3 Introduction to Fractions (The remainder becomes the numerator of the fraction.) Divide the fraction just as you would for a normal fraction (divide the numerator Add this answer to the whole number.
Example 8: into a decimal.
We have already divided 5 by 8 in Example 7, so we just add 0.625 to 12 which equals 12.625.625.121285Converting a Decimal into a Fraction Put the entire number into the numerator of the fraction with the decimal point Then count the number of digits after the decimal point and place a 1 followed by that many zeros in the denominator in the fraction.Reduce the fraction if possible (see the Simplifying Fractions section on the
Example 9: Convert 3.625 into a fraction 10003625625.3Example 10: Convert 0.31 into a fraction 1003131.0Converting Improper Fractions into Mixed NumbersDivide the numerator by the denominator.
The remainder of the division becomes the numerator of the answer.
Example 11: Convert 59 into a mixed number. 54195R
4 Introduction to Fractions To simplify a fraction you try to use smaller numbers in the numerator and denominator to represent the same value as the original fraction.The reason this can be done is that many different fractions have the same value.For example, 21423, and e often simplified so that you can see if two fractions are equivalent (represent the same value).
the two numbers (GCF).
See if you can do this again with the resulting fraction.
Example 12: Simplify 368
First, 8 and 36 have a common factor of 2; when you divide the numerator and the denominator by 2 the numerator and the denominator by 2 the fraction factors, so the fraction has been simplified.
Example 13: Simplify 1824
First, 24 and 18 have a common factor of 2; when you divide the numerator and the denominator by 2 and the denominator by 3 the fraction becomesthe fraction has been simplified.
Example 14: Simplify Since 11 and 23 do not have any common factors, 2311 is simplified.
6 Introduction to Fractions
Example 19: 439154 Convert to improper fractions.
423937 Copy the first fraction, change to 234937
Multiply the fractions.
Answer: The least common multiple of two numbers is the smallest number that is a multiple of both numbers.To find the LCM of two numbers,
Factor each number.An easy way to factor a number is by creating a factor tree.
Factor trees work by breaking the number you are factoring into two numbers that when multiplied together, equal the number you are factoring.When you cannot break the numbers down any more, you only have prime numbers, the
Factor 75 Example 21: Factor 162
3 Answer: 2 Once you have factored both numbers, then you want to see what factors are shared between the two numbers.List the shared factors.
List the factors that are not shared by the numbers.
Find the LCM of 7 and 14 Since the only thing that can multiply to get 7 is 1 and 7, 7 is already a prime number (and thus cannot be
2 = 14, so the LCM of 7 and 14 is
7 Introduction to Fractions
Example 23: Find the LCM of 14 and 36.14 and 36 share one 2, so list one 2.
3 You must have the same denominators in both fractions.To do this,
Find the LCM between the current denominators of the two fractions ill be the new denominator of the The numerators must be changed as well so that the value of the fraction denominator to find what to multiply Example 24: Which fraction is larger: 277 or
The LCM of 27 and 21 is 189.
So 277 So 215 27
7 = 189 21
So 77277 So 9215 49
45 so 277 is the larger fraction.
8 Introduction to Fractions Adding and Subtracting Fractions The denominators of both fractions must bechange them so that they are equal.To do this,
Find the LCM of the denominators of the fractions you are adding or The numerators must be changed as well so that the value of the fraction denominator to find out what to multiply by).Now multiply that number by the numerator to get the new numerator.
Add the numerators of the fractions, keeping the same denominator.Simplify, if possible.
871211The LCM of 12 and 8 is 24.So this is what the denominators of the fractions will be changed to.11 So 8?
2 = 24 8
3 = 24 So 21211 So 3387Now, add the numerators.
represents a part of a whole.A
is a mixed number written as a fraction.It is found by multiplying the whole number by the denominator and adding that answer to the numerator.(Leave the denominator the same)., factor the numerator and denominator, and then divide the original numbers by the GCF (greatest common factor) of the two numbers.When you are , it does not matter if the denominators match.When you are , remember that you must have the common (same) denominators before you add or subtract the numerators.
If you found this handout helpful, you may also like to look at these handouts: Decimals, Factions, and Percents Provided by Tutoring Services 10 Introduction to Fractions Convert the following into Mixed Numbers.
326 414 212 911 734 165 10612 or 5312 1118 3 835 81 5 Convert the following Mixed Numbers into Fractions.13.35 417 25 929 541 10126 or 563 1191 1780 861 869 Simplify the following fractions completely.2110 32 111 61 31 143 139 81 4017 21 Multiply or Divide.Write answers as improper fractions.61 235 358 5221 748 4427 31 5188 910 1136 457 16 48 231 72 60 54 422 81 1610 Equal Equal 2418 180120 201 139 10001 2259130 Add or Subtract.Write answers as improper fractions.
2117 1141 3037 1213 8073 403 21227 2073 21257 1157 2269 Add or Subtract.Write answers as mixed numbers
2111 15465 4818 3071 3592 6011 2419 301 -6 36259.
If a line is longer than 2 inches, but not as long as 3 inches, the measurement can be given as 2 whole inches plus another fraction of an inch.
When we measure a line to be .The fraction part of a mixed number is greater than 0 and less than 1.
Mixed Number Length
Mixed Number Time
1:00 to 2:00 2:00 to 3:00 3:00 to 3:30 Free Pre-Algebra
Lesson 11 page 2
2010 Cheryl Wilcox
Improper Alternative Any mixed number or whole number can also be written as an improper fraction (as opposed to the proper fractions between 0 and 1).These are formed by counting the total number of parts of the size indicated by the denominator.Improper fractions have the numerator greater than or equal to the denominator.
Improper Fraction Length There are 5 lengths of 1/2 inch, or 5/2 inches.
Improper Fraction Area
5 half fields is 5/2 fields, the same as 2 and 1/2 fields.Improper Fraction Volume
There are 5 of the half loaves, equal to 2 and 1/2 loaves.
Improper Fraction Groups
Each band has two half bands,
so there are 5 half bands in all.Improper Fraction Money
Two fifty-cent pieces make one dollar.Improper Fraction Time
1:00 to 1:30
1:30 to 2:00
2:00 to 2:30
2:30 to 3:00
3:00 to 3:30
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2010 Cheryl Wilcox
Fractions Equivalent to Whole Numbers When the numerator of a fraction is equal to its denominator, the fraction is equal to one.Since the denominator stands for the number of parts in one whole, and the numerator stands for the number of parts you have, if they are equal, you have all the parts in one whole. 2/2 parts are blue. 3/3 parts are blue. 4/4 parts are blue. 1 whole rectangle is blue. 1 whole rectangle is blue. 1 whole rectangle is blue.
Writing Whole Numbers as Improper Fractions Any whole number can be written as an improper fraction with any denominator.
The denominator tells the number of parts in 1 whole, so if you multiply the denominator by the number of wholes, you get the total number of parts.
How many 1/4ths in 3 wholes? The parts are 4ths, so each of the 3 wholes has 4 parts.
T12 fourths in all. Example:
How many 1/10ths in 4 wholes? How To Change a Mixed Number to an Improper the mixed number 2 3/8 to improper fraction form.
Step 1: The denominator of the fraction part is the same as the denominator of the improper fraction.Step 2: Change the whole number part to an improper fraction by multiplying it by the denominator.Step 3: Add the numerators of the two fractions to get the new improper fraction.
Here the denominator is 8.The parts are 8ths, so each whole has 8 parts.8 2 = 16 parts total in the 2 wholes.
16 eighths + 3 eighths = 19 eighths.
(2 wholes) Free Pre-Algebra
Lesson 11 page 6
2010 Cheryl Wilcox Lesson 11: Mixed Numbers and Improper .Divide the rectangle into 5ths.
How many 1/5ths in 1 whole?
Write 1 as an improper fraction with denominator 5.
2.Divide each rectangle into 3rds.
How many 1/3rds in 2 wholes?
Write 2 as an improper fraction with denominator 3.
Write a mixed number for the number of blue rectangles.Each rectangle is 1 whole.
To write an improper fraction, divide each of the whole rectangles into ___ parts.The improper fraction name for this amount is
______.5.Write an improper fraction for the number of blue rectangles.Each rectangle is 1 whole.
Write a mixed number for this amount.
5.Change each mixed or whole number to an improper fraction.a.
6.Change each improper fraction to a mixed or whole number.a.
7.Mark the number line in 4ths.Draw a line 5 1/4 units long on the number line.Write the length as an improper fraction.
Lesson 11 page 8
2010 Cheryl Wilcox Lesson 11: Mixed Numbers and Improper Fractions
Homework 11A Name .a.Your apartment cost is the sum of your rent and your utilities costs.Write a formula using variables for your apartment cost.Apartment Cost = Rent + Utilities
You decide to save money by finding some roommates to share costs.
Write a formula using variables for your share of the apartment costs.Your Share = Apartment Cost
Number of Roomates
c.Use the formulas to figure out your share of the apartment cost if Rent = $850, Utilities = $104, and Number of Roommates = 3.
2.Draw a line of the given length.
a.1 and 1/4 inches
2 and 7/16 inches
c.2 and 9/16 inches
3.a.Find all the factor pairs and the GCF for the given numbers.112 126 b.Use the GCF to write the given fractions in lowest terms. 4.
a.Find the prime factorizations of the given numbers. b.Use the prime factorizations to write the fractions in lowest terms. Free Pre-Algebra
Lesson 11 page 11
2010 Cheryl Wilcox
5.Write five fractions equivalent to the given fraction. 6.
Write two fraction names for the blue part of each rectangle.a. b.
7.Write the fraction in lowest terms.Use either the GCF or prime factorization method. 8.Write the whole numbers as improper fractions using the given denominator. 9.Write the mixed numbers as improper fractions. 10.Write the improper fractions as mixed numbers.
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2010 Cheryl Wilcox Lesson 11: Mixed Numbers and Improper Fractions
Homework 11B Name .a.
The cost of showing your dog is the sum of the entry fee and your travel expenses.Dog Show Cost = Entry Fee + Travel Expenses
b.The travel expenses are the product of the price per mile times the number of miles traveled.
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