Unlocking Fractions: Understanding Numerator, Denominator, and Equivalent Fractions

Notice that Emily's fractions are written in their simplest form, but Jordan's fractions are not simplified. Therefore, to find the equivalent fractions, each of Jordan's fractions will be analyzed and simplified, one at a time.

First Fraction

Begin by considering the first fraction from Jordan's list.

\frac{6}{1 2}

To simplify this fraction, its numerator and denominator should be divided by their greatest common factor (GCF). To find it, split

6

and

12

into prime factors.

612 = 2 \cdot 3 = 2 \cdot 2 \cdot 3

As shown,

6

and

12

share two common factors. Their product is the GCF of these numbers.

GCF (6, 12) = 2 \cdot 3 = 6

Finally, divide both the numerator and denominator by

6

to simplify the fraction.

\frac{6}{1 2}

ReduceFrac

$\frac{a}{b} = \frac{a / 6}{b / 6}$

\frac{6 \div 6}{1 2 \div 6}

CalcQuot

Calculate quotient

\frac{1}{2}

Therefore,

\frac{1}{2}

is an equivalent fraction to

\frac{6}{1 2} .

Second Fraction

Now, consider the second fraction from Jordan's list.

\frac{1 6}{5 6}

Again, find the GCF of the numerator

16

and the denominator

56 .

To do so, write each number as the product of prime numbers.

1656 = 2 \cdot 2 \cdot 2 \cdot 2 = 2 \cdot 2 \cdot 2 \cdot 7

There are three common factors between

16

and

56 .

Multiply them to calculate the GCF of

16

and

56 .

2 \cdot 2 \cdot 2 = 8

Next, simplify the fraction by dividing its numerator and denominator by

8 .

\frac{1 6}{5 6}

ReduceFrac

$\frac{a}{b} = \frac{a / 8}{b / 8}$

\frac{1 6 \div 8}{5 6 \div 8}

CalcQuot

Calculate quotient

\frac{2}{7}

Therefore,

\frac{1 6}{5 6}

and

\frac{2}{7}

are equivalent fractions.

Third Fraction

Similarly, examine the third fraction that Jordan wrote.

\frac{1 4}{3 2}

Just as before, determine the GCF of

14

and

32

by factoring the numbers into prime factors.

1432 = 2 \cdot 7 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2

The numbers share only one common factor,

2 .

This means that the GCF of

14

and

32

2 .

Next, simplify the fraction by dividing the numerator and denominator by

2 .

\frac{1 4}{3 2}

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

\frac{1 4 \div 2}{3 2 \div 2}

CalcQuot

Calculate quotient

\frac{7}{1 6}

It can be concluded that

\frac{7}{1 6}

is an equivalent fraction to

\frac{1 4}{3 2} .

Fourth Fraction

Finally, consider the last fraction from Jordan's list.

\frac{2 0}{1 5}

Start by rewriting the numerator and denominator as the product of prime factors.

2015 = 2 \cdot 2 \cdot 5 = 3 \cdot 5

The common factor between

20

and

15

5 .

This is their GCF. Divide both the numerator and denominator by

5

to simplify the fraction.

\frac{2 0}{1 5}

ReduceFrac

$\frac{a}{b} = \frac{a / 5}{b / 5}$

\frac{2 0 \div 5}{1 5 \div 5}

CalcQuot

Calculate quotient

\frac{4}{3}

It can be concluded that

\frac{4}{3}

is an equivalent fraction to

\frac{2 0}{1 5} .

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Catch-Up and Review

Splitting a Pizza

Presenting Rational Numbers

Rational Numbers

Definition of a Fraction

Fraction

Determining Fractions

Hint

Solution

Identifying Fractions Describing the Graph

Equivalent Fractions

How to Simplify a Fraction

Simplifying a Fraction

Extra

Pairing Equivalent Fractions

Hint

Solution

First Fraction

Second Fraction

Third Fraction

Fourth Fraction

Simplifying Fractions

Real Life Applications of Fractions

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