Relating Fractions Greater Than 1, Mixed Numbers, and Decimals
Grade 4 students in Eureka Math learn to express tenths greater than one in three equivalent forms: improper fractions, mixed numbers, and decimals. For example, 14/10 equals 1 4/10, which equals 1.4. The whole number part of the mixed number matches the digits before the decimal point, while the tenths digit matches the fraction numerator. Mastering this equivalence builds the foundation for decimal place value work throughout Chapter 29 and prepares students for comparing and ordering rational numbers in later grades.
Key Concepts
A number with tenths greater than one can be expressed in three equivalent forms: a fraction greater than 1, a mixed number, and a decimal. The relationship is shown by:.
Common Questions
How do you convert an improper fraction with tenths to a decimal?
Divide the numerator by 10. For 14/10, divide 14 by 10 to get 1.4. The quotient before the decimal is the whole number, and the remainder becomes the tenths digit.
What does 2.3 look like as a mixed number and as an improper fraction?
2.3 as a mixed number is 2 3/10. As an improper fraction it is 23/10, because 2 × 10 + 3 = 23.
Why does 3 7/10 equal 3.7?
The whole number 3 stays the same, and the fraction 7/10 means 7 tenths, which is the digit in the tenths place of the decimal 3.7.
Are improper fractions and mixed numbers equal in value?
Yes. 14/10 and 1 4/10 represent exactly the same quantity; they are just written in different forms.
When would a student prefer the decimal form over the fraction form?
Decimals are easier to add and compare on a number line or place-value chart, while fractions are more explicit about the unit size.