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.5 ½½ = 1 ÷ 2 = 0.50.5 + 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 = 6 ½ 13/2 2 13

- 12 1

• 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 2 x 3 = 6 3 ½ = 7/26 + 1 = 77/2

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!

• Read the decimal. Remember your decimal place value words.

0.25 twenty-five 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.)

0.25

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 or with GCF 25 ÷ 25 =1100 ÷ 5=20÷5 =4 100÷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

• 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!

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.”

2.25 two AND twenty-five hundredths

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

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