Simplifying Fractions

• To write a fraction in simplest form or lowest terms follow these two steps:

1 – Find the Greatest Common Factor (GCF) of the numerator and denominator.

2 – Divide both the numerator and the denominator by the GCF.

Example: 12 12 – 1,2,3,4,6,12 12 ÷ 6 = 2 18 18 – 1,2,3,6,9,18 18 ÷ 6 = 3

Write each fraction in simplest form. Write yes if the fraction is already in simplest form.

1.) 8/20 2.) 3/63 3.) 4/7

4.) 8/19 5.) 50/90 6.) 5/11

7.) 9/12 8.) 4/8 9.) 3/14

10.) 8/18 11.) 350/700

Write each fraction in simplest form. Write yes if the fraction is already in simplest form.

1.) 3/9 2.) 4/5 3.) 2/3

4.) 15/25 5.) 12/36 6.) 18/20

7.) 4/12 8.) 3/27 9.) 16/24

10.) 11/13

Simplifying Fractions POP QuizWrite each fraction in simplest form. Write yes if the

fraction is already in simplest form.

1. 8/10 =

2. 7/21 =

3. 8/16 =

4. 18/36 =

5. 3/8 =

6. 6/24 =

7. 4/14 =

8. 9/36 =

9. 5/12 =

10. 15/25 =

An improper fraction is a fraction in which the numerator is greater than or equal to the

denominator. Example: 13/5

A mixed number is a number written as a whole number and a fraction. Example: 1 3/8

Improper Fractions & Mixed Numbers

Write 13/ 5 as a mixed number.Since 13/5 means 13 ÷ 5 , use division to change an

improper fraction to a mixed number.

Write 2 3/5 as an improper fraction.- Multiply the denominator by the whole number

and add the numerator.- Write the sum over the denominator.

2 3/5 (5x2 = 10 + 3 = 13) 13/5

Improper Fractions & Mixed Numbers

• Write each mixed number as an improper fraction. Write each improper fraction as a

mixed number.

• 1.) 3 2/3

• 2.) 6 3/8

• 3.) 1 ½

• 4.) 1 2/3

5.) 18/5

6.) 23/4

7.) 9/2

8.) 15/3

Write each mixed number as an improper fraction.

1.) 3 2/3

2.) 6 3/8

3.) 1 ½

4.) 1 2/3

5.) 2 3/8

6.) 2 ¼

7.) 3 1/3

8.) 6 2/7

Write each improper fraction as a mixed number.

1.) 7/3

2.) 5/2

3.) 15/14

4.) 23/5

5.) 12/10

6.) 25/8

7.) 74/9

8.) 48/5

FRACTIONS TO DECIMALS

• TO CHANGE A FRACTION TO A DECIMAL YOU DIVIDE THE NUMERATOR BY THE DENOMINATOR. TO DO THIS – YOU HAVE TO ADD A DECIMAL POINT AND ZEROS.

EXAMPLE: .375

Numerator 3 8 3.000Denominator 8

Write each fraction as a decimal.

1.) 3/5 = 2.) 7/21 = 3.) 1/5 =4.) 9/20 =5.) 1 4/15 =6.) 7/8 =

FRACTIONS TO DECIMALS

7.) 7/20 = 8.) 5/6 = 9.) 3/25 =10.) 1/4 =11.) 5/8 =12.) 2 4/25 =

FRACTIONS TO DECIMALS HOMEWORK

WRITE THE FOLLOWING FRACTIONS AS DECIMALS:

1. 5/92. 7/103. 4/54. ¾

5. 3 2/5

DECIMAL PLACE VALUE

• http://coolmath.com/prealgebra/02-decimals/01-decimals-place-value-01.htm

TAKE NOTES!!!!

DECIMALS TO FRACTIONS• TO CHANGE A DECIMAL TO A FRACTION YOU

REMOVE THE DECIMAL POINT AND WRITE THE NUMBER AS THE NUMERATOR.

• THE DENOMINATOR IS A MULTIPLE OF 10, DEPENDING ON THE PLACE VALUE OF THE LAST DIGIT.

• WRITE THE FRACTION AND SIMPLIFY IT TO IT’S LOWEST TERMS.EXAMPLE: O.375 375 = 75 = 3

1000 200 8

Write each decimal as a fraction and write it in simplest form.

1.) .8 = 2.) .35 = 3.) .03 =4.) .15 =5.) 6.72 =6.) .21 =

7.) 2.5 = 8.) .004 = 9.) .25 =10.) .65 =11.) .012 =12.) 1.23 =

DECIMALS TO FRACTIONS

PERCENTS TO FRACTIONS & DECIMALS

PERCENT MEANS “OUT OF 100”PERCENTS CAN BE WRITTEN AS FRACTIONS WITH

DENOMINATORS OF 100. THEY CAN ALSO BE WRITTEN AS DECIMALS.

BELOW ARE THREE WAYS TO WRITE THE SAME NUMBER:3 % = 3/100 = 0.0310% = 1/10 = 0.10

20% = 1/5 = 0.275% = ¾ = 0.75

FRACTIONS/DECIMALS TO PERCENTSTO CONVERT(CHANGE) A DECIMAL TO A PERCENT –

YOU MOVE THE DECIMAL POINT TWO PLACES TO THE RIGHT.

EXAMPLE: 0.45 = 45%0.04 = 4%0.2 = 20%

TO CONVERT (CHANGE) A FRACTION TO A PERCENT – FIRST MAKE THE FRACTION A DECIMAL – THEN

CONVERT THE DECIMAL TO A PERCENT.EXAMPLE = 9/20 = 0.45 = 45%

FRACTION/DECIMAL/PERCENT PRACTICE

FRACTION DECIMAL PERCENT

3/8

0.88

35%

1 ¼

0.625

275%

FILL IN THE MISSING PARTS OF THE TABLE.

ALGORITHM FOR ADDING FRACTIONS

• RENAME FRACTIONS SO THAT THEY HAVE COMMON

DENOMINATORS

• ADD THE NUMERATORS

• THE DENOMINATOR STAYS THE SAME

• ADD YOUR WHOLE NUMBERS IF NEEDED

• SIMPLIFY YOUR ANSWER!

Practice With Adding Fractions1.) 8/15 + 2/15 =

2.) 5/12 + 11/12 =

3.) 6/13 + 4/13 =

4.) 2/5 + ½ =

5.) 5/6 + ¼ =

6.) ½ + 3/10 =

7.) 3/8 + ¾ =

8.) 5/6 + 4/6 =

9.) 1/3 + 3/6 + ¼ =

10.) 2/3 + ¼ + 1/6 =

Practice with Adding Mixed Numbers1.) 2 ¾ + 5 ¼ =

2.) 8 3/12 + 5 11/12 =

3.) 4 2/7 + 5 4/7 =

4.) 3 5/8 + 2 2/3 =

!

5.) 4 6/7 + 1 ½ =

6.) 8 3/5 + 2 1/3 =

7.) 9 7/8 + 2 ¼ =

8.) 4 6/7 + 1 ½ =

ALGORITHM FOR SUBTRACTING FRACTIONS

• RENAME FRACTIONS SO THAT THEY HAVE COMMON DENOMINATORS

• SUBTRACT THE NUMERATORS (IF YOU CAN NOT SUBTRACT THEN BORROW FROM THE WHOLE NUMBER)

• THE DENOMINATOR STAYS THE SAME

• SUBTRACT YOUR WHOLE NUMBERS IF NEEDED

• SIMPLIFY YOUR ANSWER!

ALGORITHM FOR MULTIPLYING FRACTIONS

• MAKE SURE THE NUMBERS ARE IN FRACTION FORM

• MULTIPLY THE NUMERATORS

• MULTIPLY THE DENOMINATORS

• SIMPLIFY YOUR ANSWER!

ALGORITHM FOR DIVIDING FRACTIONS

• (MAKE SURE WHEN SOLVING STORY PROBLEMS THAT YOU SET THE NUMBER SENTENCE UP

CORRECTLY)

• MAKE SURE THE NUMBERS ARE IN FRACTION FORM

• TAKE THE FIRST FRACTION AND MULTIPLY IT BY THE RECIPROCOL OF THE SECOND FRACTION

• SIMPLIFY YOUR ANSWER!