1. Fractions, Mixed numbers, and Decimals

2. Mixed Numbers to Decimals
A mixed number is the sum of a whole number and a fraction.
To turn a mixed number to a decimal:
Change the fraction to a decimal (divide the numerator by the denominator).
Add the resulting decimal and the whole number.
5 ½
½ = 1 ÷ 2 = 0.5
= 5.5

3. Practice
2 ½
1 ¾
3 9/10
6 5/8
1 3/5
6 1/5

4. Answers
2 ½ = = 2.5
1 ¾ = = 1.75
3 9/10 = = 3.9
6 5/8 = = 6.625
1 3/5 = = 1.6
6 1/5 = = 6.2

5. Improper Fractions to Decimals
To change improper fractions to decimals:
Divide the numerator by the denominator.
Represent the remainder as a decimal
A calculator is a good tool here
3/2 = 3÷2 = 1.5

6. Practice
(1) 12/5 (2) 6/5 (3) 23/2 (4) 7/4 (5) 8/5 (6) 19/8

7. Answers
(1) 12/5=12÷5=12.5 (2) 6/5=6÷5=1.5 (3) 23/2=23÷2=11.5 (4) 7/4=7÷4=1.75 (5) 8/5=8÷5=1.6 (6) 19/8=19÷8=2.375

8. Improper Fractions to Mixed Numbers
An improper fraction is a fraction that has a numerator that is greater than the denominator.
13/2; the numerator 13 is greater than the denominator 2.

9. Improper Fractions to Mixed Numbers
To change an improper fraction to a mixed number:
Divide the numerator by the denominator.
Represent the remainder as a fraction.
Remainder/ divisor
6 1/ /2 = 6 ½
13/
- 12 1

10. Don’t forget to simplify the fraction part of the mixed number if necessary.
14/6 = 14 ÷ 6 = 2 2/6 = 2 1/3

11. Practice
3/2
5/4
19/5
23/9
36/14
7/3

12. 3/2 = 3÷2=1 1/3
5/4= 5÷4=1 1/4
19/5= 19÷5=3 4/5
23/9= 23÷9=2 5/9
36/14= 36÷14=2 8/14 = 2 4/7
7/3= 7÷3=2 1/3

13. Mixed Numbers to Improper Fractions
To change a mixed number to an improper fraction:
Multiply the denominator by the whole number
Add that product to the numerator
Place that sum over the denominator
3 1/2
2 x 3 = ½ = 7/2
6 + 1 = 7
7/2

14. Practice
(1) 3 ⅓ (2) 2 ¼ (3) 5 ¾ (4) 3 ⅔ (5) 6 ⅚

15. Answers
(1) 3 ⅓ = (3x3+1)/3=10/3 (2) 2 ¼ = (4x2+1)/4=9/4 (3) 5 ¾ = (4x5+3)/4=23/4 (4) 3 ⅔ = (3x3+2)/3=11/3 (5) 6 ⅚ = (6x6+5)/6=41/6

16. Decimals to Fractions To change a decimal to a fraction: SAY IT!
WRITE IT!
SIMPLIFY!

17. SAY IT! Read the decimal. Remember your decimal place value words.
twenty-five hundredths
Ones .
Tenths
Hundredths 2 5

18. Like fractions, decimals are parts of wholes.
Decimals are divided into parts that are powers of ten.
Tenths: the whole is divided into 10 equal parts
Hundredths: the whole is divided into 100 equal parts
Etc.
tenths hundredths

19. WRITE IT!
The decimal place value words (tenths, hundredths, etc.) tell us how many parts the whole is divided into.
Remember that fractions = selected part/total number of parts in the whole.
So, the decimal place value tells us the denominator.
Tenths=1/10
Hundredths=1/100
Thousandths=1/100
Etc.

20. WRITE IT! (con.) 0.25 Twenty-five hundredths 25/100 Ones . Tenths2 5

21. SIMPLIFY IT!
Fractions need to be in simplest form. Fractions are in simplest form when the only common factor between the numerator and the denominator is 1. (also called lowest terms.)

22. SIMPLIFY IT!
To simplify fractions, divide the numerator and denominator by a common factor. Repeat if necessary. Repeating is not necessary if dividing by the Greatest Common Factor (GCF).
25 ÷ 5 = 5 ÷5 =1 or with GCF 25 ÷ 25 =1
100 ÷ 5=20÷5 = ÷25 = 4
25/100 in simplest form is equivalent to 1/4

23. Practice Write the decimals as fractions in simplest form. 0.35 0.5
0.75
0.56
0.80
0.2

24. Answers
0.35 = 35/100 = 7/20
0.5 = 5/10 = 1/2
0.75 = 75/100 = 3/4
0.56 = 56/100 = 14/50
0.8 = 8/10 = 4/5
0.2 = 2/10 = 1/5

25. Decimals to Mixed Numbers
The process is the same for writing a decimal as a mixed number. A decimal will be written as a mixed number instead of just a fraction when there is a value for places to the left of the decimal point.
SAY IT!
WRITE IT!
SIMPLIFY IT!
Ones .
Tenths
Hundredths 2 5

26. SAY IT!
Read the decimal. Remember your decimal place value words. Also, remember to start with the whole number and to read the decimal point as “and.”
two AND twenty-five hundredths
Ones .
Tenths
Hundredths 2 5

27. WRITE IT!
Remember that mixed numbers are the sum of a whole number and a fraction.
2.25
Two and twenty-five hundredths
2 25/100
Ones .
Tenths
Hundredths 2 5

28. SIMPLIFY IT!
Simplify the FRACTION ONLY of the mixed number.
2 25/100=2 1/4

29. Practice Write each decimal as a mixed number. 3.5 2.56 2.7 9.1 7.625
4.75

30. Answers
3.5 = 3 5/10 = 3 1/2
2.56 = 2 56/100 = 2 14/20
2.7 = 2 7/10
9.1 = 9 1/10
7.625 = 7 625/1000 = 7 5/8
4.75 = 4 75/100 = 4 3/4