holt ca course 1 3-4 equivalent fractions and mixed numbers ns2.4 determine the least common...
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Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
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
California Standards
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
VOCABULARY CARDS
• Numerator
• Denominator
• Equivalent Fractions• Improper Fraction• Mixed Number• Simpliest Form
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Different fractions can name the same number.
35 = = 15
256
10
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
=
To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.
In the diagram = . These are called
equivalent fractions because they are different expressions for the same nonzero number.
35
610
1525
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Find two fractions equivalent to .
Teacher Example 1: Finding Equivalent Fractions
57
5 27 2
= 1014
Multiply the numerator and denominator by 2.
5 37 3 = 15
21Multiply the numerator and denominator by 3.
Remember!A fraction with the same numerator and
denominator, such as is equal to 1.2 2
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
5 7
The fractions , , and are equivalent,
but only is in simplest form. A fraction is in
simplest form when the greatest common divisor
of its numerator and denominator is 1.
57
1014
1521
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Student Practice 1:
Find two fractions equivalent to .
6 212 2 = 12
24Multiply the numerator and denominator by 2.
6 ÷ 212 ÷ 2
= 36
Divide the numerator and denominator by 2.
612
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Write the fraction in simplest form.
Teacher Example 2: Writing Fractions in Simplest Form
1824
Find the GCD of 18 and 24.
The GCD is 6 = 2 • 3.
=1824
Divide the numerator and denominator by 6.
18 = 2 • 3 • 3
24 = 2 • 2 • 2 • 3
18 ÷ 624 ÷ 6 = 3
4
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Write the fraction in simplest form.
Student Practice 2:
1545
Find the GCD of 15 and 45.
The GCD is 15 = 3 • 5.
=1545
Divide the numerator and denominator by 15.
15 = 3 • 5
45 = 3 • 3 • 5
15 ÷ 1545 ÷ 15 = 1
3
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
Determine whether the fractions in each pair are equivalent.
Teacher Example 3A:
Determining Whether Fractions are Equivalent
and 46
2842
Simplify both fractions and compare.
46 = 4 ÷ 2
6 ÷ 2 = 23
2842
= 28 ÷ 1442 ÷ 14 = 2
3
are equivalent because both are equal to . and 46
2842
23
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Teacher Example 3B:
Determine whether the fractions in each pair are equivalent.
and 610
2025
Simplify both fractions and compare.
= 6 ÷ 210 ÷ 2 = 3
52025
= 20 ÷ 525 ÷ 5 = 4
5
610
are not equivalent because their simplestand 2025
610forms are not equal.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Student Practice 3A:
Simplify both fractions and compare.
39 = 3 ÷ 3
9 ÷ 3 = 13
= 6 ÷ 618 ÷ 6 = 1
3
and 39
618
618
Determine whether the fractions in each pair are equivalent.
are equivalent because both are equal to . and 39
618
13
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Student Practice 3B:
and 412
948
Simplify both fractions and compare.
= 4 ÷ 412 ÷ 4 = 1
3
948
= 9 ÷ 348 ÷ 3 = 3
16
412
Determine whether the fractions in each pair are equivalent.
are not equivalent because their simplestand 948
412forms are not equal.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
85 = 13
5
85 is an improper
fraction. Its numerator is greater than itsdenominator.
135 is a mixed
number. Itcontains both awhole numberand a fraction.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
4A. Write
Teacher Example 4:
Converting Between Improper Fractions and Mixed Numbers135
as a mixed number.
First divide the numerator by the denominator.
135
= 2 35
Use the quotient and remainder to write the mixed number.
4B. Write 7 23 as an improper fraction.
First multiply the denominator and whole number,and then add the numerator.
2233
+
= 3 7 + 23 = 23
3
Use the result to write the improperfraction.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Student Practice 4:
4A. Write 156 as a mixed number.
First divide the numerator by the denominator.
156
= 2 36
Use the quotient and remainder to write the mixed number.
4B. Write 8 13
as an improper fraction.
First multiply the denominator and whole number,and then add the numerator.
113388
+
= 3 8 + 13 = 25
3
Use the result to write the improperfraction.
12
= 2
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