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# Defining Fractions Practice Problems

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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."

1. and
2. and
3. and

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

Reduce each of the fractions below to its simplest form.

### Solutions

1. 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.
2. 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.
3. 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.
4. To represent the fraction, 1 out of 2 parts must be shaded. Divide the circle into 2 equal parts and shade 1 of them:
5. To represent the fraction, 5 out of 6 parts must be shaded. Divide the circle into 6 equal parts and shade 5 of them:
6. The numerator of this fraction is greater than its denominator. Because the fraction has a value that is greater than 1, it is improper.
7. The numerator of this fraction is the same as its denominator. Because the fraction has a value of –1, it is improper.
8. 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.
9. 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.
10. The denominators of these fractions are different, so these are unlike fractions.
11. The denominators of these fractions are the same, so these are like fractions.
12. Even though the second fraction is improper, the denominators of these fractions are the same, so these fractions are like.
13. The least common denominator for and is 12. =(both the numerator and denominator are 3 times bigger).
14. 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, .
15. The least common denominator for and is 10. (both the numerator and denominator are 5 times bigger). Because 5 is less than .
16. 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, .
17. Any number over itself is equal to 1, so both fractions, and  , are equal to 1, so .
18. 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  .
19. 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  .
20. 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  .
21. 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 .
22. 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  .

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