1. Exercise Set 1.2: 2, 10, 13, 17, 23, 29, 33, 41 Least Common Multiple when asked
assignment

2. Unit 1: Foundations of algebra
Section 1.3: Fractions
Learning Target: I can write equivalent fractions.

3. Definition 1. A rational number is the quotient of one integer, called the numerator, divided by another nonzero integer, called the denominator. The word fraction is commonly used to denote a rational number.
fractions

4. Fractions such as , , and that have the same value are called equivalent fractions. Multiplying or dividing the numerator and denominator of a fraction by the same nonzero integer yields an equivalent fraction. A fraction can be reduced to an equivalent fraction in lowest terms by dividing its numerator and denominator by the greatest common factor of the numerator and denominator.
Equivalent fractions

5. Example 1: Reduce the following fractions to lowest terms:
(a) (b) (c) ∗ 5 3 ∗ ∗3∗ 5 5 ∗ 7 2
Equivalent fractions

6. Note. It is easier to use the properties of exponents to reduce ∗ 5 3 ∗ ∗3∗ 5 5 ∗ directly, but our intention is to show how the GCF is used.
Equivalent fractions

7. Example 2. Reduce the algebraic fraction 24 𝑥 2 𝑦 4 𝑧 7 18 𝑥 5 𝑦 2 𝑧 to lowest terms.
Equivalent fractions

8. An improper fraction whose numerator is greater than its denominator can be written as a mixed number. For example, 23 5 is written Conversely, a mixed number such as can be written as an improper fraction Question: What process do you use to do this?
Mixed numbers

9. Mixed numbers (a) Write the improper fraction 47 6 as a mixed number.
b) Write the mixed number as an improper fraction.
Mixed numbers

10. Adding and subtracting fractions
Adding (or subtracting) two fractions with the same denominator is easy. We simply add (or subtract) the numerators of the two fractions and divide the result by the common denominator of the two fractions. When the two denominators are different, we need to rewrite the fractions as equivalent fractions with a common denominator before we can add or subtract them. Generally, we choose the least common denominator (LCD). The next example shows how this is done. What is LCD more commonly known as for us now?
Adding and subtracting fractions

11. Adding and subtracting fractions
Example 3. Add or subtract the given fractions and reduce your answer to lowest terms.
(a) (b) (c) (d) 1 2∗ ∗ 3 2 ∗5
Adding and subtracting fractions

12. Multiplying and dividing fractions
Multiplying and dividing fractions is easier than adding and subtracting them because we do not have to find any common denominators. To multiply two fractions, we simply find the product of their numerators and divide by the product of their denominators. To divide one fraction by another, we take the first fraction and multiply it by the reciprocal of the second.
Multiplying and dividing fractions

13. Multiplying and dividing fractions
Examples: Simplify the following fractions:
A ∗ B ÷ C ∗1 1 4
D. (− 1 3 ) 2 +4
Multiplying and dividing fractions

14. Evaluating expressions with fractions
Find the value of the algebraic expression
3 𝑥 2 − 2 𝑦 if 𝑥=−2 and 𝑦=−5.
Evaluating expressions with fractions