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**Brought to you by Tutorial Services – The Math Center**

Fractions Brought to you by Tutorial Services – The Math Center

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**Fractions In this workshop, you will learn to:**

Change mixed numbers to improper fractions and improper fractions to mixed numbers How to find common denominators Add and subtract fractions and mixed numbers Raise and reduce fractions Multiply and divide using fractions and mixed numbers

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**Fractions What is a numerator and a denominator? Numerator - part**

Denominator - whole

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**Mixed Numbers and Improper Fractions**

What are mixed numbers and improper fractions? How can we convert improper fractions into mixed numbers? To change an improper fraction into a mixed number: 1.Divide the numerator by denominator to get a whole number part. 2. Put the remainder over the denominator to get the fractional part of the mixed number. Example 1. Change to simpler terms Solution: 25 15 3 = 25 5 = 5 and = 15 4 = 3 5 4 4

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**Mixed Numbers and Improper Fractions**

To change a mixed number into improper fraction: 1. Multiply the whole number by the denominator. 2. Add the value to the numerator of the fraction. 3. Write the sum over the original denominator. Example 2. Change to an improper fraction. Solution: + 4 34 6 = 5 5 x

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Common Denominators To find a common denominator, you look for the lowest number that each denominator can divide into evenly. What is this number called? Lowest Common Denominator or the LCD Example 1: Find the LCD of LCD = 9 If this was not possible, and the denominators of the fractions are small, try multiplying their denominators times each other. Example 2: Find the LCD of LCD = 4 x 3 = 12

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**Common Denominators Continued**

In some occasions, you will have to go through a series of multiples of each in order to find the lowest number both the denominators can divide into equally. 4 6 4 6 Example 3: Find the LCD of 8 12 12 18 If finding an LCD becomes too time consuming, try multiplying the set of denominators by each other. Example 4: Find the LCD of LCD = 3 x 5 x 7 = 105

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**Raising and Reducing Fractions**

In some cases fractions will either be raised to higher terms or be reduced to lower terms. In either case, you are changing both the numerator and denominator of the fraction to a fraction that has the same numerical value, or an equivalent fraction. Example 1: Raise to fractions with a denominator of 20. 1 10 10 1 4 4 Solution: x and x = = 2 10 20 5 4 20 Example 2: Reduce to lowest terms. 9 9 1 Solution: = 18 9 2

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**Adding and Subtracting Fractions and Whole Numbers with Common Denominators**

So what is the LCD good for? Lets put it into practice with adding and subtracting these mixed numbers and fractions. 12 1 Example 1: = 12 2 1 Example 2: = 14 7 3 1 Example 3: 3 = 3 9 3 5 1 Example 4: 5 = 5 15 3

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**Adding and Subtracting Fractions and Whole Numbers with Unlike Denominators**

Now we need to find the common denominators in order to add these fractions. Lets try a few examples. 15 8 23 3 Example 1: + = = 1 20 20 20 20 10 3 7 Example 2: - = 15 15 15 8 3 11 Example 3: 4 + 6 = 10 12 12 12 2 6 8 2 - Example 4: 25 11 = 13 = 13 12 12 12 3

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**Multiplying Fractions and Mixed Numbers**

When you are multiplying fractions you do not have to find the LCD. Yet reducing and canceling the fraction can make the process easier. 1 1 2 3 3 8 6 2 Example 1: x x = 4 9 10 5 1 3 5 1 3 7 9 21 1 10 Example2: x = = 3 2 2 2 1

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**Dividing Fractions and Whole Numbers**

Now that we understand multiplying fractions, we can divide them as well. Dividing fractions goes hand in hand with multiplying fractions, so once we establish the reciprocal then we can multiply them. 5 5 25 1 Example 1: x = = 2 6 2 12 12 9 11 9 3 27 Example2: x = = 4 3 4 11 44

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**Tutorial Services – The Math Center**

Brought to you by Tutorial Services – The Math Center Questions?

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**Additional Fraction Help**

Fractions Handout Common Denominator Handout Fractions, Decimals, & Percentages Workshop Fractions Quiz Fractions, Decimals, & Percentages Quiz Understanding Percentages Handout

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