Transcript Equivalent fractions and mixed numbers
3-4 Equivalent Fractions and Mixed Numbers
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Warm Up
Name a common factor for each pair.
Possible answers:
1. 5 and 10
5
2. 9 and 12
3
3. 20 and 24
4
4. 10 and 14
2
5. 6 and 8
2
6. 8 and 15
1
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
California Standards
NS2.4 Determine
the least common multiple and
the greatest common divisor of whole numbers; use them to solve problems with fractions
(
e.g.
to find a common denominator to add two fractions or
to find the reduced form of a fraction
).
Also covered:
NS1.1
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Vocabulary
equivalent fractions improper fraction mixed number
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Different fractions can name the same number.
Holt CA Course 1 3 5 = 6 10 = 15 25
3-4 Equivalent Fractions and Mixed Numbers
In the diagram = 6 10 = 15 25 . These are called equivalent fractions because they are different expressions for the same nonzero number.
To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
8 5 is an improper fraction. Its numerator is greater than its denominator.
8 5 = 1 3 5
1 3 5 is a mixed number. It contains both a whole number and a fraction.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
To determine if two fractions are equivalent, simplify the fractions.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers Additional Example 1: Finding Equivalent Fractions
5 7 2 2
Multiply the numerator and denominator by 2.
5 7 3 3
Multiply the numerator and denominator by 3.
Remember!
A fraction with the same numerator and denominator, such as is equal to 1.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
5 7 simplest form when the greatest common divisor of its numerator and denominator is 1.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers Additional Example 3A: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent.
4 6
4 6 Simplify both fractions and compare.
4 6 = 4 ÷ 6 ÷ 2 2 28 42 and 28 42 14 14
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers Additional Example 3B: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent.
6 10
Simplify both fractions and compare.
6 10 2 2 6 10 20 25 5 5 are not equivalent because their simplest forms are not equal.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers Additional Example 4: Converting Between Improper Fractions and Mixed Numbers A. Write 13 5 as a mixed number.
First divide the numerator by the denominator.
13 5 = 2 3 5
Use the quotient and remainder to write the mixed number.
B. Write 7 2 3 as an improper fraction.
First multiply the denominator and whole number, and then add the numerator.
+ 2 3 = 3 7 + 2 3
Use the result to write the improper fraction.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers Check It Out!
Example 1
6 12 2 2 6 ÷ 12 ÷ 2 2
Holt CA Course 1
Multiply the numerator and denominator by 2.
Divide the numerator and denominator by 2.
3-4 Equivalent Fractions and Mixed Numbers Check It Out!
Example 2
Find the GCD of 15 and 45.
15 = 3 • 5
The GCD is 15 = 3 • 5.
45 = 3 • 3 • 5 15 45 = 15 ÷ 45 ÷ 15 15
Divide the numerator and denominator by 15.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers Check It Out!
Example 3A Determine whether the fractions in each pair are equivalent.
3 9 and 6 18
Simplify both fractions and compare.
3 9 = 6 18 3 ÷ 9 ÷ 3 3 6 6 3 9 and 6 18
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers Check It Out!
Example 4 A. Write 15 6 as a mixed number.
First divide the numerator by the denominator.
15 6 = 2 3 6 = 2 1 2
Use the quotient and remainder to write the mixed number.
B. Write 8 1 3 as an improper fraction.
First multiply the denominator and whole number, and then add the numerator.
+
8
1 3 = 3 8 + 1 3
Use the result to write the improper fraction.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers Lesson Quiz
1 2 , 3 6 no 1 3 2 1 8 31 7
Holt CA Course 1