All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 6 Lesson 12 Use Models to Divide Decimals will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 6 Lesson 12 Use Models to Divide Decimals
You can use models to divide decimals by decimals.
Build It
How many groups of 8 tenths are in 2.4? Find 2.4 ÷ 0.8.
1. The model shows 2.4.
Answer: 2.4
Explanation:
2.4 ÷ 0.8= 3
Check: Use multiplication to check your answer.
0.8 × 3 = 2.4
2. Since you are dividing by tenths, replace both of the wholes with tenths.
Each whole equals how many tenths? _____________
How many tenths do you have altogether after replacing the two wholes with tenths? ____________
Answer:
3 tenths.
Explanation:
Since we are dividing by tenths, replace both of the wholes with tenths.
Each whole equals how many tenths 3
Separate the tenths into groups of eight tenths to show dividing by 0.8.
3. Separate the tenths into groups of eight tenths to show dividing by 0.8.
How many groups will you have? ____________
Are there any left over? _____________
Draw the result at the right.
So 2.4 ÷ 0.8= ______________.
Check: Use multiplication to check your answer.
0.8 × 3 = 2.4
Answer:
3
Explanation:
Since we are dividing by tenths, replace both of the wholes with tenths.
Each whole equals how many tenths 3
Separate the tenths into groups of eight tenths to show dividing by 0.8.
How many groups will you have : 3 groups
Are there any left over : nil
Draw the result at the right.
Try It
How many groups of 6 hundredths are in 3 tenths? Find 0.3 ÷ 0.06.
1. The decimal model shows 0.3.
How many hundredths are in 3 tenths? _______________
Answer:
5 hundredths.
Explanation:
0.3 ÷ 0.06 = 5
Multiply with 100 both sides to remove decimals.
0.3 x 100 = 30
0.06 x 100 = 6
30 ÷ 6 = 5
2. Separate these hundredths into groups of 6 hundredths. Draw the equal groups.
How many groups will you have? _____________
Are there any left over? _____________
So, 0.3 ÷0.06 = _____________.
Answer:
5 groups,
Nothing is left.
Explanation:
Number of hundredths are in 3 tenths = 5
Separate these hundredths into groups of 6 hundredths.
Draw the equal groups.
Number of groups will you have : 5 groups
Are there any left over = Nil
So, 0.3 ÷ 0.06 = 5
Talk About It
Question 1.
Mathematical PRACTICE Look for a Pattern The table shows some quotients. Study the table. Write a rule you can use to find the quotient of two decimals, both to the tenths place, without using models.
Answer:
Rule to convert whole number
Multiply both top and bottom by 10
for 2 digits after the decimal point so that is 10×10 = 1,00
for 3 digits after the decimal point so that is 10×10×10 = 1,000
\(\frac {24}{10}\) = 2.4
\(\frac {36}{10}\) = 3.6
\(\frac {28}{10}\) = 2.8
Explanation:
0.8 x 3 = 2.4
0.8 x 10 = 8
80 x 3 = 24
3.6 x 10 = 36
0.9 x 10 = 9
4 x 9 = 36
Question 2.
Mathematical PRACTICE Draw a Conclusion Use your rule from Exercise 1 to find 4.8 ÷ 0.8 without using models. Explain the process you used.
Answer:
6
Explanation:
Given, 4.8 ÷ 0.8
Multiply both sides with 10.
4.8 x 10 = 48
0.8 x 10 = 8
48 ÷ 8 = 6
6 X 8 = 48
0.8 X 6 = 4.8
Practice It
Use models to find each quotient. Draw the equal groups.
Question 3.
2.4 ÷ 0.3 = _____________
Answer:
8 equal groups
Explanation:
Given, 2.4 ÷ 0.3
Multiply both sides with 10.
0.3 x 8 = 2.4
2.4 x 10 = 24
0.3 x 10 = 3
24 ÷ 3 = 8
Question 4.
1.6 ÷ 0.4 = _____________
Answer:
4
Explanation:
Given, 1.6 ÷ 0.4
Multiply both sides with 10.
1.6 X 10 = 16
0.4 X 10 = 4
16 ÷ 4 = 4
Question 5.
0.1 ÷ 0.05 = ______________
Answer:
2
Explanation:
Given, 0.1 ÷ 0.05 = 2
Multiply both sides with 100.
0.05 x 100 = 5
0.1 x 100 = 10
10 ÷ 5 = 2
Question 6.
0.2 ÷ 0.04 = ______________
Answer:
5
Explanation:
Given, 0.2 ÷ 0.04
Multiply both sides with 100.
0.2 x 100 =20
0.04 x 100 = 4
20 ÷ 4 = 5
Question 7.
0.27 ÷ 0.03 = ______________
Answer:
9
Explanation:
Given, 0.27 ÷ 0.03 = 9
Multiply both sides with 100.
0.27 x 100 = 27
0.03 x 100 = 3
27 ÷ 3 = 9
Apply It
Question 8.
Mathematical PRACTICE Use Math Tools Grace purchased some packages of gum for $1.50. If each package costs $0.50, how many packages did Grace purchase? Use models to help you divide.
Answer:
3 packages.
Explanation:
Grace purchased some packages of gum for $1.50.
If each package costs $0.50,
Total packages did Grace purchase,
$1.50 ÷ $0.50
Multiply both sides with 100.
1.50 x 100 = 15
0.50 x 100 = 5
15 ÷ 5 = 3
Question 9.
Aidan purchased 1.5 feet of wood to make a napkin holder. If he used 0.5 foot of wood for each side, how many sides does the napkin holder have? Use models to help you divide.
Answer:
3 sides.
Explanation:
Aidan purchased 1.5 feet of wood to make a napkin holder.
If he used 0.5 foot of wood for each side,
Number of sides does the napkin holder have,
1.5 ÷ 0.5
Multiply both sides with 10.
1.5 x 10 = 15
0.5 x 10 = 5
15 ÷ 5 = 3
Question 10.
Ryan used 2.5 cups of flour to make bread. If he used 0.5 cup of flour for each loaf, how many loaves of bread did Ryan make? Use models to help you divide.
Answer:
5 loaves of bread.
Explanation:
Ryan used 2.5 cups of flour to make bread.
If he used 0.5 cup of flour for each loaf,
Number of loaves of bread did Ryan make,
2.5 ÷ 0.5
Multiply both sides with 10.
2.5 x 10 = 25
0.5 x 10 = 5
25 ÷ 5 = 5
Question 11.
Mathematical PRACTICE Explain to a Friend Explain how to use models to divide 2.1 by 0.7.
Answer:
3
Explanation:
To divide decimals using models,
first shade in the first number, your dividend.
Then, circle groups of the second number, your divisor.
The number of circled groups is your answer, or quotient.
2.1 ÷ 0.7
There are 7 groups.
So, 2.1 ÷ 0.7 = 3.
Write About It
Question 12.
How can I use models to divide decimals by decimals?
Answer:
Using models to divided decimals by decimals,
first we shade the decimal models to represent the dividend.
then we cut the models to groups that are each the size of divisor.
the number of same sized groups is quotient.
for each whole number we shade a 100 unit block.
Explanation:
For example;
2.4 ÷ 0.8= 3
Explanation:
Since we are dividing by tenths, replace both of the wholes with tenths.
Each whole equals how many tenths 3
Separate the tenths into groups of eight tenths to show dividing by 0.8.
How many groups will you have : 3 groups
Are there any left over : nil
Draw the result at the right.
McGraw Hill My Math Grade 5 Chapter 6 Lesson 12 My Homework Answer Key
Practice
Use models to find each quotient. Draw the equal groups.
Question 1.
0.4 ÷ 0.05 = _____________
Answer:
8
Explanation:
0.4 x 100 = 40
0.05 x 100 = 5
40 ÷ 5 = 8
8 x 0.05 = 0.4
Question 2.
0.2 ÷ 0.02 = ______________
Answer:
10
Explanation:
0.2 x 100 = 20
0.02 x 100 = 2
20 ÷ 2 = 10
Problem Solving
Question 3.
Mathematical PRACTICE Use Math Tools Adam used 1.8 pieces of paper to make his project. He decorated 0.2 of each piece of paper with a different color. How many sections does Adam’s art project have? Draw models to help you divide.
Answer:
9
Explanation:
Adam used 1.8 pieces of paper to make his project.
He decorated 0.2 of each piece of paper with a different color.
Number of sections Adam’s art project have,
1.8 ÷ 0.2 = 9
1.8 x 10 = 18
0.2 x 10 = 2
18 ÷ 2 = 9
0.2 x 9 = 1.8
Question 4.
Beverly used 2.4 yards of ribbon on the border of a quilt. If each side used 0.6 yard of ribbon, how many sides did she use the ribbon on? Draw models to help you divide.
Answer:
4
Explanation:
Beverly used 2.4 yards of ribbon on the border of a quilt.
If each side used 0.6 yard of ribbon,
Number sides she use the ribbon on,
2.4 ÷ 0.6 = 4
2.4 x 10 = 24
0.6 x 10 = 6
0.6 x 4 = 2.4
Question 5.
Melanie purchased some packages of pencils for $1.60. If each package costs $0.80, how many packages did Melanie purchase? Draw models to help you divide.
Answer:
2 packages.
Explanation:
Melanie purchased some packages of pencils for $1.60.
If each package costs $0.80,
Number of packages Melanie purchase,
$1.60 ÷ 0.80 = 2
1.6 x 10 = 16
0.8 x 10 = 8
16 ÷ 8 = 2
Question 6.
Evan had 2.2 pounds of candy to give to his friends. If he gave 0.2 pound to each friend, how many friends did Evan give candy to? Draw models to help you divide.
Answer:
11 friends.
Explanation:
Evan had 2.2 pounds of candy to give to his friends.
If he gave 0.2 pound to each friend,
Number of friends Evan give candy to,
2.2 ÷ 0.2 = 11
2.2 x 10 = 22
0.2 x 10 = 2
22 ÷ 2 = 11
