Mathematical Magnitude Comparison: Determining Greater Values

Q: Why can't I just compare the top numbers?

Because the denominators are different! $ \frac{9}{11} $ means 9 pieces out of 11, while $ \frac{7}{9} $ means 7 pieces out of 9. The piece sizes are different, so you need to account for both parts.

Q: What's the easiest way to compare these fractions?

Cross multiplication is usually fastest! Multiply the numerator of the first fraction by the denominator of the second, then compare. For $ \frac{9}{11} $ vs $ \frac{7}{9} $: 9×9 = 81 and 7×11 = 77.

Q: Could I convert to decimals instead?

Yes! $ \frac{9}{11} $ ≈ 0.818 and $ \frac{7}{9} $ ≈ 0.778. But be careful with rounding errors - cross multiplication gives exact results every time.

Q: What if I want to find a common denominator?

That works too! The LCD of 11 and 9 is 99. So $ \frac{9}{11} = \frac{81}{99} $ and $ \frac{7}{9} = \frac{77}{99} $. Now you can easily see 81 > 77.

Q: How do I remember which cross product goes with which fraction?

Think of making an X pattern! Draw lines connecting opposite corners: top-left × bottom-right, and top-right × bottom-left. The fraction with the larger cross product is larger.

Fraction Comparison with Cross Multiplication

Which is larger?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the largest

00:06 Take the 2 fractions with the largest numerator

00:13 The smaller the denominator, the larger the fraction

00:22 Now let's compare this fraction with another fraction

00:30 Multiply each fraction by the denominator of the other fraction

00:33 To find a common denominator

00:50 When the denominator is equal, the larger numerator is the larger fraction

01:03 Again use the same method, find a common denominator

01:22 When the denominator is equal, the larger numerator is the larger fraction

01:33 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

Which is larger?

Final Answer

$\frac{9}{11}$

Key Points to Remember

Essential concepts to master this topic

Rule: Cross multiply to compare fractions with different denominators
Technique: Convert $\frac{9}{11}$ vs $\frac{7}{9}$ : 9×9 = 81, 7×11 = 77
Check: Larger cross product identifies the larger fraction: 81 > 77 ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators and denominators separately
Don't just compare 9 > 7 and assume $\frac{9}{11}$ > $\frac{7}{9}$ = wrong answer! Different denominators make direct comparison impossible. Always cross multiply or find common denominators to compare accurately.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{25}☐\frac{1}{5}$

FAQ

Everything you need to know about this question

Why can't I just compare the top numbers?

Because the denominators are different! $\frac{9}{11}$ means 9 pieces out of 11, while $\frac{7}{9}$ means 7 pieces out of 9. The piece sizes are different, so you need to account for both parts.

What's the easiest way to compare these fractions?

Cross multiplication is usually fastest! Multiply the numerator of the first fraction by the denominator of the second, then compare. For $\frac{9}{11}$ vs $\frac{7}{9}$ : 9×9 = 81 and 7×11 = 77.

Could I convert to decimals instead?

Yes! $\frac{9}{11}$ ≈ 0.818 and $\frac{7}{9}$ ≈ 0.778. But be careful with rounding errors - cross multiplication gives exact results every time.

What if I want to find a common denominator?

That works too! The LCD of 11 and 9 is 99. So $\frac{9}{11} = \frac{81}{99}$ and $\frac{7}{9} = \frac{77}{99}$ . Now you can easily see 81 > 77.

How do I remember which cross product goes with which fraction?

Think of making an X pattern! Draw lines connecting opposite corners: top-left × bottom-right, and top-right × bottom-left. The fraction with the larger cross product is larger.

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