By LearningExpress Editors

Updated on Aug 24, 2011

To review these concepts, go to Defining Fractions Study Guide.

### Practice

Write the shaded part of each circle below as a fraction.

Use the circles shown below each fraction to represent that fraction.

Label each fraction as "proper" or "improper."

Label each pair of fractions as "like" or "unlike."

- and
- and
- and

Place the proper symbol (>, <, or =) between each pair of fractions.

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- –
- –
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Reduce each of the fractions below to its simplest form.

### Solutions

- This circle is divided into 3 equal parts, so the denominator of the fraction will be 3. There are 2 parts of the circle that are shaded, so the numerator of the fraction will be 2. Because 2 out of 3 parts are shaded, of the circle is shaded.
- This circle is divided into 4 equal parts, so the denominator of the fraction will be 4. There are 3 parts of the circle that are shaded, so the numerator of the fraction will be 3. Because 3 out of 4 parts are shaded, of the circle is shaded.
- This circle is divided into 5 equal parts, so the denominator of the fraction will be 5. There are 4 parts of the circle that are shaded, so the numerator of the fraction will be 4. Because 4 out of 5 parts are shaded, of the circle is shaded.
- To represent the fraction, 1 out of 2 parts must be shaded. Divide the circle into 2 equal parts and shade 1 of them:
- To represent the fraction, 5 out of 6 parts must be shaded. Divide the circle into 6 equal parts and shade 5 of them:
- The numerator of this fraction is greater than its denominator. Because the fraction has a value that is greater than 1, it is improper.
- The numerator of this fraction is the same as its denominator. Because the fraction has a value of –1, it is improper.
- The numerator of this fraction is less than its denominator. Because the fraction has a value that is less than 1 and greater than –1, it is proper.
- The numerator of this fraction is less than its denominator. Because the fraction has a value that is less than 1 and greater than –1, it is proper.
- The denominators of these fractions are different, so these are unlike fractions.
- The denominators of these fractions are the same, so these are like fractions.
- Even though the second fraction is improper, the denominators of these fractions are the same, so these fractions are like.
- The least common denominator for and is 12. =(both the numerator and denominator are 3 times bigger).
- The least common denominator for and is 24. (both the numerator and denominator are 3 times bigger) and numerator and denominator are 4 times bigger). Because 21 is greater than 20, .
- The least common denominator for and is 10. (both the numerator and denominator are 5 times bigger). Because 5 is less than .
- The least common denominator for and is 35. (both the numerator and denominator are 7 times bigger) and (both the numerator and denominator are 5 times bigger). Because 21 is greater than 20, .
- Any number over itself is equal to 1, so both fractions, and , are equal to 1, so .
- First, list the factors of the numerator and the denominator. The factors of 10 are 1,
**2**, 5, and 10, and the factors of 16 are 1,**2**, 4, 8, and 16. The greatest common factor is 2: and ; reduces to . - List the factors of the numerator and the denominator. The factors of 12 are 1, 2, 3,
**4**, 6, and 12, and the factors of 20 are 1, 2,**4**, 5, and 20. The greatest common factor is 4. and . reduces to . - List the factors of the numerator and the denominator. The factors of 24 are 1, 2,
**3**, 4, 6, 8, 12, and 24, and the factors of 27 are 1,**3**, 9, and 27. The greatest common factor is 3. and . reduces to . - List the factors of the numerator and the denominator. The factors of 30 are 1, 2, 3, 5,
**6**, 10, 15, and 30, and the factors of 48 are 1, 2, 3, 4,**6**, 8, 12, 16, 24 and 48. The greatest common factor is 6. and . reduces to . - List the factors of the numerator and the denominator. The factors of 56 are 1, 2, 4, 7,
**8**, 14, 28, and 56, and the factors of 72 are 1, 2, 3, 4, 6,**8**, 9, 12, 18, 24, 36 and 72. The greatest common factor is 8. and . reduces to .

From Express Review Guides: Fractions, Percentages, & Decimals. Copyright © 2008 by LearningExpress, LLC. All Rights Reserved.

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