What is a fraction bigger than 2 3?

Number line models show show how to compare unlike fractions using a common denominator.

COMPARE FRACTIONS WITH NUMBER LINE MODELS INSTRUCTIONS

Follow the directions in the dialog box after pressing the <START> button. The <EXPLAIN> button may be pressed to see how to do the example.

When Compare Fractions starts,  you will be given two fractions to compare, as in the example below:

You are to decide if the fraction on the left is less than, equal to, or greater than the fraction on the right. You will choose < for less than, = for equal to, or > for greater than. Shown in the dialog box are your choices of <, >, or =.

If the denominators are the same, the fraction with the larger numerator is larger and if the numerators are the same, the fraction with the larger denominator is smaller.

The following cmpare fractions illustration was made by Compare Fractions With Lines Designer:

The fractions 3⁄4 and 2⁄3 are pictured with number lines below:

Let's make the denominators the same so that we can compare the numerators. Fractions with the same denominators are like fractions.

Here, we will introduce the idea of the least common denominator or LCD.  LCD is an idea that will be used in comparing, adding, and subtracting fractions. The LCD is the smallest number that both 4 and 3 will divide into evenly. The LCD for the fractions 3⁄4 and 2⁄3 is 12 because both denominators 4 and 3 divide evenly into 12. 

Then, write each fraction with the common denominator 12 to make them like. The illustration shows that 3⁄4 is equal to 9⁄12 and 2⁄ 3 is equal to 8/12. Once each fraction is renamed with a common denominator, you can compare the numerators - the larger the numerator the larger the fraction.

Since 3⁄4 is greater than 2⁄3, you will select the > symbol.

See the program  RENAME IN HIGHER TERMS for more information on renaming fractions.

One way to find the LCD is to see if the smaller denominator 3 will divide evenly into the larger denominator 4.  If not, multiply the larger denominator 4 by 2 to get 8.  Will the smaller denominator 3 divide into 8? No, so multiply the larger denominator by 3 to get 12. Will 3 divide evenly into 12? Yes, so 12 is the LCD for the denominators 3 and 4. If not, then multiply by 4, then 5, etc. until the smaller denominator divides into the product.

Also, thinking of the pictures of the fractions will help you decide which is the larger.

Choose the < (less than) button if you think the first fraction is smaller than the second. Choose the = (equal button) if you think the two fractions are the same size. Choose the > (greater than) if you think the fraction is larger. If correct, number lines showing the comparative sizes of the two fractions will appear. Press the <EXPLAIN> button to see each fraction with the common denominator.

For more instruction on comparng fractions go to How To Compare Fractions.

After you press the <, =, or > button you may press the <REPORT> button. The report will ask for your name but you may submit a code for your name. This report will give same results as on the dialog box. The report may be printed or e-mailed.

Explanation:

To check which of the two factors is bigger,

we should make the denominator of two factors same by finding GCD and then making each of the denominator equal to their GCD.

Here in #3/4# and #2/3# denominators are #4# and #3# and their GCD is #12#. Now let us make each denominator equal to #12#.

#3/4=(3xx3)/(3xx4)=9/12# and

#2/3=(4xx2)/(4xx3)=8/12#

Now as #9/12>8/12#, we have #3/4>2/3#

hence #3/4# is bigger.

How Do You Compare Fractions?

The answer to that question depends on whether you are comparing fractions with the same denominators or if you are comparing fractions with different denominators.

Comparing Fractions with Same Denominators

Comparing fractions with the same denominators (bottom number) is easy. All you do is compare the numerators to see which fraction is greater, like this:

Comparison with Same Denominators

Comparing Fractions with Different Denominators

Comparing fractions with different denominators requires a little more work (unless you use the compare fractions calculator on this page), because in order to compare the fractions you must first turn their different denominators into the same denominators. You do that by finding the least common multiple (LCM) of the denominators.

To illustrate how you use LCM to turn different denominators into same denominators, let's suppose you want to compare the fraction 2/3 to the fraction 3/4 to see which is greater.

The first step is to find the lowest number that both 3 and 4 will divide into evenly (the LCM). According to my calculations, the LCM of the two denominators (3 & 4) is 12.

Once we have found the LCM for the two denominators, the next step is to multiply the top and bottom of each fraction by the number of times each fraction's denominator goes into the LCM.

Since 3 goes into 12 a total of 4 times, you would multiply the top and bottom of 2/3 by 4, which results in 8/12.

Next, since 4 goes into 12 a total of 3 times, you would multiply the top and bottom of 3/4 by 3, which results in 9/12.

Finally, since both denominators are now the same, you compare the numerators (8 and 9) to determine which fraction is greater. Since 9 is greater than 8, 9/12 is greater than 8/12 -- therefore 3/4 is greater than 2/3. Here is how our example of comparing fractions with different denominators might appear on paper:

Comparing Fractions with Different Denominators

So for like denominators you simply compare the numerators and for unlike denominators you multiply the top and bottom by the least common multiple of each denominator, and then compare the numerators.

Which Fraction is Bigger Calculator

Greater Than Less Than Fractions Calculator

The following calculator will generate a list of fractions greater than or less than the selected fraction between 1/1 and 20/20.

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