Learn around Equivalent fractions With instance Problems and Interactive Exercises.

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Use the complying with examples and also interactive exercises to learn about equivalent fractions.

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What carry out the fountain in example 1 have in common?

Example 1

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Each fraction in instance 1 represents the same number. This are equivalent fractions.

Definition: Equivalent fractions are different fractions the name the exact same number.

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Let"s look in ~ some an ext examples:

Example 2
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Two-thirds is indistinguishable to four-sixths.
Example 3

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The fractions three-fourths, six-eighths, and also nine-twelfths are equivalent.

What would happen if we did not have shapes such as circles and rectangles come refer to? look at at example 4 below.

Example 4

We require an arithmetic technique for finding same fractions.

 

Procedure:To find equivalent fractions, multiply the numerator and also denominator by the very same nonzero whole number.

This procedure is provided to solve instance 4.

Example 4
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You deserve to multiply the numerator and also the denominator that a fraction by any type of nonzero totality 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 displayed in component A above. But you cannot multiply the molecule by 3 and the denominator by 5. You deserve to multiply the numerator and the denominator by 4, as shown in component B above. Yet you cannot multiply the molecule by 4 and the denominator by 2.

The numerator and also the denominator that a portion must be multiplied by the very same nonzero whole number in order to have actually equal fractions. You might be wondering why this is so. In the last lesson, us learned the a fraction that has the exact same numerator and denominator is equal to one. This is shown below.

2/2 = 1 (Two-halves)

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3/3 = 1 (Three-thirds)

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4/4 = 1 (Four-fourths)

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5/5 = 1 (Five-fifths)

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6/6 = 1 (Six-sixths)

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So, multiply a fraction by one walk not adjust its value. Recapping example 4, we get:

Example 4
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Multiplying the numerator and also the denominator of a portion by the same nonzero totality number will readjust that fraction into an same fraction, however it will not change the value. Same fractions may look different, but they have the same value, hence equal.

Let"s look in ~ some more examples:

Example 5
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Example 6
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In instance 6, the portion given in part a is a proper fraction; vice versa, the fractions provided in parts b and also c are improper fractions. Note that the procedure for finding identical fractions is the exact same for both types of fractions. Looking in ~ each component of instance 6, the answer vary, depending on the nonzero totality number chosen. However, the equivalent fractions uncovered in each part all have the very same value.

Example 7
Write the fraction five-sixths together an equivalent portion with a denominator of 24.
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In instance 7, us multiplied the numerator and also the denominator through 4.

Example 8
Write the portion two-sevenths as an equivalent fraction with a denominator the 21.
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In instance 8, we multiplied the numerator and also the denominator by 3.

Example 9
Write the fraction three-eighths as an equivalent portion with a molecule of 15.
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In example 9, us multiplied the numerator and also the denominator through 5.

We can now redefine the terms fraction and equivalent fraction as follows:

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Summary: Equivalent fractions are various fractions that name the exact same number. The numerator and the denominator that a fraction must be multiplied by the exact same nonzero totality number in order to have actually equivalent fractions.

Exercises

In exercises 1 v 5, click when in response BOX and kind in your answer; then click ENTER. After girlfriend click ENTER, a article will show up in the outcomes BOX to indicate whether her answer is exactly or incorrect. To begin over, click CLEAR. Note: To write the portion two-thirds, enter 2/3 into the form.

1.Are the fractions three-fourths and also fourteen-sixteenths identical (Yes or No)?
 
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2.Write the portion two-thirds together an equivalent portion with a denominator that 18. (Enter the entire fraction into the form.)
 
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3.Write the portion eight-fifths as an equal fraction with a numerator of 40. (Enter the entire portion into the form.)
 
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Write the portion seven-sevenths as an equivalent portion with a denominator the 19. (Enter the entire portion into the form.)
 
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5.Write the portion eleven-sevenths as an equal fraction with a denominator the 56. (Enter the entire fraction into the form.)
 
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