place and the denominator taking the numerator’s place. When the fraction and its reciprocal are multiplied, the product is 1.

Question:
How do we divide fractions?

Answer:
Step 1: Find the reciprocal of the 2nd fraction.
Step 2: Change the division sign to a multiplication sign.
Step 3: Multiply the numerator.
Step 4: Multiply the denominator.
Step 5: Simplify

Example:
2/5 ÷ 5/6
Step 1: Reciprocal of 5/6 is 6/5
Step 2:
2/5 ● 6/5
Step 3: 2 x 6 = 12
Step 4: 5 x 5 = 25
Answer: 12/25

Adding & Subtracting Mixed Numbers

Question:
How do we add/subtract mixed numbers?

Answer:
Step 1: Rename the fractions so that they have the same denominator.
Step 2: Add/Subtract the fractions.
Step 3: Add/Subtract the whole numbers.
Step 4: Simplify.

Example:
Add:
1 1/2 + 2 3/4
Step 1:
1/2 x 2/2 = 2/4
3/4 x 1/1 = 3/4
Step 2:
2/4 + 3/4 = 5/4
Step 3:
1 + 2 = 3
Answer: 3 5/4
***Because the fractional part you have to change it into a mixed number and add it to your answer.
New Mixed number is 1 1/4
Add the Whole number parts together and keep the new fractional part.
Final Answer: 4 1/4

Example:
Add:
4 5/8 + 3 1/4
Step 1:
5/8 x 1/1 = 5/8
1/4 x 2/2 = 2/8
Step 2:
5/8 + 2/8 = 7/8
Step 3: 4 + 3 = 7
Answer: 7 7/8

Example:
Subtract:
5 1/5 – 2 ½
Step 1:
1/5 x 2/2 = 2/10
1/2 x 5/5 = 5/10
Step 2:
Because 5 > 2 you have to borrow from the whole number in order to create a bigger equivalent fraction.
So: 5 2/10 = 4 12/10
5 – 1 (10/10) = 4 Then add the borrowed 10 to the fractional part. So 2/10 becomes 12/10
Now you can subtract.
4 – 2 = 2
12/10 – 5/10 = 7/10
Answer: 2 7/10

Mulitplying & Dividing Mixed Numbers

Question:
How do we multiply mixed numbers?

Answer:
Step 1: Change the mixed number to an improper fraction.
Step 2: Multiply the numerator.
Step 3: Multiply the denominator.
Step 4: Simplify

Example:
1 1/2 ● 12
Step 1:
3/12 ● 12/1
Step 2:
3 x 12 = 36
Step 3:
12 x 1 = 12
Answer: 36/2
Step 4:
36/2 = 18

Example:
2 2/3 ● 1 1/4
Step 1:
7/3 ● 5/4
Step 2:
7 x 5 = 35
Step 3:
3 x 4 = 12
Answer: 35/12
Step 4:
2 11/12

Question:
What is a reciprocal?

Answer:
To find the reciprocal of a fraction “flip” the fraction, with the numerator taking the denominator’s place and the denominator taking the numerator’s place. When the fraction and its reciprocal are multiplied, the product is 1.

Question:
How do we divide mixed numbers?
Answer:
Step 1: Change the mixed number to an improper fraction.
Step 2: Find the reciprocal of the 2nd fraction.
Step 3: Change the division sign to a multiplication sign.
Step 4: Multiply the numerator.
Step 5: Multiply the denominator.
Step 6: Simplify

Example:
2 3/4 ÷ 1 1/2
Step 1:
11/4 ÷ 3/2
Step 2:
Reciprocal of 3/2 is 2/3
Step 3:
11/4 ● 2/3
Step 4:
11 x 2 = 22
Step 5:
4 x 3 = 12
Answer:
22/12
Step 6:
22/12 ÷ 2/2 = 11/6 = 1 5/6

Example:
1 4/5 ÷ 1 1/2
Step 1:
9/5 ÷ 3/2
Step 2:
Reciprocal of 3/2 is 2/3
Step 3:
9/5 ●2/3
Step 4;
9 x 2 = 18
Step 5:
5 x 3 = 15
Answer:
18/15
Step 6:
1 3/15 = 1 1/5
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