How to Find a Fraction Between Two Fractions

How to Find a Fraction Between Two Fractions
••• jenifoto/iStock/GettyImages

A fraction is a value in two parts; each part, the numerator or denominator, is an integer. The numerator is the fraction's top number, while the denominator is its bottom number. Lower-order fractional math like addition and subtraction requires that the denominators of the involved fractions be the same value. When finding a fraction that comes between two others, you ignore normal fractional math in favor of a simpler method.

    Obtain two fractions for example purposes. For this example, let the fractions be

    \frac{1}{2} \text{ and } \frac{3}{4}

    Sum the fractions' numerators. In this example,

    1 + 3 = 4

    Sum the fraction's denominators. In this example,

    2 + 4 = 6

    Write a new fraction with the numerators' sum as the new numerator and the denominators' sum as the new denominator. In this example, the new fraction is

    \frac{4}{6}

    Simplify the fraction by eliminating the greatest common factor shared by the numerator and denominator. To do this, list the factors of each number and factor out the largest shared number.

    In this case, the factors of 4 are 1, 2 and 4, and the factors of 6 are 1, 2, 3 and 6. Both numbers have 1 and 2 as factors, with 2 being the greatest factor.

    Eliminating 2 from both the numerator and denominator results in

    \frac{4 ÷ 2}{6 ÷ 2} = \frac{2}{3}

    Tips

    • To check your answer, write the fractions with common denominators and compare the numerators. The example fractions of 1/2, 2/3 and 3/4 with common denominators become 6/12, 8/12 and 9/12. The numerator 8 is between 6 and 9, so the fraction you created – 8/12, or 2/3 when simplified – is between the two fractions you started with.

Related Articles

How to Subtract Percentages
How to Convert a Fraction to a Ratio
How to Compare Negative Fractions
How to Find a Fraction of a Number
How to Subtract, Add & Simplify Fractions
How to Get the Fraction Equivalent of a Whole Number
How to Add & Subtract Improper Fractions
How to Divide Rational Numbers
How to Arrange Fractions in Size Order
How to Add Fractions with Mixed Numbers
How to Divide Negative Fractions
How to Calculate the Percentage of Another Number
How to Solve a Math Factor Puzzle
How to Find the Height of a Rectangular Pyramid
How to Divide in Scientific Exponents
How to Square a Fraction With a Variable
How to Find a Percent of a Fraction
How to Calculate the Midpoint Between Two Numbers
How to Multiply Fractions With Negative Numbers
How to Do Fractions on a TI-30X IIS

Dont Go!

We Have More Great Sciencing Articles!