Composing and Decomposing Numbers with Hundredths
This Grade 4 Eureka Math skill teaches students to compose and decompose numbers with hundredths by breaking them into tenths and hundredths components. The core relationship is that a/10 + b/100 = (10a+b)/100. Students learn to decompose 62/100 into 6/10 + 2/100, and to compose 1/10 + 3/100 into 13/100 by converting the tenth to 10/100 first. In decimal form, 0.45 = 0.4 + 0.05 = 4/10 + 5/100. This skill from Chapter 30 of Eureka Math Grade 4 bridges fractions and decimal notation.
Key Concepts
Numbers with hundredths can be written as a sum of tenths and hundredths. This relationship is key to composing and decomposing these numbers. $$\frac{a}{10} + \frac{b}{100} = \frac{10a + b}{100}$$.
Common Questions
How do you decompose 62/100 into tenths and hundredths?
Separate the hundredths into groups of ten: 62/100 = 60/100 + 2/100 = 6/10 + 2/100. The 6 tenths come from 60 hundredths.
How do you compose 1/10 and 3/100 into a single fraction?
Convert 1/10 to hundredths: 1/10 = 10/100. Then add: 10/100 + 3/100 = 13/100.
How does 0.45 break into tenths and hundredths?
0.45 = 0.4 + 0.05 = 4/10 + 5/100. The 4 is in the tenths place and the 5 is in the hundredths place.
Why is the formula a/10 + b/100 = (10a+b)/100 useful?
It shows the relationship between tenths and hundredths. Since 1 tenth equals 10 hundredths, multiplying a by 10 converts tenths to hundredths so you can add them.
What does composing a number mean in this context?
Composing means combining smaller parts (tenths and hundredths) into a single fraction or decimal. For example, 4/10 + 5/100 composes into 45/100 or 0.45.