Use the symbols <, >, or = to compare 6/11 and 9/11.
Step 1: Only compare fractions when the denominators are equal. These two fractions have the same denominator.
6 < 9, so 6/11 < 9/11
like fractions: Fractions that have the same denominator.
unlike fractions: Fractions that have different denominators.
A fraction with the numerator 1 is called a unit fraction. Unit fractions can have denominators of any number. A unit is one whole. A unit fraction is part of one whole.
Think: If you cut one sandwich into two pieces, and one sandwich into eight pieces, how do the pieces compare? The 1/2 piece is larger than the 1/8 piece. 1/2 is greater than 1/8.
Some problems will have the same answer in two places, just written in a different way. Answer b says 1/2 is less than 1/3. Answer d says 1/3 is greater than 1/2. These have the same meaning, but neither is correct.
multiple: The product of a number and any whole number. Multiples of 2 are 2, 4, 6, . . .
common multiples: Numbers that are multiples of two or more numbers in a group. Some common multiples of 2 and 3 are 6, 12, and 18.
least common multiple: The smallest multiple, other than zero, that two or more numbers have in common.
Compare 1/3 and 3/8.
Step 1: Write unlike fractions as like fractions using the least common denominator. Find the least common multiple of the denominators, 3 and 8.
List the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, . . .
List the multiples of 8: 8, 16, 24, 32, 48, . . .
The least common multiple of 3 and 8 is 24.
Step 2: Write both fractions with a denominator of 24. To change a denominator of 3 to a denominator of 24, multiply the numerator and denominator by 8, because 3 × 8 = 24. To change a denominator of 8 to a denominator of 24, multiply the numerator and denominator by 3, because 8 × 3 = 24.
Step 3: Compare like fractions by comparing the numerators.
