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How Do Common Denominators Simplify the Process of Comparing Fractions?

When you want to compare fractions, using a common denominator makes things a lot easier. Let’s talk about what that means and how it helps us.

What is a Common Denominator?

A common denominator is a number that both fractions can share. This means it’s a multiple of the numbers in the bottom part of each fraction, called the denominators.

Let’s look at the fractions (\frac{1}{3}) and (\frac{1}{4}).

Here, the denominators are 3 and 4.

  • The multiples of 3 are: 3, 6, 9, 12...
  • The multiples of 4 are: 4, 8, 12, 16...

The smallest number that appears in both lists is 12. This is our common denominator.

Changing to Common Denominators

Now, we need to change both fractions so they both have this common denominator of 12.

  1. For (\frac{1}{3}): [ \frac{1}{3} \times \frac{4}{4} = \frac{4}{12} ]

  2. For (\frac{1}{4}): [ \frac{1}{4} \times \frac{3}{3} = \frac{3}{12} ]

Comparing the Fractions

Now that both fractions are written with the common denominator of 12, we can easily compare them by looking at the top part of the fractions, called the numerators:

  • (\frac{4}{12}) (which comes from (\frac{1}{3}))
  • (\frac{3}{12}) (which comes from (\frac{1}{4}))

Since 4 is bigger than 3, we can say:

[ \frac{1}{3} > \frac{1}{4} ]

In Summary

Using common denominators makes comparing fractions simpler and helps us avoid mistakes that can happen if we try to compare fractions with different denominators.

So remember this: finding a common denominator is a super important step when comparing fractions. This skill will be helpful in Year 7 math and beyond!

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How Do Common Denominators Simplify the Process of Comparing Fractions?

When you want to compare fractions, using a common denominator makes things a lot easier. Let’s talk about what that means and how it helps us.

What is a Common Denominator?

A common denominator is a number that both fractions can share. This means it’s a multiple of the numbers in the bottom part of each fraction, called the denominators.

Let’s look at the fractions (\frac{1}{3}) and (\frac{1}{4}).

Here, the denominators are 3 and 4.

  • The multiples of 3 are: 3, 6, 9, 12...
  • The multiples of 4 are: 4, 8, 12, 16...

The smallest number that appears in both lists is 12. This is our common denominator.

Changing to Common Denominators

Now, we need to change both fractions so they both have this common denominator of 12.

  1. For (\frac{1}{3}): [ \frac{1}{3} \times \frac{4}{4} = \frac{4}{12} ]

  2. For (\frac{1}{4}): [ \frac{1}{4} \times \frac{3}{3} = \frac{3}{12} ]

Comparing the Fractions

Now that both fractions are written with the common denominator of 12, we can easily compare them by looking at the top part of the fractions, called the numerators:

  • (\frac{4}{12}) (which comes from (\frac{1}{3}))
  • (\frac{3}{12}) (which comes from (\frac{1}{4}))

Since 4 is bigger than 3, we can say:

[ \frac{1}{3} > \frac{1}{4} ]

In Summary

Using common denominators makes comparing fractions simpler and helps us avoid mistakes that can happen if we try to compare fractions with different denominators.

So remember this: finding a common denominator is a super important step when comparing fractions. This skill will be helpful in Year 7 math and beyond!

Related articles