Transcript Fraction Concepts

Fraction Concepts
Fraction Concepts
• A fraction is a piece of something.
• For example, a fraction can be:
– A piece of cake
– A piece of pie
– A slice of pizza
– A portion of an apple
Fraction Concepts
• A fraction is shown as a number over another
number with a line separating them (X/W)
Fraction Concepts
• The top number is the numerator.
• The numerator represents how much you
have to split up. For example: 2 pizzas, 3
sandwiches, 5 pies
Fraction Concepts
• The denominator is the bottom number.
• The number represents how things are being
split up or divided.
Fraction Concepts
• In a regular fraction, the denominator is a
higher number than the numerator.
Fraction Concepts
Fraction and Division Are Related
• Fractions and division are related.
• The numerator in a fraction is the same as the
dividend in a division equation
• The denominator is the same as the divisor in
a division equation
Fraction Concepts
Equivalent Fractions
• Equivalent fractions are two or more different
fractions that represent the same amount.
• For example: ½ = 2/4 = 3/6 = 4/8 = 5/10
Fraction Concepts
Determining an Equivalent Fraction
• To determine an equivalent fraction, multiply
the numerator and the denominator by the
same amount.
• You get a different fraction, but it is the same
amount.
• For example: 2/4 x 2/2 = 4/8
Fraction Concepts
Determining an Equivalent Fraction: Another Way
• You can also divide the numerator and the
denominator by the same amount to get an
equivalent fraction.
• For example: 4/8 ÷ 2/2 = 2/4
Fraction Concepts
Why Do I Need Equivalent Fractions
• Equivalent fractions are needed to add and
subtract fractions with different denominators.
• For example: 1/4 + 1/3
• Step 1: Find a common multiple for 4 and 3 which
is 12.
• Step 2: Convert 1/4 and 1/3 to equivalent
fractions with a denominator of 12 (3/12 and
4/12).
• Step 3: Add the numerators of the equivalent
fractions to solve the equation (7/12).
Fraction Concepts
• To convert a fraction to an equivalent fraction
in a simplest form, divide the numerator and
denominator by the same common factor.
• If the resulting fraction is even, ends in 5, or is
divisible by 3, continue simplifying.
• For example: 4/12 ÷ 4/4 = 1/3
Fraction Concepts
Mixed Numbers and Improper Fractions
• A mixed number is a combination of a whole
number and a fraction. For example: 4 ½
• An improper fraction is a fraction when the
numerator is greater than the denominator.
For example: 12/5
Fraction Concepts
Converting a Mixed Number to an Improper Fraction
• To convert a mixed number to an improper
fraction ( 4 3/5):
– Convert the whole number to a fraction: 4 = 4/1
– Convert the fraction to an equivalent fraction with
the same denominator as the fraction piece:
4/1 x 5/5 = 20/5
– Add the equivalent whole number fraction to the
fraction piece: 20/5 + 3/5 = 23/5.
Fraction Concepts
Converting an Improper Fraction to a Mixed Number
• To convert an improper fraction to a mixed
number:
– Rewrite the fraction as a division equation:
23/5 = 23 ÷ 5
– Solve the division equation. 23÷5= 4 r 3
• The quotient is the whole number of the mixed number
• The remainder is the numerator of the fraction piece
• The denominator is the original denominator
– For example: 23/5 = 4 3/5
Fraction Concepts
Adding Fractions with Same Denominators
• To add fractions with the same denominator,
add the numerators only.
• Do not add the denominators. They are the
noun of the fractions representing the size of
the piece.
• Example: 3/8 + 4/8 = 7/8
Fraction Concepts
Subtracting Fractions with Same Denominator
• To subtract fractions with same denominator,
subtract the numerators.
• Do not subtract the denominators.
• For example: 4/5 – 2/5 = 2/5
Fraction Concepts
Adding Mixed Numbers with Same Denominator
• Step 1: Rewrite the equation in vertical format
• Step 2: Add the fraction pieces of the mixed
number
– If the result is a regular fraction, continue to step 2
– If the result is an improper fraction, convert the
improper fraction to a mixed number
– Add the whole number to the first whole number
– Leave the fraction alone.
• Step 3: Add the whole number pieces of the
equation.
Fraction Concepts
Adding Mixed Numbers with Same Denominator
• Example 1
– 3 2/5 + 2 1/5 = 5 3/5
• Example 2
– 3 4/5 + 4 2/5
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Step 1: 4/5 + 2/5 = 6/5
Convert to a mixed number: 6÷5 = 1 r 1 = 1 1/5
Step 2: 1+3+4 = 8
Solution 8 1/5
Fraction Concepts
Subtracting Mixed Numbers with Same Denominators
• Step 1: Rewrite the equation in vertical format
• Step 2: Subtract the fraction pieces
– If the top fraction is greater than the bottom
fraction, subtract the numerators
– If the top fraction is less than the bottom fraction,
• Regroup one of the ones from the whole number as a
fraction with the same denominator as the fraction
• Add the regrouped fraction to the original fraction
• Subtract the lower fraction from the upper fraction.
• Step 3: Subtract the whole numbers
Fraction Concepts
Subtracting Mixed Numbers with Same Denominators
• Example 1: 5 ¾ - 2 ¼ = 3 2/4 = 3 ½
• Example 2: 5 ¼ - 2 ¾
– Step 1: Convert the 5 to 4 and take the 1 and
convert it to a fraction with 4 as the denominator
(4/4)
– Step 2: Add 4/4 to ¼ to get 5/4
– Step 3 Subtract ¾ from 5/4 to get 2/4 or ½
– Step 4: Subtract 2 from 4 to get 2.
– Solution: 2 2/4 or 2 ½
Fraction Concepts
Applying Your Knowledge
• To add or subtract fractions with uncommon
denominators, convert the two fractions to
equivalent fractions with the same denominator.
• For example: 1/3 + ¼
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3 and 4 share 12 as a common multiple
Convert 1/3 to 4/12 (1/3 x 4/4 = 4/12)
Convert ¼ to 3/12 ( ¼ x 3/3 = 3/12)
Add the numerators of the two equivalent fractions
• 4/12 + 3/12 = 7/12
Fraction Concepts
Applying Your Knowledge
• When you are multiplying a fraction, you are
taking a fraction of the first fraction. You
multiply the numerators and then multiply
denominators.
• For example ¾ x ½ means you are taking ½ of
¾.
• To solve: ¾ x ½ =3/8
Fraction Concepts
Applying Your Knowledge
• Dividing two numbers is the same as
multiplying the dividend by the reciprocal of
the divisor.
• For example: 6 ÷ 2 = 6 x ½
• A reciprocal is flipping the numerator and the
denominator. For example 2 = 2/1. the
reciprocal of 2 is ½.