1. Where in life is this useful?
a) Cooking: [pic]
b) Measurements (construction, remodeling, etc): [pic] c) Time: [pic]
d) Money: [pic]

2. Fractions with the same (“common”) denominators
Example: (without converting back & forth from mixed numbers):

[pic]

[pic]

3. Fractions with different denominators
In order to add (or subtract) fractions with different denominators (as a reminder, that’s the bottom number), you’ll need to convert them to have the same denominators. This is one place where we get to use the “least common multiple” that we talked about a while ago.

Let’s start with money, because we all do that conversion frequently, and without thinking about what we’re doing. If we add a quarter & a nickel, we know off the top of our head that we have 30 cents, or 30/100 of a dollar. But what is the math that we’re doing?

[pic]

First, we need to convert to a common denominator. For money, rather than worrying about the lowest common denominator, we automatically convert to hundredths. We do that by multiplying by one in the form of a fraction: [pic]. We can do this because multiplying a number by 1 does not change its value. So, we now have: [pic]. All we’ve done is converted the quarter to 25 cents and the nickel to 5 cents. From this point, we can add them: [pic]. We don’t give much thought to all these steps that we go through, but as soon as it is phrased as “adding fractions”, it seems to get much harder!

Now, let’s try a more abstract case. For no particular reason, we need to add 1/3 to 1/4. The LCM for 3 & 4 is 12 (if you get stuck finding the LCM, and don’t mind dealing with larger numbers, you can multiply the denominators and reduce your answer at the end). So: [pic]. With a little practice, you’ll be able to skip writing 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...

...Fraction (mathematics)
A fraction (from Latin: fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: \tfrac{1}{2} and 17/3) consists of an integer numerator, displayed above a line (or before a...

...Fractions
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...

...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...

...Lacsap’s Fractions
IB Math 20 Portfolio
By: Lorenzo Ravani
Lacsap’s Fractions Lacsap is backward for Pascal. If we use Pascal’s triangle we can identify patterns in Lacsap’s fractions. The goal of this portfolio is to ﬁnd an equation that describes the pattern presented in Lacsap’s fraction. This equation must determine the numerator and the denominator for every row possible.
Numerator
Elements of the Pascal’s triangle form...

...Partial Fractions
Introduction to Partial Fractions Given a rational function of the form p(x) q (x) where the degree of p(x) is less than the degree of q (x), the method of partial fractions seeks to break this rational function down into the sum of simpler rational functions. In particular, we are going to try to write the original function as a sum of rational functions where the degrees of the polynomials involved are as small as possible. The...

...Mixed Fractions
(Also called "Mixed Numbers")
| | A Mixed Fraction
is a
whole number
and a proper fraction
combined.
such as 1 3/4. |
1 3/4 | | |
(one and three-quarters) | | |
Examples
2 3/8 | 7 1/4 | 1 14/15 | 21 4/5 |
See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number).
Names
We can give names to every...

...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...

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