Which is the correct symbol to make the resulting inequality true?
4 4/3 > 4 1/2
Or
4 4/3 < 4 1/2
What does this mean?
The symbol > means the first number is greater than the second.
The symbol < means the first number is less than the second.
These are true statements.
5 > 2
3 < 10
Your answer is 4 4/3 > 4 1/2
> means greater than
< means less than.
Examples:
4 > 3
3 < 4
-8>-1
To determine which symbol (greater than > or less than <) makes the resulting inequality true, we need to compare the two given mixed numbers: 4 4/3 and 4 1/2.
One approach to comparing two mixed numbers is to convert them into improper fractions and then find a common denominator.
Let's convert 4 4/3 into an improper fraction:
4 x 3 = 12. Adding the numerator, we have 12 + 4 = 16. So, 4 4/3 as an improper fraction is 16/3.
Now, let's convert 4 1/2 into an improper fraction:
4 x 2 = 8. Adding the numerator, we have 8 + 1 = 9. So, 4 1/2 as an improper fraction is 9/2.
Now that we have both fractions, we can compare them:
16/3 > 9/2
To compare fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 2 is 6. Therefore, we can convert both fractions to have a denominator of 6.
Multiplying the numerator and denominator of 16/3 by 2, we get 32/6.
Multiplying the numerator and denominator of 9/2 by 3, we get 27/6.
Now the comparison becomes:
32/6 > 27/6
Since the numerators are different, we can directly compare the fractions' numerators:
32 > 27
Therefore, the correct symbol to make the resulting inequality true is > (greater than).
In terms of the meaning of the inequality, 4 4/3 > 4 1/2 means that 4 4/3 is greater than 4 1/2.