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How to Solve Improper Fraction Math Problems

How to Write an Equivalent Fraction With a Given Denominator

Improper fractions contain a numerator that is equal to or greater than the denominator. These fractions are described as improper because a whole number can be pulled out from them, yielding a mixed number fraction. This mixed number fraction is a simplified version of the number and, therefore, is more desirable because it removes complexity in further operations that may be preformed. Performing operations on improper fractions is a pre-algebra exercise that allows students to become familiar with the concept of rational numbers.

Complete all operations indicated on an improper fraction as normal. For example, (3/2 ) * ( 5/2) = 15/4.

Divide the top number by the bottom number. If there is a remainder write it down for later use. In our example, 4 divides into 15 three times. This yields 3 with a remainder of 3.

Write down the whole number.

Create a fraction beside the whole number with the original denominator value. Continuing from above, 3 ( /4).

Place the remainder from above into the blank numerator. In conclusion, 15 / 4 = 3 3/4.

Check your work by multiplying the denominator by the whole number portion of the mixed number and adding the product to the numerator. Checking the above yields ((4 * 3) + 3)) / 4 = 15 / 4. This check proves the operation was a success and that the improper fraction was simplified properly.

Related Articles

How to convert a fraction to a ratio, how to do fractions on a ti-30x iis, how to add fractions with mixed numbers, how to divide rational numbers, how to write the remainder as a whole number, multiplying fractions, how to calculate a percentage and solve percent problems, how to add & subtract radical expressions with fractions, what is the identity property of multiplication, how to divide radicals, how to subtract, add & simplify fractions, how to convert mixed fractions to ratios, how to get rid of cubed power, how to solve distributive properties with fractions, how to multiply 3 fractions, how to divide negative fractions, how to simplify algebraic expressions, how to get the fraction equivalent of a whole number, how to square a fraction with a variable.

• "Introductory and Intermediate Algebra"; Marvin L. Bittinger and Judith A. Beecher; 2007
• Purplemath; Fractions Review - Mixed Numbers and Improper Fractions; Elizabeth Stapel; 2000

About the Author

Gabriel Dockery began writing in 2009, with his work published on various websites. He is working toward a Bachelor of Science in neuroscience in a transfer program between Ivy Tech College and Indiana State University.

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• What is fraction? A fraction is a numerical quantity that is not a whole number. For example, ½ is a fraction of 1 as numerator and 2 as a denominator

Fractions having the same denominator are called like fractions. For example, ½,3/2, 5/2, 7/2, are all like fractions.

• Fractions having different denominators are called, unlike fractions. For example, ½, 2/3, ¾, 4/5, are all unlike fractions
• A fraction whose numerator is less than the denominator is called proper fraction. For example, 8/9, 7/8, 6/7, 5/6 are all proper fractions.
• A fraction whose numerator is greater than the denominator is called improper fraction. For example, 3/2, 4/3, 5/4, 6/5 are all improper fractions.

EXAMPLE 1: Find the fraction of shaded and unshaded part.

EXAMPLE 2: Find the fraction of red balls, green balls and blue balls.

SOLUTION: Total number of balls= 10 Number of red balls= 4

Fraction of red balls= 4/10= 2/5

Fraction of green balls= 5/10= ½

Fraction of blue balls= 1/10

Fraction as a division

• Any fraction can be expressed as a division by writing its numerator as dividend and denominator as divisor

Numerator/Denominator

= Dividend ÷ Divisor

=Dividend/Divisor

EXAMPLE 1: Write 1÷2 as a fraction.

SOLUTION: ½

EXAMPLE 2: Write 2/3 as division.

SOLUTION: 2÷3

To convert a mixed no. into an improper fraction & vice versa

• To convert a mixed number into an improper fraction multiply the quotient with the divisor and add the product with remainder in the numerator. The denominator will contain the divisor.

• To convert an improper fraction into a mixed number, divide the numerator of the fraction by the denominator. Write the quotient as the whole number. The remainder in the numerator and the divisor in the denominator.

Finding and checking equivalent fraction

• To find the equivalent fraction to a given fraction, divide or multiply the numerator or denominator by the same number. (other than zero)

• To check for equivalent fractions, we need two equivalent fraction.

SOLUTION: 2x4=8 3X3=9 8≠9

Hence, the fractions are not equal.

To find a fraction in its lowest term

• A fraction is in its lowest term when the numerator and the denominator don’t have a common factor, except 1.
• There are two methods of finding a fraction in its lowest term. They are: Method 1: Divide the numerator and denominator with their common factor till we are left with only the common factor 1

Method 2: Divide the numerator and denominator of the given fraction with their HCF.

To find the fraction of a number or quantity

• Divide the number by the denominator. Then, multiply the quotient so obtained by the numerator.

EXAMPLE 1: A group has 120 children. 4/5 of them are girls. Find the number of boys.

No. of boys= (120-96) = 24

EXAMPLE 2: Find 1/4 of a year in months.

SOLUTION: A year has 12 months. ¼ X 12 = 3 months [ANS]

To compare unlike fractions

• First find the LCM of the denominators of the given fractions.
• Then convert the unlike fractions into equivalent like fraction with LCM as their common denominator.
• Compare the like fractions.

Convert mixed fractions into improper fractions to compare them.

To add/subtract unlike fractions

• Find the LCM of the denominator of unlike fraction.
• Then convert the unlike fraction into equivalent like fraction with LCM as common denominator.
• Add/subtract the like fraction so obtained.

EXAMPLE 1: Add/subtract ½ and/from 1/6.

SOLUTION: LCM of 2 and 6 is = 2x3=6 2| 2,6 1,3

Reciprocal of a fractional number

• When the product of two fraction is 1, we say that each of the fraction is the reciprocal or multiplicative inverse of the other.

Division of fractions

• Division is repeated subtraction.
• Division by a fraction is same as multiplication by its reciprocal. 0 has no reciprocal. The reciprocal of 1 is 1. 0 divided by any non-zero number = 0

Practice these questions

• LCM of denominators is to be found only while performing addition or subtraction of unlike fractions.
• While multiplying fractions we can change their order, but the product remains the same. (commutative property)
• If a fraction is multiplied by 0, the product is always zero.
• If a fraction is multiplied by 1, the product is the same fraction.
• A fraction is in the lowest term when the only common factor between the numerator and the denominator is 1
• If any of the fraction is a mixed number or a whole number, change it to an improper function and then multiply.

Quiz for Fractions

Your Score: 0 /10

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The four operations

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Equivalent Fractions Year 5 Fractions Free Resource Pack

Step 1: Equivalent Fractions Year 5 Spring Block 2 Resources

Equivalent Fractions Year 5 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Spring Block 2.

What's included in the pack?

This pack includes:

• Equivalent Fractions Year 5 Teaching PowerPoint.
• Equivalent Fractions Year 5 Varied Fluency with answers.
• Equivalent Fractions Year 5 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 5: (5F2b)  Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

Differentiation:

Varied Fluency Developing Questions to support finding fractions equivalent to a half, a third, a quarter or a fifth using pictorial support where the original denominator is represented first. Expected Questions to support finding equivalent unit and non-unit fractions using pictorial support where the original denominator is represented first. Greater Depth Questions to support finding equivalent fractions of unit and non-unit fractions using pictorial support where the image represent a multiple of the denominator.

Reasoning and Problem Solving Questions 1, 4 and 7 (Reasoning) Developing Describe an error in a model of equivalent fractions of a half, a third, a quarter or a fifth using pictorial support where the original denominator is represented first. Expected Describe an error in a model of equivalent unit and non-unit fractions using pictorial support where the original denominator is represented first. Greater Depth Describe an error in a model of equivalent fractions of unit and non-unit fractions using pictorial support where the image represents a multiple of the denominator.

Questions 2, 5 and 8 (Reasoning) Developing Correct and explain errors when shading equivalent fractions of a half, a third, a quarter or a fifth where the original denominator is represented first. Expected Correct and explain errors when shading equivalent unit and non-unit fractions where the original denominator is represented first, Greater Depth Correct and explain errors when calculating equivalent fractions of unit and non-unit fractions.

Questions 3, 6 and 9 (Problem Solving) Developing Find 2 possibilities for a missing function used to create equivalent fractions of a half, a third, a quarter or a fifth using pictorial support where the image represents a multiple of the denominator. Expected Find 2 possibilities for a missing function used to create equivalent unit or non-unit fractions. Greater Depth Find 2 possibilities for two missing functions used to create equivalent fractions of unit and non-unit fractions.

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