Fractions Mixed numbers and Decimals Mixed Numbers to

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 + 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 2 x 3=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 = (3 x 3+1)/3=10/3 (2) 2 ¼ = (4 x 2+1)/4=9/4 (3) 5 ¾ = (4 x 5+3)/4=23/4 (4) 3 ⅔ = (3 x 3+2)/3=11/3 (5) 6 ⅚ = (6 x 6+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 =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