How do you find two different ways to show how you know whether 3/4 is greater than 2/3?
Multiply the numerator and denominator by 3
Multiply the numerator and denominator by 4
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One way to determine if ( \frac{3}{4} ) is greater than ( \frac{2}{3} ) is to find a common denominator for both fractions and then compare their numerators. Another approach is to convert both fractions into decimals and compare their decimal representations. Let's demonstrate both methods:
Method 1: Comparing with a Common Denominator [ \frac{3}{4} ) and ( \frac{2}{3} ) both have denominators of 4 and 3 respectively. The least common denominator (LCD) is 12. [ \frac{3}{4} = \frac{9}{12} ) and ( \frac{2}{3} = \frac{8}{12} ). Since ( 9 > 8 ), ( \frac{3}{4} ) is greater than ( \frac{2}{3} ).
Method 2: Comparing Decimals Divide 3 by 4 to get ( 0.75 ) and divide 2 by 3 to get ( 0.666...). Since ( 0.75 > 0.666... ), ( \frac{3}{4} ) is greater than ( \frac{2}{3} ).
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To compare whether ( \frac{3}{4} ) is greater than ( \frac{2}{3} ), you can use two different methods:

Common Denominator Method: Find a common denominator for both fractions and compare the numerators.
 Multiply ( \frac{3}{4} ) by ( \frac{3}{3} ) to get a common denominator with ( \frac{2}{3} ), resulting in ( \frac{9}{12} ).
 Compare ( \frac{9}{12} ) and ( \frac{8}{12} ). Since ( 9 > 8 ), ( \frac{9}{12} ) is greater than ( \frac{8}{12} ).
 Therefore, ( \frac{3}{4} ) is greater than ( \frac{2}{3} ).

Cross Multiplication Method: Cross multiply the fractions and compare the products.
 Cross multiply: ( 3 \times 3 = 9 ) for ( \frac{3}{4} ) and ( 2 \times 4 = 8 ) for ( \frac{2}{3} ).
 Compare the products: ( 9 > 8 ).
 Therefore, ( \frac{3}{4} ) is greater than ( \frac{2}{3} ).
Both methods yield the same result, confirming that ( \frac{3}{4} ) is indeed greater than ( \frac{2}{3} ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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