Math Problem Statement

Compare the following fractions using the symbols >, <, or =. Show all the calculations to support your answer.

Solution

To compare two fractions, we need to determine which fraction is larger, smaller, or if they are equal. The most common method is to find a common denominator or convert the fractions into decimals.

Since you haven't provided the specific fractions, let's consider the general approach:

1. Finding a Common Denominator

Given two fractions:

abandcd\frac{a}{b} \quad \text{and} \quad \frac{c}{d}

To compare these fractions, we can find a common denominator:

ab=adbd,cd=cbdb\frac{a}{b} = \frac{a \cdot d}{b \cdot d}, \quad \frac{c}{d} = \frac{c \cdot b}{d \cdot b}

Both fractions now have the same denominator bdb \cdot d. We can then directly compare their numerators:

adandcba \cdot d \quad \text{and} \quad c \cdot b

If ad>cba \cdot d > c \cdot b, then ab>cd\frac{a}{b} > \frac{c}{d}.

If ad<cba \cdot d < c \cdot b, then ab<cd\frac{a}{b} < \frac{c}{d}.

If ad=cba \cdot d = c \cdot b, then ab=cd\frac{a}{b} = \frac{c}{d}.

2. Converting Fractions to Decimals

Alternatively, we can convert the fractions into decimals by performing division:

Decimal value of ab=ab,Decimal value of cd=cd\text{Decimal value of } \frac{a}{b} = \frac{a}{b}, \quad \text{Decimal value of } \frac{c}{d} = \frac{c}{d}

By comparing the decimal values, we can determine which fraction is greater, smaller, or if they are equal.


Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Fractions
Comparison of Fractions

Formulas

Common Denominator: (a/b = a*d / b*d) and (c/d = c*b / d*b)
Fraction to Decimal Conversion: Decimal value of a/b = a ÷ b

Theorems

None

Suitable Grade Level

Grade 7-8