Composing One Whole with Tenths
This Grade 4 Eureka Math skill teaches students that one whole equals 10 tenths, and that pairs of tenths can be added to compose one whole. For example, 0.3 + 0.7 = 1.0, which is equivalent to 3/10 + 7/10 = 10/10 = 1. Students explore all complementary pairs of tenths that sum to 1: 0.2 + 0.8, 0.6 + 0.4, and so on. This foundational understanding from Chapter 29 of Eureka Math Grade 4, the Exploration of Tenths, builds decimal number sense and supports later work with hundredths, fraction equivalence, and decimal addition.
Key Concepts
One whole is equivalent to 10 tenths. Pairs of tenths can be added together to compose one whole, which is written as $1.0$ or $\frac{10}{10}$. $$0.3 + 0.7 = 1.0$$ $$\frac{3}{10} + \frac{7}{10} = \frac{10}{10} = 1$$.
Common Questions
How many tenths make one whole?
10 tenths make one whole. This is written as 10/10 = 1, or in decimal form as 1.0.
What pairs of tenths add to make 1?
Any pair where the tenths digits sum to 10: 0.1+0.9, 0.2+0.8, 0.3+0.7, 0.4+0.6, 0.5+0.5, 0.6+0.4, 0.7+0.3, 0.8+0.2, 0.9+0.1.
How do you verify that 0.3 + 0.7 = 1?
In fraction form: 3/10 + 7/10 = 10/10 = 1. In decimal form: 0.3 + 0.7 = 1.0. Both confirm that 3 tenths and 7 tenths compose one whole.
How does composing one whole with tenths connect to fraction equivalence?
It shows that 1 = 10/10 = any n/n. Understanding one whole as 10 tenths is the gateway to understanding 1 = 100/100 = 1,000/1,000 and all fraction equivalence concepts.
What is the decimal notation for 10 tenths?
10 tenths = 10/10 = 1.0. Just as 10 ones regroup to 1 ten, 10 tenths regroup to 1 whole.