1. Introducing: fraction form mixed form higher terms lower terms lowest terms identity HOW TO RENAME FRACTIONS

2. This picture shows the fraction 1 2 / 3. The complete circle on the left is selected and 2 / 3 of the other circle is selected. A fraction such as 1 2 / 3 that has a whole number and a fraction is a mixed number. Mixed Form To Fraction Form 1

3. We can write the complete unit 1 as 3 / 3. Add 3 / 3 to the partial unit 2 / 3 for a fraction form of 5 / 3. This picture shows that 1 2 / 3 = 3 / 3 + 2 / 3 = 5 / 3. Mixed Form To Fraction Form 2

4. Another way to write from mixed to fraction form is to multiply the whole number 1 by the denominator 3 and then add the numerator 2 for a numerator of 5 in the fraction form. Mixed Form To Fraction Form 3

5. The same amount, 1 2 / 3, is shown with a number line. Mixed Form To Fraction Form 4

6. The amount shown at the arrow can be written as 3 1 / 4 or 13 / 4. Mixed Form To Fraction Form 5

7. This picture shows the mixed fraction 2 5 / 8. If you were to count all the parts that are colored you would have a total of 21 parts, giving the fraction 21 / 8. Mixed Form To Fraction Form 6

8. Since each unit or circle has 8 parts the completely colored circles can be written as 8 / 8. This gives us 8 / 8 + 8 / 8 + 5 / 8 circles for a total of 21 / 8 circles. Mixed Form To Fraction Form 7

9. Or you can multiply the whole number 2 times the denominator 8 and then add the numerator 5 for a numerator of 21 in the fraction form. Mixed Form To Fraction Form 8

10. To write 3 4 / 5 in fraction form multiply the whole number 3 by the denominator 5. Then add the numerator 4 for a numerator of 19 in the fraction form. Mixed Form To Fraction Form 9

11. The picture shows two fractions that are the same size. The fraction on the right is in higher terms because the numerator and denominator are larger. The parts are smaller in the fraction on the right, but there are more parts. Rename To Higher Terms 1

12. To rename a fraction in higher terms, multiply both the numerator and denominator by the same number. The picture shows that the numerator 3 and the denominator 4 are both multiplied by 3, giving the fraction 9 / 12. Rename To Higher Terms 2

13. The number 3 / 3 is equal to 1. Multiplying by 1 or any form of 1 will not change the size of the number. One is the identity for multiplication. Rename To Higher Terms 3

14. The top fraction shows 5 / 8 and the lower fraction shows 10 / 16. Notice how 5 / 8 and 10 / 16 are the same amounts on the number lines. Multiplying both the numerator and the denominator by 2 will give a numerator of 10 and a denominator of 16. Rename To Higher Terms 4

15. Here, you are asked to write the fraction 3 / 8 as 32’s. Determine what the denominator 8 is multiplied by to get a denominator 32. In this case 4. Rename To Higher Terms 5

16. This picture shows that 3 / 8 and 12 / 32 have the same position on the number line. 3 / 8 is renamed as 12 / 32 by multiplying by 4 / 4. Rename To Higher Terms 6

17. These fractions are the same size. The fraction on the right is in lower terms because both the numerator and denominator are smaller than the fraction on the left. Rename To Lower Terms 1

18. Notice that both the numerator and denominator in the fraction 21 / 24 are divided by 3. Actually, you are dividing the fraction 21 / 24 by 3 / 3, a form of 1. Rename To Lower Terms 2

19. The picture shows that 8 and 16 are both divided by 2. A number that divides evenly into other numbers is called a common factor of the numbers. Two is a common factor of 8 and 16. Rename To Lower Terms 3

20. The numerator and denominator 8 / 16 can also be divided by 8. Eight is the largest number that divides evenly into 8 and 16. 2, 4, and 8 are common factors of 8 an 16, but 8 is the greatest common factor of 8 and 16. Rename To Lower Terms 4

21. Dividing the numerator and denominator by the greatest common factor will rename the fraction to lowest terms. The fraction 1 / 2 is in lowest terms because there is no number larger than 1 that will divide evenly into 1 and 2. Rename To Lower Terms 5

22. This picture shows the fraction 18 / 30. The greatest common factor of 18 and 30 is 6. Divide both 18 and 3 by the greatest common factor 6 will rename 18 / 30 in lowest terms. Rename To Lower Terms 6