#### Comparing Fractions

I. Basic Reminders

II. Comparing Fractions With the Same Denominators

III. Comparing Fractions With the Same Numerators

IV. Comparing Fractions Using Cross Multiplication

V. Comparing Fractions By Converting to Decimals

I. Basic Reminders

Comparison Symbols:

= means equal

< means less than

> means greater than

The signs are read from left to right. Thus 25 > 16 is read twenty-five is greater than sixteen. Memory tip: Think of > as a hungry animal’s mouth looking to eat the largest of everything; in this case, it’s numbers. What animal did you choose?

A few more reminders:

**A fraction is divided into equal parts.

Part..........................................................Numerator

----------------------------------------------- = ------------------

Whole or Total Number of Equal Parts.........Denominator

II. Comparing Fractions With the Same Denominators

If a fraction has the same denominator, it means the object the fraction represents requires the same number of equal parts to make a one whole. For example, 3/8 and 5/8 are both divided into eight equal parts. So, compare the numerators. Since 5 is larger than 3, 5/8 is larger than 3/8. Use the comparison symbol as follows: 5/8 > 3/8 or 3/8 < 5/8.

III. Comparing Fractions With the Same Numerator

For example 4/5 and 4/8

This time each fraction requires a different number of parts to make a whole. 4/5

requires five equal parts. One more equal part would become 5/5 which is a whole. The other fraction 4/8 requires eight equal parts to make a whole. Four more equal parts are required to make a whole.

Which fraction is closer to making a whole? (4/5) Therefore 4/5 > 4/8

Another way to visualize this example is to think of two pies the same size. If you want the largest serving, would you choose four pieces of the pie cut into eight equal parts or five equal parts? Yes, the slices are larger on the pie cut into 5 slices.

IV. Comparing Fractions Using Cross Multiplication

Another method to compare fractions is to use cross multiplication. Let’s look at 4/5 and 4/8 again. Pay close attention to the numerators.

1st fraction: multiply the numerator times the denominator of the 2nd fraction -- 4 x 8 = 32

2nd fraction: multiply the numerator times the denominator of the 1st fraction – 4 x 5 = 20

The first equation with the 1st numerator has the largest product. Thus, the first fraction 4/5 > 4/8.

Try another one: 6/9 and 5/8

Cross multiply: the 1st numerator times the 2nd denominator --- 6 x 8 = 48

Then multiply the 2nd numerator times the 1st denominator --- 5 x 9 = 45

The equation with the first numerator has the largest product. Thus, the first fraction 6/9 > 5/8.

V. Compare Fractions by Converting to Decimals

Let’s use the fractions in the previous example, 6/9 and 5/8

Note: the line between the numbers six and nine is called the fraction bar. When you look at the fraction bar, think of the words, “divided by.”

So, read 6.9 as six “divided by” 9. 6/9= .666

Read 5/8 as five “divided by” 8. 5/8 = .625

Write the decimal numbers vertically making certain to line up the decimals. Start from the decimal and compare each digit. 6 = 6; 6 is greater than 2. Thus 6/9 is greater than 5/8 or 6/9 > 5/8.

The related links below will give you practice. Refer to this article to help you win the games. Note: Once you activate the game, press F11 to play the game on a full screen. Press F11 again to return to your normal screen. Have Fun!

II. Comparing Fractions With the Same Denominators

III. Comparing Fractions With the Same Numerators

IV. Comparing Fractions Using Cross Multiplication

V. Comparing Fractions By Converting to Decimals

I. Basic Reminders

Comparison Symbols:

= means equal

< means less than

> means greater than

The signs are read from left to right. Thus 25 > 16 is read twenty-five is greater than sixteen. Memory tip: Think of > as a hungry animal’s mouth looking to eat the largest of everything; in this case, it’s numbers. What animal did you choose?

A few more reminders:

**A fraction is divided into equal parts.

Part..........................................................Numerator

----------------------------------------------- = ------------------

Whole or Total Number of Equal Parts.........Denominator

II. Comparing Fractions With the Same Denominators

If a fraction has the same denominator, it means the object the fraction represents requires the same number of equal parts to make a one whole. For example, 3/8 and 5/8 are both divided into eight equal parts. So, compare the numerators. Since 5 is larger than 3, 5/8 is larger than 3/8. Use the comparison symbol as follows: 5/8 > 3/8 or 3/8 < 5/8.

III. Comparing Fractions With the Same Numerator

For example 4/5 and 4/8

This time each fraction requires a different number of parts to make a whole. 4/5

requires five equal parts. One more equal part would become 5/5 which is a whole. The other fraction 4/8 requires eight equal parts to make a whole. Four more equal parts are required to make a whole.

Which fraction is closer to making a whole? (4/5) Therefore 4/5 > 4/8

Another way to visualize this example is to think of two pies the same size. If you want the largest serving, would you choose four pieces of the pie cut into eight equal parts or five equal parts? Yes, the slices are larger on the pie cut into 5 slices.

IV. Comparing Fractions Using Cross Multiplication

Another method to compare fractions is to use cross multiplication. Let’s look at 4/5 and 4/8 again. Pay close attention to the numerators.

1st fraction: multiply the numerator times the denominator of the 2nd fraction -- 4 x 8 = 32

2nd fraction: multiply the numerator times the denominator of the 1st fraction – 4 x 5 = 20

The first equation with the 1st numerator has the largest product. Thus, the first fraction 4/5 > 4/8.

Try another one: 6/9 and 5/8

Cross multiply: the 1st numerator times the 2nd denominator --- 6 x 8 = 48

Then multiply the 2nd numerator times the 1st denominator --- 5 x 9 = 45

The equation with the first numerator has the largest product. Thus, the first fraction 6/9 > 5/8.

V. Compare Fractions by Converting to Decimals

Let’s use the fractions in the previous example, 6/9 and 5/8

Note: the line between the numbers six and nine is called the fraction bar. When you look at the fraction bar, think of the words, “divided by.”

So, read 6.9 as six “divided by” 9. 6/9= .666

Read 5/8 as five “divided by” 8. 5/8 = .625

Write the decimal numbers vertically making certain to line up the decimals. Start from the decimal and compare each digit. 6 = 6; 6 is greater than 2. Thus 6/9 is greater than 5/8 or 6/9 > 5/8.

The related links below will give you practice. Refer to this article to help you win the games. Note: Once you activate the game, press F11 to play the game on a full screen. Press F11 again to return to your normal screen. Have Fun!

**You Should Also Read:**

Comparing Fraction Game Practice

Fractions - Adding Unlike Denominators - LCM

Fraction Fun - Book Review

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