Transcript Fractions, Mixed numbers, and Decimals

Fractions, Mixed numbers, and
Decimals
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.
5½
½ = 1 ÷ 2 = 0.5
0.5 + 5 = 5.5
Practice
(1) 2 ½
(2) 1 ¾
(3)3 9/10
(4)6 5/8
(5)1 3/5
(6)6 1/5
Answers
(1) 2 ½ = 0.5 + 2 = 2.5
(2) 1 ¾ = 0.75 + 1 = 1.75
(3)3 9/10 = 0.9 + 3 = 3.9
(4)6 5/8 = 0.625 + 6 = 6.625
(5)1 3/5 = 0.6 + 1 = 1.6
(6)6 1/5 = 0.2 + 6 = 6.2
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
Practice
(1) 12/5
(2) 6/5
(3) 23/2
(4) 7/4
(5) 8/5
(6) 19/8
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
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.
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
13/2
2
13
- 12
1
13/2 = 6 ½
• Don’t forget to simplify the fraction part of the
mixed number if necessary.
14/6 = 14 ÷ 6 = 2 2/6 = 2 1/3
Practice
(1)3/2
(2) 5/4
(3)19/5
(4)23/9
(5)36/14
(6)7/3
(1) 3/2 = 3÷2=1 1/3
(2) 5/4= 5÷4=1 1/4
(3) 19/5= 19÷5=3 4/5
(4) 23/9= 23÷9=2 5/9
(5) 36/14= 36÷14=2 8/14 = 2 4/7
(6) 7/3= 7÷3=2 1/3
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
2x3=6
6+1=7
7/2
3 ½ = 7/2
Practice
(1) 3 ⅓
(2) 2 ¼
(3) 5 ¾
(4) 3 ⅔
(5) 6 ⅚
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
Decimals to Fractions
•
•
•
•
To change a decimal to a fraction:
SAY IT!
WRITE IT!
SIMPLIFY!
SAY IT!
.
Tenths
Hundredths
0.25
Ones
• Read the decimal. Remember your decimal
place value words.
0
.
2
5
twenty-five hundredths
• 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
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.
WRITE IT! (con.)
Ones
.
Tenths
Hundredths
0.25
0
.
2
5
Twenty-five hundredths
25/100
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.)
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
100 ÷ 5=20÷5 =4
or with GCF
25 ÷ 25 =1
100÷25 = 4
25/100 in simplest form is equivalent to 1/4
Practice
• Write the decimals as fractions in simplest form.
(1)0.35
(2)0.5
(3)0.75
(4)0.56
(5)0.80
(6)0.2
Answers
(1) 0.35 = 35/100 = 7/20
(2) 0.5 = 5/10 = 1/2
(3) 0.75 = 75/100 = 3/4
(4) 0.56 = 56/100 = 14/50
(5) 0.8 = 8/10 = 4/5
(6) 0.2 = 2/10 = 1/5
Decimals to Mixed Numbers
Ones
.
Tenths
Hundredths
• 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!
2
.
2
5
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.”
Ones
.
Tenths
Hundredths
2.25
2
.
2
5
two AND twenty-five
hundredths
WRITE IT!
2 25/100
Ones
.
Tenths
Hundredths
Remember that mixed numbers are the sum of a
whole number and a fraction.
2.25
Two and twenty-five
hundredths
2
.
2
5
SIMPLIFY IT!
• Simplify the FRACTION ONLY of the mixed
number.
2 25/100=2 1/4
Practice
• Write each decimal as a mixed number.
(1) 3.5
(2) 2.56
(3) 2.7
(4) 9.1
(5) 7.625
(6) 4.75
Answers
(1) 3.5 = 3 5/10 = 3 1/2
(2) 2.56 = 2 56/100 = 2 14/20
(3) 2.7 = 2 7/10
(4) 9.1 = 9 1/10
(5) 7.625 = 7 625/1000 = 7 5/8
(6) 4.75 = 4 75/100 = 4 3/4