1.4: Fractions, decimals and percentages

 Fractions

1. Basics

• A fraction shows part of a whole.

• Written as: a/b where a is the numerator and b is the denominator.

• Example: three over four means 3 parts out of 4. Written as 3/4

2. Proper and Improper Fractions

• Proper fraction: numerator is less than denominator. Value of the whole fraction is less than 1.

• Example: two over five = 2/5 = 0.4<1 so it's a proper fraction

• Improper fraction: numerator is equal to or greater than denominator. Value is 1 or more.

• Example: seven over four = 7/4> 1

3. Mixed Numbers

• A whole number and a fraction together.

• Example: one and one half = 1 1/2

• Converting seven over four to mixed number: one and three quarters.

4. Simplifying Fractions

• Reduce to lowest terms by dividing numerator and denominator by their highest common factor.

• Example: 8/12 becomes 2/3 since 8/4=2 and 12/4=3

1. Converting Fractions to Decimals

• Divide the numerator by the denominator through long division.

• Example: 

  • 1/2= 0.5.

  • 3/4 = 0.75.

  • 2/5 = 0.4.

2. Converting Decimals to Fractions

• Write the decimal over its place value and simplify.

• Example:

  • 0.25 = 25/100 = 1/4

  • 0.6 = 6/10 = 3/5

  • 0.2 = 2/10 = 1/5

3. Recurring Decimals

• Decimals that repeat forever.

• Notation: bar over repeating digit.

• Example: 

• 0.3 repeating = 0.333... with fraction: 1/3

• 0.6 repeating = 0.666... with fraction: 2/3

4. Percentages

• Percent means "per hundred".

• Example: 

  • 25%= 25/100 = 0.25

  • 50%= 50/100 = 0.5.

• Convert fraction to percent:

  • Example: 3/4 = 0.75 x 100 = 75 %.

  • Example: 2/5 = 0.4 x 100 = 40 %.

• Convert decimal to percent:

  • Example: 0.6 x 100= 60 %

  • Example: 0.8 x 100 = 80 %.

How to change a recurring decimal into a fraction?

Example: turn 0.17777.... into a fraction

1. Let x = 0.177777...

2. Multiply both sides by 10 (right before the recurring number) 10x = 1.77777...

3. Include 1 digit of the recurring digits by multiplying by 10: 100x = 17.77777...

4. Subtract 10x from 100x (the 2 equations): 100x - 10x = 17.777 - 1.7777

5. Simplify: 90x = 16

6. Solve for x by dividing: x = 16/90 = 8/45

Example: turn 0.8888... into a fraction

1. Let x = 0.8888...

2. Multiply both sides by 10 (include 1 digit of the recurring number): 10x = 8.888

3. Subtract x from 10x: 10x - x = 8.888 - 0.888

4. Simplify: 9x = 8

5. Solve for x by dividing: x = 8/9

• What made the 2 examples different is that for 0.888888..., you only need 1 shift to line up repeats while for 0.177777..., you need 2 shifts (first to move the 1, second to match the repeat).

NOTES DONE BY FARIDA SABET

CLICK HERE TO GO TO THE PREVIOUS TOPIC

CLICK HERE TO GO TO THE NEXT TOPIC

CLICK HERE TO GO BACK TO THE NOTES MENU