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Equivalent Fractions |
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Unit 14 > Lesson 3 of 11 |
What do the fractions in example 1 have in common?
Each fraction in example 1 represents the same number. These fractions are equivalent.
| Definition: |
Equivalent fractions are different fractions that name the same number. |
Let's look at some more examples of equivalent fractions.
| Example 2 |
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Two-thirds is equivalent to four-sixths.
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| Example 3 |
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The fractions three-fourths, six-eighths, and nine-twelfths are
equivalent.
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What would happen if we did not have shapes such as circles and
rectangles to refer to? Look at example 4 below.
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Example 4
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We need an arithmetic method for finding equivalent fractions.
| Procedure: |
To find equivalent fractions,
multiply the numerator AND denominator by the same nonzero whole
number. |
This procedure is used to solve example 4.
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Example 4
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You can multiply the numerator and the denominator of a fraction by any nonzero
whole number, as long as you multiply both by the
same whole number! For example, you can multiply the numerator and the denominator by
3, as shown in part A above. But you cannot multiply the
numerator by 3 and the denominator by 5. You can multiply the numerator and the denominator by
4, as shown in part B above. But you cannot multiply the
numerator by 4 and the denominator by 2.
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| The numerator and the denominator of a fraction must be multiplied by
the same nonzero whole number in order to have equivalent fractions. You may be wondering
why this is so. In the last lesson, we learned that a fraction that has the same
numerator and denominator is equal to one. This is shown below.
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| two-halves |
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| three-thirds |
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| four-fourths |
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| five-fifths |
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| six-sixths |
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So, multiplying a fraction by one does not change its value. Recapping example 4, we get:
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Example 4
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Multiplying the numerator and the denominator of a fraction by the same nonzero whole number will change
that fraction into an equivalent fraction, but it will not change its value.
Equivalent fractions may look different, but they have the same value. Let's look at some more examples of equivalent fractions.
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Example 5
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In example 6, the fraction given in part a is a proper fraction; whereas the fractions given
in parts b and c are improper fractions. Note that the procedure for finding equivalent
fractions is the same for both types of fractions. Looking at each part of example
6, the answers vary, depending on the nonzero whole number chosen. However, the equivalent fractions
found in each part all have the same value.
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Example 7
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Write the fraction five-sixths as an equivalent fraction with a denominator of 24.
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In example 7, we multiplied the numerator AND the denominator by 4.
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Example 8
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Write the fraction two-sevenths as an equivalent fraction with a denominator of 21.
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| Step 4:
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In example 8, we multiplied the numerator AND the denominator by 3.
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Example 9
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Write the fraction three-eighths as an equivalent fraction with a numerator of 15.
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In example 9, we multiplied the numerator AND the denominator by 5.
We can now redefine the terms fraction and equivalent fraction as follows:
| Summary: |
Equivalent fractions are different
fractions that name the same number. The numerator and the denominator of a fraction must be multiplied by
the same nonzero whole number in order to have equivalent fractions. |
Exercises
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In Exercises 1 through 5, click once
in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to
indicate whether your answer is correct or incorrect. To start over, click
CLEAR. Note: To write the fraction two-thirds, enter 2/3 into the form.
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| 1. |
Are the fractions three-fourths and fourteen-sixteenths equivalent (Yes or
No)?
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| 2. |
Write the fraction two-thirds as an equivalent fraction with a
denominator of 18. (Enter the entire fraction into the form.)
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| 3. |
Write the fraction eight-fifths as an equivalent fraction with a
numerator of 40. (Enter the entire fraction into the form.)
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| 4. |
Write the fraction seven-sevenths as an equivalent fraction with a
denominator of 19. (Enter the entire fraction into the form.)
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| 5. |
Write the fraction eleven-sevenths as an equivalent fraction with a
denominator of 56. (Enter the entire fraction into the form.)
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