# Into Math Grade 4 Module 12 Lesson 1 Answer Key Represent Tenths as Fractions and Decimals

We included HMH Into Math Grade 4 Answer Key PDF Module 12 Lesson 1 Represent Tenths as Fractions and Decimals to make students experts in learning maths.

## HMH Into Math Grade 4 Module 12 Lesson 1 Answer Key Represent Tenths as Fractions and Decimals

I Can use a visual model and decimal notation to represent fractions, mixed numbers, and decimals in tenths.

The diagram shows the heights of a plant at the end of each of 3 weeks. After Week 1, the plant is $$\frac{3}{10}$$ meter tall. Another way to represent the height is 0.3 meter. Both $$\frac{3}{10}$$ and 0.3 can be read as three tenths. They represent 3 parts of 10 equal parts of a whole.

How can you represent the heights of the plant at the end of each week with a visual model? How can you label the heights of the plant on a number line in two different ways?

Explanation:
From the given data the plant grows $$\frac{3}{10}$$ in the 1st week.
In the 22nd week it grows $$\frac{5}{10}$$ meters.
In 3rd week it grows $$\frac{7}{10}$$ meters.

Turn and Talk How did you represent a meter with your visual model? How is your representation like those of your classmates? How is it different?
There are different ways to represent a meter in visual model.
We can represent with line diagram and bar diagram models.

Build Understanding

Question 1.
One of the tomatoes from a garden is 1$$\frac{1}{10}$$ pounds.

Represent the weight of the tomato on a tenths model and a number line.
1$$\frac{1}{10}$$

A. How did you represent 1$$\frac{1}{10}$$ on the tenths models?

B. How did you locate the weight of the tomato on the number line?

Connect to Vocabulary
A tenth is one of ten equal sized parts. A decimal point is a dot that separates the ones place from the tenths place in a number. A decimal is a number that has one or more digits to the right of a decimal point.

C. How can you represent 1$$\frac{1}{10}$$ pounds using digits and a decimal point?
1$$\frac{1}{10}$$

Explanation:
One of the tomatoes from a garden is 1$$\frac{1}{10}$$ pounds.
1$$\frac{1}{10}$$ on the tenths models means each set is divided into ten parts to make a whole.

Turn and Talk How is a mixed number similar to a decimal greater than 1?
Mixed fraction
using mixed fraction representation.
Explanation:
When we convert an improper fraction to a decimal,
the decimal is always greater than 1.
Question 2.
The tenths models show how many cups of water Tina uses to water a tomato plant.

A. Write a sentence to describe the amount of water Tina uses.
Tina uses 2$$\frac{8}{10}$$ of water
Explanation:
In the above 10th model given,
two complete blocks filled with blue color and 8/10 part is also filled with blue color.
So, the total amount of water is represented as 2$$\frac{8}{10}$$

B. How can you write the amount of water that Tina as a mixed number and as a decimal?
2.8
Explanation:
$$\frac{8}{10}$$ = 0.8
2.0 + 0.8 = 2.8

Check Understanding

Question 1.
Duke plants each tomato plant meter apart. Represent the distance on the tenths model and the number line.

Write the distance as a decimal. _______
0.6

Explanation:
A tenth is one of ten equal sized parts.
To represent a decimal on a number line, divide each segment of the number line into ten equal parts.

Question 2.
Write the amount shown as a mixed number and as a decimal.

3.5
1 + 1 + 1 + 0.5 = 3.5
Explanation:
Each box represent 1 whole divided into 10 parts.
From the above information 3 complete sets and in the 4th set 5 are shaded.
So, 3 $$\frac{5}{10}$$

Question 3.
STEM Hydroponics is a way of growing plants in water rather than soil. The nutrients that plants need to grow are put into the water. Tanya designs a hydroponic system and fills the reservoir with $$\frac{8}{10}$$ gallon of water. Use the tenths model to show the amount of water in the reservoir.

Write the amount of water as a decimal. __________
0.8

Explanation:
$$\frac{8}{10}$$
A tenth is one of ten equal sized parts.
A decimal point is a dot that separates the ones place from the tenths place in a number.

Question 4.
Use Tools Liz plants 1$$\frac{6}{10}$$ packs of tomato seeds. On the number line, show the amount of packs of seeds that Liz plants.

Write the amount of packs of seeds as a decimal. __________
1.6

Explanation:
A tenth is one of ten equal sized parts.
To represent a decimal on a number line, divide each segment of the number line into ten equal parts.

Question 5.
Use Structure Write the amount shown as a mixed number and as a decimal.

2.9
2$$\frac{9}{10}$$
1 + 1 + 0.9 = 2.9
Explanation:
Each box represent 1 whole divided into 10 parts.
From the above information 2 complete sets and in the 3rd set 9 are shaded.
So, 2 $$\frac{9}{10}$$ = 2.9

I’m in a Learning Mindset!

What strategies can I use to write a decimal for a visual model and to draw a visual model for a decimal?