Compare Fractions: Determine the Symbol Between 3/4 and 1/9

Q: Why can't I just look at the numerators and denominators separately?

You can't compare fractions by just looking at parts! $ \frac{3}{4} $ has a smaller numerator than some fractions but could still be larger. Cross-multiplication considers both parts together for accurate comparison.

Q: What exactly is cross-multiplication doing?

Cross-multiplication finds a common comparison point. When you multiply 3 × 9 = 27 and 4 × 1 = 4, you're essentially comparing $ \frac{27}{36} $ vs $ \frac{4}{36} $ with the same denominator!

Q: Does the order matter when I cross-multiply?

Yes, order matters! Always multiply the first numerator × second denominator, then first denominator × second numerator. This keeps your comparison consistent.

Q: Can I use this method for any fraction comparison?

Absolutely! Cross-multiplication works for any two fractions, whether they have small or large numbers. It's especially helpful when denominators are different and hard to compare mentally.

Fraction Comparison with Cross-Multiplication Method

Fill in the missing sign:

$\frac{3}{4}☐\frac{1}{9}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 We want to find a common denominator

00:09 Therefore, we'll multiply each fraction by the denominator of the other fraction

00:12 Remember to multiply both numerator and denominator

00:24 Now we'll use the same method for the second fraction

00:27 Remember to multiply by the denominator of the second fraction

00:30 Remember to multiply both numerator and denominator

00:34 Now we have a common denominator between the fractions

00:40 When denominators are equal, the larger the numerator, the larger the fraction

00:45 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$\frac{3}{4}☐\frac{1}{9}$

Step-by-step solution

To determine the correct inequality sign to compare $\frac{3}{4}$ and $\frac{1}{9}$ , we'll use the technique of cross-multiplication. This method involves multiplying the numerator of each fraction by the denominator of the other fraction. By calculating and comparing these products, we can determine the relative size of the fractions.

Let's perform the cross-multiplication:

Multiply the numerator of the first fraction by the denominator of the second fraction:

\ 3 \times 9 = 27

Multiply the denominator of the first fraction by the numerator of the second fraction:

\ 4 \times 1 = 4

Now we compare these two results. Since $27$ is greater than $4$ , we conclude that:

\ \frac{3}{4} > \frac{1}{9}

Therefore, the correct inequality sign to fill in the blank is $>$ .

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare fractions using cross-multiplication when denominators differ
Technique: Multiply 3 × 9 = 27 and 4 × 1 = 4
Check: Since 27 > 4, then 3/4 > 1/9 ✓

Common Mistakes

Avoid these frequent errors

Converting to decimals incorrectly
Don't convert 3/4 = 0.75 and 1/9 = 0.11 without careful division = rounding errors! This can lead to wrong comparisons with close fractions. Always use cross-multiplication for accurate fraction comparison.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{9}☐\frac{3}{9}$

FAQ

Everything you need to know about this question

Why can't I just look at the numerators and denominators separately?

You can't compare fractions by just looking at parts! $\frac{3}{4}$ has a smaller numerator than some fractions but could still be larger. Cross-multiplication considers both parts together for accurate comparison.

What exactly is cross-multiplication doing?

Cross-multiplication finds a common comparison point. When you multiply 3 × 9 = 27 and 4 × 1 = 4, you're essentially comparing $\frac{27}{36}$ vs $\frac{4}{36}$ with the same denominator!

Does the order matter when I cross-multiply?

Yes, order matters! Always multiply the first numerator × second denominator, then first denominator × second numerator. This keeps your comparison consistent.

Can I use this method for any fraction comparison?

Absolutely! Cross-multiplication works for any two fractions, whether they have small or large numbers. It's especially helpful when denominators are different and hard to compare mentally.

What if both cross-products are equal?

If both products are equal, then the fractions are equal too! For example, if 2 × 6 = 3 × 4 = 12, then $\frac{2}{3} = \frac{4}{6}$ .

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