compare the mixed numbers. write <, >, or = ro each .
1. 1 1/3 > 1 5/8.
2. 6 5/6 < 6 2/6.
order the mixed number froms least to greatest.
5 1/8, 5 2/3, 5 4/9.
# 2 is correct. The other two are wrong.
Change the fractions so that all of them in the same group have a common denominator.
I only need examples of simplest form
To compare mixed numbers, you need to first convert them into improper fractions. Then you can compare the fractions to determine which one is greater, lesser, or equal.
1. Let's compare 1 1/3 and 1 5/8:
To convert 1 1/3 into an improper fraction, you multiply the whole number by the denominator and add the numerator:
1 * 3 + 1 = 4.
So, 1 1/3 as an improper fraction is 4/3.
To convert 1 5/8 into an improper fraction, you multiply the whole number by the denominator and add the numerator:
1 * 8 + 5 = 13.
So, 1 5/8 as an improper fraction is 13/8.
Now you can compare the improper fractions:
4/3 > 13/8.
To compare fractions with different denominators, you need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 8 is 24.
Multiply both the numerators and denominators by the appropriate factors to find equivalent fractions with the same denominator:
4/3 * 8/8 = 32/24.
13/8 * 3/3 = 39/24.
Now you can compare the fractions:
32/24 > 39/24.
Therefore, 1 1/3 is greater than 1 5/8. So, the answer is > (greater than).
2. Now let's compare 6 5/6 and 6 2/6:
To convert 6 5/6 into an improper fraction, you multiply the whole number by the denominator and add the numerator:
6 * 6 + 5 = 41.
So, 6 5/6 as an improper fraction is 41/6.
To convert 6 2/6 into an improper fraction, you multiply the whole number by the denominator and add the numerator:
6 * 6 + 2 = 38.
So, 6 2/6 as an improper fraction is 38/6.
Now you can compare the improper fractions:
41/6 > 38/6.
Therefore, 6 5/6 is greater than 6 2/6. So, the answer is > (greater than).
To order the mixed numbers from least to greatest:
3. Let's order 5 1/8, 5 2/3, and 5 4/9.
To compare these mixed numbers, you can compare the improper fractions.
To convert 5 1/8 into an improper fraction, you multiply the whole number by the denominator and add the numerator:
5 * 8 + 1 = 41.
So, 5 1/8 as an improper fraction is 41/8.
To convert 5 2/3 into an improper fraction, you multiply the whole number by the denominator and add the numerator:
5 * 3 + 2 = 17.
So, 5 2/3 as an improper fraction is 17/3.
To convert 5 4/9 into an improper fraction, you multiply the whole number by the denominator and add the numerator:
5 * 9 + 4 = 49.
So, 5 4/9 as an improper fraction is 49/9.
Now you can compare the improper fractions:
41/8, 17/3, 49/9.
To find the least common denominator, you can take the least common multiple (LCM) of the denominators (8, 3, 9), which is 72.
You can then convert the fractions to equivalent fractions with a common denominator of 72:
41/8 * 9/9 = 369/72.
17/3 * 24/24 = 408/72.
49/9 * 8/8 = 392/72.
Now you can compare the fractions:
369/72 < 408/72 < 392/72.
Therefore, the correct order from least to greatest is:
5 1/8, 5 4/9, 5 2/3.