Compare Fractions and Decimals: Is 6/9 > 0.7?

Fraction-Decimal Comparison with Common Denominators

Choose the appropriate sign:

69?0.7 \frac{6}{9}?0.7

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate sign
00:05 Convert decimal number to fraction
00:22 Multiply each fraction by the second denominator to find the common denominator
00:27 Be sure to multiply numerator by numerator and denominator by denominator
00:40 Now let's compare the fractions
00:44 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the appropriate sign:

69?0.7 \frac{6}{9}?0.7

2

Step-by-step solution

First, let's convert 0.7 to a simple fraction.

Since there is only one digit after the decimal point, the number divides by 10 as follows:

0.7=710 0.7=\frac{7}{10}

Now we have two simple fractions with different denominators.

In order to compare them, note that the smallest common denominator between them is 90.

We'll multiply each one to reach the common denominator as follows:

69×1010=6090 \frac{6}{9}\times\frac{10}{10}=\frac{60}{90}

710×99=6390 \frac{7}{10}\times\frac{9}{9}=\frac{63}{90}

Now we can compare the two fractions and see that:

6090<6390 \frac{60}{90}<\frac{63}{90}

3

Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Conversion Rule: Convert decimal to fraction using place value position
  • Common Denominator: Use 69=6090 \frac{6}{9} = \frac{60}{90} and 710=6390 \frac{7}{10} = \frac{63}{90}
  • Compare Numerators: When denominators match, 60 < 63 so 6090<6390 \frac{60}{90} < \frac{63}{90}

Common Mistakes

Avoid these frequent errors
  • Comparing fractions directly without common denominators
    Don't compare 69 \frac{6}{9} and 710 \frac{7}{10} by just looking at 6 vs 7 = wrong comparison! Different denominators mean different-sized pieces, so you can't compare numerators alone. Always find a common denominator first or convert both to the same form.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

\( 0.23\stackrel{?}{=}0.32 \)

FAQ

Everything you need to know about this question

Why can't I just compare 6 and 7 directly?

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Because 69 \frac{6}{9} and 710 \frac{7}{10} have different denominators! Think of it like comparing 6 slices of a 9-piece pizza vs 7 slices of a 10-piece pizza - the pieces are different sizes.

Is there an easier way than finding common denominators?

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Yes! You can convert both to decimals instead. 69=0.667... \frac{6}{9} = 0.667... and 0.7=0.700 0.7 = 0.700 , so 0.667 < 0.700.

How do I find the least common denominator quickly?

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For denominators 9 and 10, list their multiples:

  • 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
  • 10: 10, 20, 30, 40, 50, 60, 70, 80, 90
The first number that appears in both lists is your LCD!

What if I get confused with the inequality signs?

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Remember: the inequality sign always points to the smaller number. Since 6090 \frac{60}{90} is smaller than 6390 \frac{63}{90} , we write 6090<6390 \frac{60}{90} < \frac{63}{90} .

Should I always simplify fractions before comparing?

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It's helpful but not required! 69=23 \frac{6}{9} = \frac{2}{3} when simplified, but you can compare either way. Sometimes it's easier to work with the original fractions.

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