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Find the sum: 4 4 7 + 1 2 7 .

5 6 7

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Find the sum: 2 3 11 + 5 6 11 .

7 9 11

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In [link] , the sum of the fractions was a proper fraction . Now we will work through an example where the sum is an improper fraction.

Find the sum: 9 5 9 + 5 7 9 .

Solution

9 5 9 + 5 7 9
Add the whole numbers and then add the fractions.
9 5 9 + 5 7 9 _____ 14 12 9
Rewrite 12 9 as an improper fraction. 14 + 1 3 9
Add. 15 3 9
Simplify. 15 1 3
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Find the sum: 8 7 8 + 7 5 8 .

16 1 2

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Find the sum: 6 7 9 + 8 5 9 .

15 1 3

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An alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.

Add by converting the mixed numbers to improper fractions: 3 7 8 + 4 3 8 .

Solution

3 7 8 + 4 3 8
Convert to improper fractions. 31 8 + 35 8
Add the fractions. 31 + 35 8
Simplify the numerator. 66 8
Rewrite as a mixed number. 8 2 8
Simplify the fraction. 8 1 4

Since the problem was given in mixed number form, we will write the sum as a mixed number.

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Find the sum by converting the mixed numbers to improper fractions:

5 5 9 + 3 7 9 .

9 1 3

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Find the sum by converting the mixed numbers to improper fractions:

3 7 10 + 2 9 10 .

6 3 5

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[link] compares the two methods of addition, using the expression 3 2 5 + 6 4 5 as an example. Which way do you prefer?

Mixed Numbers Improper Fractions
3 2 5 + 6 4 5 9 6 5 9 + 6 5 9 + 1 1 5 10 1 5 3 2 5 + 6 4 5 17 5 + 34 5 51 5 10 1 5

Model subtraction of mixed numbers

Let’s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.

We will use fraction circles (pizzas!) to help us visualize the process.

Start with one whole.

A shaded circle is shown. Below it is a 1. There are arrows pointing to a shaded circle divided into 2 equal parts. Below it is 2 over 2. Next to this are two circles, each divided into 2 equal parts. The top circle has the right half shaded and the bottom circle has the left half shaded.

Algebraically, you would write:

On the left, it says 1 minus 1 half. There is an arrow pointing to 2 over 2 minus 1 over 2. There is another arrow pointing to 2 over 2 minus 1 over 2 equals 1 over 2.

Use a model to subtract: 1 1 4 .

3 4

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Use a model to subtract: 1 1 5 .

4 5

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What if we start with more than one whole? Let’s find out.

Use a model to subtract: 2 1 5 .

9 5

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Use a model to subtract: 2 1 3 .

5 3

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In the next example, we’ll subtract more than one whole.

Use a model to subtract: 2 1 1 3 .

2 3

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Use a model to subtract: 2 1 1 4 .

3 4

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What if you start with a mixed number    and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a $1 bill and one quarter. What could you do? You could change the dollar bill into 4 quarters. The value of 4 quarters is the same as one dollar bill, but the 4 quarters are more useful for the parking meter. Now, instead of having a $1 bill and one quarter, you have 5 quarters and can put 3 quarters in the meter.

This models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.

We can also model this using fraction circles, much like we did for addition of mixed numbers.

Use a model to subtract: 1 1 4 3 4

Solution

Rewrite vertically. Start with one whole and one fourth. . .
Since the fractions have denominator 4, cut the whole into 4 pieces.
You now have 4 4 and 1 4 which is 5 4 .
. .
Take away 3 4 .
There is 1 2 left.
. .
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Questions & Answers

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They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
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Genetics is the study of heredity
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the study of living organisms and their interactions with one another and their environments
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the study of living organisms and their interactions with one another and their environment.
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list any five characteristics of the blood cells
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is like gone fail us
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cells is the basic structure and functions of all living things
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is organisms that are similar into groups called tara
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A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
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Diversity of living thing
ISCONT
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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