 # Simplifying Fractions

## Presentation on theme: "Simplifying Fractions"— Presentation transcript:

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: – 1,2,3,4,6, ÷ 6 = 2 – 1,2,3,6,9, ÷ 6 = 3

Write each fraction in simplest form
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 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 Quiz
Write each fraction in simplest form. Write yes if the fraction is already in simplest form. 8/10 = 2. 7/21 = /16 = /36 = /8 = /24 = /14 = /36 = /12 = /25 =

Improper Fractions & Mixed Numbers
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 = = 13) 13/5

Write each mixed number as an improper fraction
Write each mixed number as an improper fraction. Write each improper fraction as a mixed number. 1.) /3 2.) /8 3.) ½ 4.) /3 5.) 18/5 6.) 23/4 7.) 9/2 8.) 15/3

Write each mixed number as an improper fraction.
1.) /3 2.) /8 3.) 1 ½ 4.) /3 5.) /8 6.) 2 ¼ 7.) /3 8.) /7 Write each improper fraction as a mixed number. 1.) 7/3 2.) 5/2 3.) /14 4.) /5 5.) /10 6.) /8 7.) /9 8.) /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: Numerator Denominator 8

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

FRACTIONS TO DECIMALS HOMEWORK
WRITE THE FOLLOWING FRACTIONS AS DECIMALS: 5/9 7/10 4/5 /5

TAKE NOTES!!!! DECIMAL PLACE VALUE
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 = 75 = 3

DECIMALS TO FRACTIONS 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.) = 9.) .25 = 10.) .65 = 11.) = 12.) =

PERCENTS TO FRACTIONS & DECIMALS
PERCENT MEANS “OUT OF 100” PERCENTS CAN BE WRITTEN AS FRACTIONS WITH DENOMINATORS OF THEY CAN ALSO BE WRITTEN AS DECIMALS. BELOW ARE THREE WAYS TO WRITE THE SAME NUMBER: 3 % = 3/100 = 0.03 10% = 1/10 = 0.10 20% = 1/5 = 0.2 75% = ¾ = 0.75

FRACTIONS/DECIMALS TO PERCENTS
TO 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
FILL IN THE MISSING PARTS OF THE TABLE. FRACTION DECIMAL PERCENT 3/8 0.88 35% 1 ¼ 0.625 275%

1.) 8/15 + 2/15 = 2.) 5/ /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 = 9.) 1/ /6 + ¼ = 10.) 2/3 + ¼ + 1/6 =

5.) / ½ = 6.) / /3 = 7.) / ¼ = 8.) / ½ = 1.) 2 ¾ ¼ = 2.) 8 3/ /12 = 3.) 4 2/ /7 = 4.) 3 5/ /3 = !

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!