Numeric Fractions
Section 2.1
Numeric Fractions
Slide: 1
Section 2.1
Numeric Fractions A fraction is a rational number written as one integer divided by another non-zero integer.
Numerator
Denominator
Slide: 2
1 2
Fraction Bar This is read as “one divided by two”, “one-half” or “one over two.”
Section 2.1
Numeric Fractions A fraction is a rational number written as one integer divided by another non-zero integer.
A fraction implies that you have a fraction, or a part, of a whole quantity.
3 8 Slide: 3
The numerator shows the number of pieces you kept for yourself.
The denominator represents the total number of pieces you split the pie in.
Section 2.1
Numeric Fractions A fraction where one integer is divided by another non-zero integer is called a rational number.
Examples:
4 7
3 5
6 2
The denominator of a fraction cannot be zero, since zero cannot represent a whole unit. Slide: 4
Section 2.1
Numeric Fractions A fraction can be represented on a number line.
One unit divided into 6 equal parts: 1 6
0 1 6
Slide: 5
2 6
1 6
3 6
1 6
4 6
1 6
5 6
1 6
6 6
1 1 6
Section 2.1
Proper Fractions A proper fraction is a fraction in which the absolute value of the numerator is less than the absolute value of the denominator, i.e. the absolute value of the entire fraction is less than 1.
This is a proper fraction as
33
Slide: 7
8 = 2.67 3
The decimal value is more than 1.
Mixed Number A mixed number consists of both a whole number and a fraction, written side-by-side, which implies that the whole number and the proper fraction are added.
1 24 Slide: 8
In terms of the pie, this means that you have 2 whole pies, and one quarter of a pie.
Section 2.1
Section 2.1
Complex Fractions A complex fraction is a fraction in which one or more fractions are found in the numerator or denominator.
3
() 1 5
Slide: 9
() 1 2
4
1 68 3 4
()
Converting a Mixed Number to an Improper Fraction. To convert a mixed number into an improper fraction, multiply the whole number by the denominator of the fraction, and add this value to the numerator of the fraction.
1 = 1 2
Slide: 10
Section 2.1
What is 2 3 expressed as an improper fraction? 4
3 24 Slide: 11
=
Section 2.1
Converting an Improper Fraction to a Mixed Number
Section 2.1
To convert an improper fraction into a mixed number, divide the numerator by the denominator: the quotient becomes the whole number and the remainder becomes the numerator of the fraction.
43 = 8
Slide: 12
What is 59 expressed as a mixed number? 6
59 6
Slide: 13
=
Section 2.1
Section 2.1
Reducing or Simplifying a Fraction A fraction where the numerator and denominator have no factors in common (other than 1) is said to be a fraction in its lowest (or simplest) terms.
Method 1: Dividing both the numerator and denominator by the Highest Common Factor.
40 45 Slide: 14
Section 2.1
Reducing or Simplifying a Fraction A fraction where the numerator and denominator have no factors in common (other than 1) is said to be a fraction in its lowest (or simplest) terms.
Method 2: Dividing by the common prime factors of the numerator and denominator.
40 45 Slide: 15
Lowest Common Denominator The Least or Lowest Common Denominator (LCD) of a set of two or more fractions is the smallest whole number that is divisible by each of the denominators.
To find the LCD of
Slide: 16
5 6
and
3 4
, you must find the LCM of 6 and 4.
Section 2.1
Addition of Fractions Addition of fractions requires that the denominator of every fraction is the same.
Adding Fractions that Have the Same Denominator 3 2 + = 6 6 When the denominators of two fractions are the same we add the numerators and write the same denominator.
Slide: 17
Section 2.1
Addition of Fractions Addition of fractions requires that the denominator of every fraction is the same.
Adding Fractions that Have the Different Denominators 12 5 = + 21 9 When the fractions have different denominators we find the common denominator and change each fraction to its equivalent fraction with that denominator.
Slide: 18
Section 2.1
5 18 Add 21 and 6 .
Slide: 19
Section 2.1
Subtraction of Fractions
Section 2.1
Subtraction of fractions requires that the denominator of every fraction is the same.
Subtracting Fractions that Have the Same Denominator 5 7
−
3 = 7
When the denominators of two fractions are the same we subtract the numerators and write the common denominator.
Slide: 20
Subtraction of Fractions
Section 2.1
Subtraction of fractions requires that the denominator of every fraction is the same.
Subtracting Fractions that Have Different Denominators 54 13 = − 72 27 When the fractions have different denominators we find the common denominator and change each fraction to its equivalent fraction with that denominator. Slide: 21
8 21 Subtract from . 17 34
Slide: 22
Section 2.1
Evaluate the following expression:
Slide: 23
1 5 7 + − 4 8 12
Section 2.1
Section 2.1
Multiplication of Fractions When multiplying fractions, simply multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator.
Multiply the two numerators.
5× 2 = 7 3 Multiply the two denominators. Slide: 24
Section 2.1
Multiplication of Fractions When multiplying fractions, you can reduce the fractions before multiplying by finding common factors between any numerator and denominator in the expression.
10 3 × = 21 25
Slide: 25
Section 2.1
Reciprocal of a Fraction
When the numerator and denominator of a fraction are interchanged the resulting fraction in called the reciprocal of the original fraction.
4 7 Slide: 26
7 is the 4 reciprocal of 4 7
Section 2.1
Division of Fractions The division of fractions is done by multiplying one fraction by the reciprocal of the dividing fraction.
5 ÷ 2 = 7 3 Slide: 27
Section 2.1
Divide 13 by 7 . 47 9
Slide: 28
Section 2.1
Operations with Mixed Numbers To perform operations with mixed numbers, convert the mixed numbers to improper fractions, and perform the operations normally.
1 6×2 = 8
Slide: 29
Evaluate the following expression:
Slide: 30
2 1 7 × 4 5 2−7
Section 2.1
Evaluate the following expression:
Slide: 31
2 1 7 × 4 5 2−7
Section 2.1
Section 2.1
Powers and Roots of Fractions
To take a power of a fraction, take the power of the numerator and denominator.
3 1 3 3 9 ( ) = × = 5 5 5 25 To take a root of a fraction, take the root of the numerator and denominator.
Slide: 32
9 9 3 1 = = = 36 36 6 2
Numeric Fractions
Slide: 1
Section 2.1
Numeric Fractions A fraction is a rational number written as one integer divided by another non-zero integer.
Numerator
Denominator
Slide: 2
1 2
Fraction Bar This is read as “one divided by two”, “one-half” or “one over two.”
Section 2.1
Numeric Fractions A fraction is a rational number written as one integer divided by another non-zero integer.
A fraction implies that you have a fraction, or a part, of a whole quantity.
3 8 Slide: 3
The numerator shows the number of pieces you kept for yourself.
The denominator represents the total number of pieces you split the pie in.
Section 2.1
Numeric Fractions A fraction where one integer is divided by another non-zero integer is called a rational number.
Examples:
4 7
3 5
6 2
The denominator of a fraction cannot be zero, since zero cannot represent a whole unit. Slide: 4
Section 2.1
Numeric Fractions A fraction can be represented on a number line.
One unit divided into 6 equal parts: 1 6
0 1 6
Slide: 5
2 6
1 6
3 6
1 6
4 6
1 6
5 6
1 6
6 6
1 1 6
Section 2.1
Proper Fractions A proper fraction is a fraction in which the absolute value of the numerator is less than the absolute value of the denominator, i.e. the absolute value of the entire fraction is less than 1.
This is a proper fraction as
33
Slide: 7
8 = 2.67 3
The decimal value is more than 1.
Mixed Number A mixed number consists of both a whole number and a fraction, written side-by-side, which implies that the whole number and the proper fraction are added.
1 24 Slide: 8
In terms of the pie, this means that you have 2 whole pies, and one quarter of a pie.
Section 2.1
Section 2.1
Complex Fractions A complex fraction is a fraction in which one or more fractions are found in the numerator or denominator.
3
() 1 5
Slide: 9
() 1 2
4
1 68 3 4
()
Converting a Mixed Number to an Improper Fraction. To convert a mixed number into an improper fraction, multiply the whole number by the denominator of the fraction, and add this value to the numerator of the fraction.
1 = 1 2
Slide: 10
Section 2.1
What is 2 3 expressed as an improper fraction? 4
3 24 Slide: 11
=
Section 2.1
Converting an Improper Fraction to a Mixed Number
Section 2.1
To convert an improper fraction into a mixed number, divide the numerator by the denominator: the quotient becomes the whole number and the remainder becomes the numerator of the fraction.
43 = 8
Slide: 12
What is 59 expressed as a mixed number? 6
59 6
Slide: 13
=
Section 2.1
Section 2.1
Reducing or Simplifying a Fraction A fraction where the numerator and denominator have no factors in common (other than 1) is said to be a fraction in its lowest (or simplest) terms.
Method 1: Dividing both the numerator and denominator by the Highest Common Factor.
40 45 Slide: 14
Section 2.1
Reducing or Simplifying a Fraction A fraction where the numerator and denominator have no factors in common (other than 1) is said to be a fraction in its lowest (or simplest) terms.
Method 2: Dividing by the common prime factors of the numerator and denominator.
40 45 Slide: 15
Lowest Common Denominator The Least or Lowest Common Denominator (LCD) of a set of two or more fractions is the smallest whole number that is divisible by each of the denominators.
To find the LCD of
Slide: 16
5 6
and
3 4
, you must find the LCM of 6 and 4.
Section 2.1
Addition of Fractions Addition of fractions requires that the denominator of every fraction is the same.
Adding Fractions that Have the Same Denominator 3 2 + = 6 6 When the denominators of two fractions are the same we add the numerators and write the same denominator.
Slide: 17
Section 2.1
Addition of Fractions Addition of fractions requires that the denominator of every fraction is the same.
Adding Fractions that Have the Different Denominators 12 5 = + 21 9 When the fractions have different denominators we find the common denominator and change each fraction to its equivalent fraction with that denominator.
Slide: 18
Section 2.1
5 18 Add 21 and 6 .
Slide: 19
Section 2.1
Subtraction of Fractions
Section 2.1
Subtraction of fractions requires that the denominator of every fraction is the same.
Subtracting Fractions that Have the Same Denominator 5 7
−
3 = 7
When the denominators of two fractions are the same we subtract the numerators and write the common denominator.
Slide: 20
Subtraction of Fractions
Section 2.1
Subtraction of fractions requires that the denominator of every fraction is the same.
Subtracting Fractions that Have Different Denominators 54 13 = − 72 27 When the fractions have different denominators we find the common denominator and change each fraction to its equivalent fraction with that denominator. Slide: 21
8 21 Subtract from . 17 34
Slide: 22
Section 2.1
Evaluate the following expression:
Slide: 23
1 5 7 + − 4 8 12
Section 2.1
Section 2.1
Multiplication of Fractions When multiplying fractions, simply multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator.
Multiply the two numerators.
5× 2 = 7 3 Multiply the two denominators. Slide: 24
Section 2.1
Multiplication of Fractions When multiplying fractions, you can reduce the fractions before multiplying by finding common factors between any numerator and denominator in the expression.
10 3 × = 21 25
Slide: 25
Section 2.1
Reciprocal of a Fraction
When the numerator and denominator of a fraction are interchanged the resulting fraction in called the reciprocal of the original fraction.
4 7 Slide: 26
7 is the 4 reciprocal of 4 7
Section 2.1
Division of Fractions The division of fractions is done by multiplying one fraction by the reciprocal of the dividing fraction.
5 ÷ 2 = 7 3 Slide: 27
Section 2.1
Divide 13 by 7 . 47 9
Slide: 28
Section 2.1
Operations with Mixed Numbers To perform operations with mixed numbers, convert the mixed numbers to improper fractions, and perform the operations normally.
1 6×2 = 8
Slide: 29
Evaluate the following expression:
Slide: 30
2 1 7 × 4 5 2−7
Section 2.1
Evaluate the following expression:
Slide: 31
2 1 7 × 4 5 2−7
Section 2.1
Section 2.1
Powers and Roots of Fractions
To take a power of a fraction, take the power of the numerator and denominator.
3 1 3 3 9 ( ) = × = 5 5 5 25 To take a root of a fraction, take the root of the numerator and denominator.
Slide: 32
9 9 3 1 = = = 36 36 6 2
