Comparing Numbers in Different Forms
This Grade 4 Eureka Math skill teaches students to compare numbers that appear in different forms — such as decimals, fractions, and mixed numbers — by first converting all values to a common form, typically a decimal. For example, to compare 0.8 and 75/100, students convert 75/100 to 0.75 and see that 0.8 is greater. For 3 and 2/10 versus 3.25, the mixed number converts to 3.2, which is less than 3.25. Covered in Chapter 31 of Eureka Math Grade 4, this decimal comparison skill builds fluency across number representations.
Key Concepts
To compare numbers written in different forms (e.g., fraction, mixed number, unit form), first convert them to a common form, such as a decimal.
Common Questions
How do you compare a decimal and a fraction?
Convert the fraction to its decimal equivalent, then compare place value by place value. For example, 75/100 = 0.75, which is less than 0.8.
How do you compare 3 and 2/10 with 3.25?
Convert 3 and 2/10 to decimal: 3.2. Then compare: 3.20 is less than 3.25, so 3 and 2/10 is less than 3.25.
How do you compare unit form with a decimal?
Convert unit form to a decimal. For 4 tenths 1 hundredth: 4 tenths = 0.4, 1 hundredth = 0.01, total = 0.41. Compare: 0.41 > 0.40.
Why is converting to decimal the best strategy for comparing mixed forms?
Decimals share a common place value structure, making side-by-side comparison straightforward. Once all numbers share the same form, you compare digit by digit from the largest place value.
What symbols are used to record comparisons?
Use > (greater than), < (less than), or = (equal to). For example, 0.8 > 75/100 because 0.8 is greater than 0.75.