Comparing Mixed Numbers by Finding Common Denominators
Comparing Mixed Numbers by Finding Common Denominators is a Grade 4 math skill that teaches students to compare two mixed numbers with different fractional denominators by converting both fractions to a common denominator and then comparing. For example, to compare 3 2/3 and 3 3/4: convert to twelfths — 3 8/12 vs. 3 9/12. Since 9 > 8, then 3 3/4 > 3 2/3. Covered in the fraction comparison chapters of Eureka Math Grade 4, this skill extends fraction comparison strategy to the case where whole numbers are equal and fractional parts have unlike denominators.
Key Concepts
To compare two mixed numbers, first compare their whole number parts. If the whole numbers are equal, then compare their fractional parts by finding a common denominator. The mixed number with the larger fractional part is the greater number.
Common Questions
How do I compare mixed numbers with different denominators?
First compare the whole number parts — the larger whole number wins immediately. If whole numbers are equal, find a common denominator for the fractional parts, convert both fractions, and compare numerators. The mixed number with the larger fraction is greater.
How do I compare 3 2/3 and 3 3/4?
Whole numbers are equal (both 3). Find a common denominator for 2/3 and 3/4: use 12. Convert: 2/3 = 8/12 and 3/4 = 9/12. Since 9/12 > 8/12, then 3 3/4 > 3 2/3.
How do I find a common denominator for two fractions?
Find the least common multiple (LCM) of the two denominators. For 3 and 4, the LCM is 12. Convert both fractions to 12ths: multiply each numerator and denominator by the factor needed to reach 12. Then compare numerators directly.
What is the least common multiple and how do I find it?
The least common multiple (LCM) of two numbers is the smallest number both are factors of. For 3 and 4: multiples of 3 are 3, 6, 9, 12; multiples of 4 are 4, 8, 12. The first number in both lists is 12, so LCM(3,4) = 12.
What other strategies can I use to compare mixed numbers?
If whole numbers differ, compare them directly. If one fraction is visually close to a benchmark (like 1/2 or 1), use benchmark comparison. Common denominator is the universal strategy that always works but requires the most computation.
What chapter in Eureka Math Grade 4 covers comparing mixed numbers with unlike denominators?
Comparing fractions and mixed numbers with unlike denominators is developed in the fraction comparison chapters of Eureka Math Grade 4, building on equivalence work in Chapter 22 and applied in Chapter 23 and Chapter 24.