The problem here is to add and|
These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before adding them together.

For the denominators here, the 8 and 14, a common denominator for both is 56. With the common denominator, the
becomes a
and the
becomes a
So now our addition problem becomes this...
The problem here is to add and|
Since these two fractions have the same denominators (the numbersunder the fraction bar), we can add them together by simply adding the numerators (the 21 and 36 = 57), while keeping the same denominator (the 56).

Our answer here is:
The fraction is an improper fraction (the numerator is greater than the denominator). While there is nothing incorrect about this, an improper fraction is typically simplified further into a mixed number.

The whole number part of the mixed number is found by dividing the 57 by the 56. In this case we get 1.
The fractional part of the mixed number is found by using the remainder of the division, which in this case is 1 (57 divided by 56 is 1 remainder 1). The final answer is: |

The problem here is to add and|

These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before adding them together.

For the denominators here, the 9 and 12, a common denominator for both is 36. With the common denominator, the
becomes a
and the
becomes a
So now our addition problem becomes this...
The problem here is to add and|
Since these two fractions have the same denominators (the numbersunder the fraction bar), we can add them together by simply adding the numerators (the 20 and 21 = 41), while keeping the same denominator (the 36).

And, we just add the whole number parts, or 7 + 2 = 9.
Our answer here is:
The fraction is an improper fraction (the numerator is greater than the denominator). While there is...

...In order to teach students the concept of equivalence when working with fractions with unlike denominators or finding equivalent fractions, there are some skills that the students must already possess. These are as follows:
Students are able to both recognize and write fractions
Students understand the ‘breakdown’ of a fraction where the top is the numerator and the bottom is the denominator
Students must have some understanding of equivalence and what it means
Students must be able to both multiply and divide with relative ease
The concept of finding equivalent fractions could be introduced using manipulative. One of these manipulative that would be extremely useful would be the pies. The ‘pie kit’ could be made or purchased, but both would include a large amount of pies with each being cut into different sizes with each ‘slice’ having a specific value on it (i.e. 1/3, 1/4, 1/2, 1/16, etc.). Using this visual manipulative, students would able to see the equivalent of various fractions (i.e. 1/2 is equivalent to 2/4 and 3/3 is equivalent to 16/16).
The steps for finding equivalent fractions would begin by having an overhead (for a large class) or having the children at a large group table (for a smaller class). Either one of these ways would allow the teacher to utilize the pie manipulative to show the students equivalents. To begin the students could see...

...multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
Standard Based Objective:
When given division problems with fractions, students will use the rules for dividing fractions to solve problems with 80% accuracy as measure by student work samples by the end of the week.
Materials
Paper
Pencils
White Board
Yellow and Pink Post it’s (teacher use)
Dry Erase Markers
Elmo Projector
Classwork pg. 134 (12-20)
Opening
Attention
“Okay you guys, lets begin.”
Review
Teacher writes 1) 4/7 x 8/7= 2) 1/3 x 4/5 = on the white board. “So for the last couple of days we have been learning how to multiply fractions. Before we move on I want to review them.” Teacher passes out paper. I want you to try problems #1 and #2 on your own; I will give you five minutes. Teacher allows students to work. Ok who can tell me what’s the first step we have to do to this problems. Yes we make sure the fractions are lined up horizontally. And then? Then we multiply across. Good. So what do we multiply first? Yes, we take the numerators and multiply which is 4 x 8= 32, what do we do next? Good we multiply the denominators, 7 x 7= 49. Ok, so is my answer 32/49. Teacher follows the same procedure for problem #2.
Goals
“Today we are going to make our fractions do tricks like flip in reverse, move from the top to the bottom and to the bottom...

...In elementary math there are several concepts about fractions. One concept students in fourth grade will need to master is learning how to tell if fractions are equivalent with unlike denominators. There are a few prerequisite skills that are necessary in order for the students to understand this concept. The first thing students need to know is what fractions are. Fractions are a way of counting parts of a whole. Secondly, the students need to know how to identify parts of a fraction. The top number in a fraction is the numerator. The numerator is the number of parts in a whole (Eather). The bottom number in a fraction is the denominator. The denominator is the number of parts the whole is divided into (Eather). Lastly, the student will need to have a basic knowledge of their multiplication and division facts. This will help the students in deciding whether or not the fraction is indeed equivalent or not.
The first step in teaching students about equivalent fractions is to have a whole class conversation using manipulatives or visual aides. I would start the lesson with an overhead projection or use of a mimeo board in order to show the students what equivalent fractions look like. I would start with two circles on the board, one divided into two pieces and one divided into four. You can show the students by coloring in one of the...

...Definition: A Mixed Fraction is a
whole number and a fraction combined,
such as 1 3/4.
1 3/4
(one and three-quarters)
To make it easy to add and subtract them, just convert to Improper Fractions first:
4/43/4
Quick Definition: An Improper fraction has a
top number larger than or equal to
the bottom number,
such as 7/4 or 4/3
(It is "top-heavy")
7/4
(seven-fourths or seven-quarters)
Adding MixedFractions
I find this is the best way to add mixed fractions:
convert them to Improper Fractions
then add them (using Addition of Fractions)
then convert back to Mixed Fractions:
Example: What is 2 3/4 + 3 1/2 ?
Convert to Improper Fractions:
2 3/4 = 11/4
3 1/2 = 7/2
Common denominator of 4:
11/4 stays as 11/4
7/2 becomes 14/4
(by multiplying top and bottom by 2)
Now Add:
11/4 + 14/4 = 25/4
Convert back to Mixed Fractions:
25/4 = 6 1/4
When you get more experience you can do it faster like this:
Example: What is 3 5/8 + 1 3/4
Convert them to improper fractions:
3 5/8 = 29/8
1 3/4 = 7/4
Make same denominator: 7/4 becomes 14/8 (by multiplying top and bottom by 2)
And add:
29/8 + 14/8 = 43/8 = 5 3/8
Subtracting Mixed Fractions
Just follow the same method, but subtract instead of add:
Example: What is 15 3/4 - 8 5/6 ?
Convert to Improper...

...Fractions are ways to represent parts of a whole. Common fractions are ½ and ¾. These are proper or regular fractions. Some fractions are called mixed numbers. These are represented by a whole number with a fraction (proper fraction). 1 ½ and 2 ¾ are good examples. An improper fraction has a larger number on the top than on the bottom, such as 9/8. I will explain how to convert thesefractions to decimals. I will show you how to change an improper fraction to a mixed number. Operations (addition, subtraction, multiplication, and division) will be explained as well.
CONVERSIONS
This section will explain how to convert a fraction into a decimal. First, let's get an example fraction. How about 3/8? To find a decimal, divide the numerator (top number) by the denominator (bottom number). So we would divide 3 by 8. 3)8=0.375 or .38. Lets do another. Try 1/3. 1)3=.33333... So 1/3 is equal to about.33.
Next comes the mixed numbers to the improper fractions . All you do is multiply the denominator by the whole number and add the numerator. This is the numerator of the improper fraction. You keep the same denominator. Let's try 2¾. Four times two is eight. Eight plus three is eleven. Keep the denominator and you have 11/4. Now to convert the improper fraction into a mixed number. You...

...In Lacsap’s Fractions, En(r) refers to the (r+1)th term in the nth row. The numerator and denominator are found separately, therefore to find the general statement, two different equations, one for the numerator and one for the denominator, must be found. Let M=numerator and let D=denominator so that En(r) = M/D.
To find the numerator for any number of Lacsap’s Fractions, an equation must be made that uses the row number to find the numerator. Because the numerator changes depending on the row, the two variables (row number and numerator) must be compared. To find this equation, the relationship between the row number and numerator must be found, put it graph form, and the equation for the graph will be the equation needed.
Row Number, n | Numerator, N |
1 | 1 |
2 | 3 |
3 | 6 |
4 | 10 |
5 | 15 |
Numerator
Numerator
Row Number
Row Number
The equation for the numerator can be derived by using quadratic regression on a graphing calculator. The equation is; y = .5x2 + .5x. This translates into; M=.5n2+.5n, where n=row number, and M=numerator. This means that any numerator from a certain row number can be found by using this equation. For example, to find the numerator of the sixth row, “6” needs to be substituted in for n.
M= .5n2 + .5n
M= .5(6)2 + .5(6)
M= .5(36) + .5(6)
M= 18 + 3
M= 21
The Numerator for row six is 21
They method to find the equation for the denominator is similar, but...

...Grade 7 Math Test
Fractions, decimals and percents
Part A: Multiple Choice - Circle the letter of the correct answer. (20 marks)
1. Estimate which answer is less than 1.
a) b) c) d)
2. Which quiz mark would be the same as 80%?
a) b) c) d)
3. What is the best estimate for the percentage that is shaded in the diagram?
a) 33% b) 50% c) 66% d) 110%
4. How much is of 35 ?
a) 175 b) 70 c) 14 d) 7
5. A recipe calls for of a cup of sugar. Jordan wants to make of the recipe. How much sugar will Jordan need?
A. B. C. D.
6. In the gym of the people are men, of the people are women, and the rest are children. If there are 420 people in the gym, how many are children?
A. 105 B. 175 C. 245 D. 120
7. Which answer is least ?
A. 3 - 1
B. +
C. 1 + 1
D. 2 -
8. Which of the following fractions can be written as a terminating decimal?
A. B. C. D.
9. Which decimal represents ?
A. 0.125 B. 0.58 C. 0.6 D. 0.625
10. 1 is fractions between which set of numbers?
A. 1.3 and 1.4
B. 1.2 and 1.3
C. 1.1 and 1.2
D. 1.4 and 1.5
11. Write the fraction in simplest form (lowest terms)
A.
B.
C.
D.
12. Which does not mean 75%?
A.
B. 0.75
C.
D.
13. If = 0.090909…. = 0.181818…. = 0.272727….. Then 0.6363636……would equal:
A.
B....

...Once students get to the fourth grade, learning equivalence in fractions with unlike denominators is something that they can look forward to...or not look forward to. It can be a very tough lesson and something that is hard for the children to understand. They need to have a simple understanding of fractions already. They need to know what they are and how they add up together. Meaning that they need to understand that fractions are a part of a whole...a fraction of something, and that if the fractions are equal they can add up to create a whole. The easiest way to describe this and review it is with a circle representing a pie. Each slice comes from the pie and all put together its a whole. Also the stronger the students is with their multiplication tables and the corresponding division facts, the easier this lesson is going to be for them. But by the time the students get to the fourth grade they should have already been introduced to them and have a firm understanding of what they are and how to identify them.
One of the best ways to introduce the ideas of equialent fractions with unlike denominators are with visual aids. A fantastic way to introduce this is with a hands on activity for the children. Each child will have a baggie of "pie pieces" or wedge pieces of a circle in different fractions, and a sheet of paper with a whole circle drawn on it. (I have attached a...