# Everyday Math Grade 5 Answers Unit 4 Decimal Concepts; Coordinate Grids

## Everyday Mathematics 5th Grade Answer Key Unit 4 Decimal Concepts; Coordinate Grids

Use the place-value chart below to complete Problems 1–8.  Explanation:
Estimate : 8,430 X 8 = 67,440 and
multiplying 8,429 with 8 as
8,429 X 8 = 67,432,
So 67,440 ≈ 67,432.

Write each decimal in words.
Question 1.
2.598 ____Two and five hundred ninety-eight thousandths_____
Two and five hundred ninety-eight thousandths,

Explanation:
Given 2.598 in words is two and
five hundred ninety-eight thousandths.

Question 2.
0.21 ____Twenty-one hundreths______
Twenty-one hundreths,

Explanation:
Given 0.21 in words is twenty one hundreths.

Question 3.
1.006 __One and six thousandths________
One and six thousandths,

Explanation
Given 1.006 in words is one and six thousandths.

Write each decimal using numerals.
Then write the value of 9 in each decimal.
Question 4.
a. three and nine tenths ___3.9_______
b. 9 is worth ____0.9______
a. three and nine tenths 3.9,
b. 9 is worth 0.9,

Explanation:
Given a. three and nine tenths in numerals is 3.9 and
b. the worth of 9 is 0.9.

Question 5.
a. thirty-nine hundredths ____0.39______
b. 9 is worth ___0.09_______
a. thirty-nine hundredths 0.39,
b. 9 is worth 0.09,

Explanation:
Given a. three-nine hundredths in numerals is 0.39 and
b. the worth of 9 is 0.09.

Question 6.
a. six hundred thirty-nine thousandths __0.639____
b. 9 is worth ___0.009_______
a. six hundred thirty-nine thousandths 0.639,
b. 9 is worth 0.009,

Explanation:
Given a. six hundred thirty-nine thousandths is 0.639 and
b. the worth of 9 is 0.009.

Solve the place-value puzzles.
Question 7.
Use the clues to write the mystery number.
Write 3 in the thousandths place.
Write 8 in the tenths place.
Write 5 in the hundredths place.
Write 0 in the ones place.
__0____ . ____8___ ____5___ ___3__
The mystery number is 0.853,

Explanation:
Used the clues to write the mystery number,
Wrote 3 in the thousandths place as 0.003
Wrote 8 in the tenths place as 0.8
Wrote 5 in the hundredths place as 0.05
Wrote 0 in the ones place as 0,
So the mystery number is 0.853.

Question 8.
Make the following changes to the
number 2.614:
Make the 1 worth $$\frac{1}{10}$$ as much.
Make the 4 worth $$\frac{1}{10}$$ times as much.
Make the 2 worth $$\frac{1}{10}$$ as much.
Make the 6 worth $$\frac{1}{10}$$ times as much.
___6___ . ___2____ ___4____ __1___
After changes the number is 6.241,

Explanation:
Given number is 2.614 now the changes are
Made the 1 worth $$\frac{1}{10}$$ as much
so 0.01 becomes 0.001,
Made the 4 worth $$\frac{1}{10}$$ times as much
so 0.004 becomes 0.04,
Made the 2 worth $$\frac{1}{10}$$ as much
so 2 becomes 0.2,
Made the 6 worth $$\frac{1}{10}$$ times as much
so 0.6 becomes 6, therefore after changes the number is 6.241.

Practice
Make an estimate and solve using U.S. traditional multiplication.
Question 9.  Explanation:
Estimate : 8,430 X 8 = 67,440 and
multiplying 8,429 with 8 as
8,429 X 8 = 67,432,
So 67,440 ≈ 67,432.

Question 10.  Explanation:
Estimate of 531 X 72 is 38,232 as shown above.

Representing Decimals
For Problems 1 and 2, use words, fractions, equivalent decimals,
or other representations to write at least three names for each
decimal in the name-collection box.
Then shade the grid to show the decimal.
Question 1.  Explanation:
Wrote three names for 0.550 decimal
in the name-collection box as
1. zero and fifty five hundreths,
3. subtracting 0.05 from 0.60 and then shadeed
the grid to show the 0.550 decimal as shown above.

Question 2.  Explanation:
Wrote three names for 0.09 decimal
in the name-collection box as
1. nine hundreths,
3. subtracting 0.01 from 0.10 and then shadeed
the grid to show the 0.09 decimal as shown above.

Practice
Make an estimate and solve. Show your work on the back of the page.
Question 3.
Estimate: ___21_______ 322 ÷ 15 → ____21 R7 ______ Explanation:
Estimate : 320 ÷ 15 = 21.3
If we divide 322 by 15 we get 21 as quotient
and remainder as 7, So 21.3 ≈ 21.

Question 4.
Estimate: ____205______ 4,319 ÷ 21 → ___205 R14_______ Explanation:
Estimate : 4,320 ÷ 21 = 205.7
If we divide 4,319 by 21 we get 205 as quotient
and remainder as 14, So 205.7 ≈ 205.

Representing Decimals in Expanded Form

Numbers can be written in standard notation or expanded form. When numbers are written in expanded form, the value of each digit is clearly shown. The number 3.924 is written in standard notation. The examples below show 3.924 using different versions of expanded form.

• 3 + 0.9 + 0.02 + 0.004
• 3 ones + 9 tenths + 2 hundredths + 4 thousandths
• (3 ∗ 1) + (9 ∗ 0.1) + (2 ∗ 0.01) + (4 ∗ 0.001)
• (3 ∗ 1) + (9 ∗ $$\frac{1}{10}$$ ) + (2 ∗ $$\frac{1}{100}$$ ) + (4 ∗ $$\frac{1}{1000}$$)

In Problems 1–4, represent each decimal using one version of expanded form.
Question 1.
0.571
0.571 = 0 + 0.5 + 0.07 + 0.001,

Explanation:
The expanded form of 0.571 is
0.571 = 0 + 0.5 + 0.07 + 0.001.

Question 2.
4.203
4.203 = 4 ones + 2 tenths + 0 hundredths + 3 thousandths,

Explanation:
The expanded form of 4.203 is
4.203 = 4 ones + 2 tenths + 0 hundredths + 3 thousandths.

Question 3.
0.068
0.068 = (0 ∗ 0) + (0 ∗ 0.1) + (6 ∗ 0.01) + (8 ∗ 0.001),

Explanation:
The expanded form of 0.068 is
0.068 = (0 ∗ 0) + (0 ∗ 0.1) + (6 ∗ 0.01) + (8 ∗ 0.001).

Question 4.
8.415
8.415 = (8 ∗ 1) + (4 ∗ $$\frac{1}{10}$$ ) +
(1 ∗ $$\frac{1}{100}$$ ) + (5 ∗ $$\frac{1}{1000}$$),

Explanation:
The expanded form of 8.415 is
8.415 = (8 ∗ 1) + (4 ∗ $$\frac{1}{10}$$ ) +
(1 ∗ $$\frac{1}{100}$$ ) + (5 ∗ $$\frac{1}{1000}$$).

In Problems 5–8 an expanded form of a decimal is given.
Write the decimal in standard notation.
Question 5.
9 ones + 5 tenths + 7 hundredths + 0 thousandths ___
9.570,

Explanation:
The decimal in standard notation form of
9 ones + 5 tenths + 7 hundredths + 0 thousandths is
9.570.

Question 6.
3 + 0.6 + 0.02 + 0.004 ___
3.624,

Explanation:
The decimal in standard notation form of
3 + 0.6 + 0.02 + 0.004 is 3.624.

Question 7.
(5 ∗ $$\frac{1}{10}$$ ) + (8 ∗ $$\frac{1}{100}$$ ) +
(9 ∗ $$\frac{1}{1000}$$) __________
0.589,

Explanation:
The decimal in standard notation form of
(5 ∗ $$\frac{1}{10}$$ ) + (8 ∗ $$\frac{1}{100}$$ ) +
(9 ∗ $$\frac{1}{1000}$$) is 0.589.

Question 8.
(2 ∗ 1) + (3 ∗ 0.1) + (7 ∗ 0.01) + (1 ∗ 0.001) __________
2.371,

Explanation:
The decimal in standard notation form of
(2 ∗ 1) + (3 ∗ 0.1) + (7 ∗ 0.01) + (1 ∗ 0.001) is
2.371.

Practice
Question 9.
There 30 colored circles on a rug. $$\frac{1}{5}$$
of the circles are red. How many red circles are on the rug?
____6_____ red circles
6 red circles are on the rug,

Explanation:
Given there are 30 colored circles on a rug and
$$\frac{1}{5}$$ of the circles are red so
number of red circles are 30 * $$\frac{1}{5}$$ = 6,
(5 X 6 = 30), So there are 6 red circles are on the rug.

Question 10.
Jerome did a survey to find out his classmates’ favorite sports.
He found that $$\frac{1}{3}$$ of the 24 students in
his class chose soccer as their favorite sport.
How many students chose soccer?
____8______ students
8 students chose soccer,

Explanation:
Given Jerome did a survey to find out his classmates’ favorite sports.
He found that $$\frac{1}{3}$$ of the 24 students in
his class chose soccer as their favorite sport.
So number of students chose soccer are
24 * $$\frac{1}{3}$$ = 8, (8 X 3 = 24),
So there are 8 students who chose soccer.

Comparing and Ordering Decimals

Darryl and Charity are playing Decimal Top-It. Their record sheet is shown below. Question 1.
Compare their decimals for each round and write >, <, or = in the middle column. Use the place-value chart above to help you.  Explanation:
Compared Player 1 – Darryl and Player 2- Charity
with their decimals for each round as
Round 1:
0.378 is less than 0.860 so 0.378 < 0.860,
Round 2:
0.9 is greater than 0.59 so 0.9 > 0.59,
Round 3:
0.804 is less than 0.92 so 0.804 < 0.92,
Round 4:
0.547 is less than 0.6 so 0.547 < 0.6,
Round 5:
0.72 is greater than 0.098 so 0.72 > 0.098.

Question 2.
Who won the most rounds?
Charity won the most rounds,

Explanation:
If we see out of five rounds,
3 rounds Round 1, 3, 4 player 2 is having most,
So Charity won the most rounds.

Question 3.
a. Put Darryl’s decimals in order from least to greatest.
__0.378_,_0.547_, __0.72__, __0.804__, ___0.9__,
0.378, 0.547, 0.72, 0.804, 0.9,

Explanation:
Kept Darryl’s decimals in order from least to greatest as
0.378, 0.547, 0.72, 0.804, 0.9.

b. Put Charity’s decimals in order from least to greatest.
__0.098__, _0.59__, _0.6__, __0.860__, __0.92__,
0.098, 0.59, 0.6, 0.860, 0.92,

Explanation:
Kept Charity’s decimals in order from least to greatest as
0.098, 0.59, 0.6, 0.860, 0.92.

Question 4.
a. What was the largest decimal of the whole game?
b. How do you know?
a. The largest decimal of the whole game is 0.92,
b. By checking,

Explanation:
On comparing the greatest decimal of Darryl’s and
Charity’s we have 0.9 and 0.92, as 0.92 is more
therefore the largest decimal of the whole game is 0.92.

Practice
Use the fractions below to complete Problems 5–7.
Use each fraction only once. Question 5.
$$\frac{3}{8}$$ + ______ < 1
$$\frac{1}{4}$$,

Explanation:
Given $$\frac{3}{8}$$ + ______ < 1,
we take missing number as $$\frac{1}{4}$$,
so $$\frac{3}{8}$$ + $$\frac{1}{4}$$ =
$$\frac{5}{8}$$ whose value is less than 1,
if we take $$\frac{2}{3}$$ the value is greater than 1,
if we take $$\frac{7}{8}$$ the value is equal to 1 and
if we take $$\frac{3}{4}$$ the value is greater than 1,
therefore the correct value would be $$\frac{1}{4}$$.

Question 6.
_______ – $$\frac{1}{8}$$ < 1
$$\frac{7}{8}$$

Explanation:
Given _______ – $$\frac{1}{8}$$ < 1
we take missing number as $$\frac{7}{8}$$,
so $$\frac{7}{8}$$ – $$\frac{1}{8}$$ =
$$\frac{6}{8}$$ whose value is less than 1,
even if we take other 2 values are also coming true.

Question 7. _____ + ______ > 1
$$\frac{2}{3}$$ and $$\frac{3}{4}$$,

Explanation:
Given _____ + ______ > 1, we have now
$$\frac{2}{3}$$ and $$\frac{3}{4}$$,
So $$\frac{2}{3}$$ + $$\frac{3}{4}$$ =
$$\frac{17}{12}$$ we get value more than 1,
therefore we took $$\frac{2}{3}$$ and $$\frac{3}{4}$$.

Rounding Decimals

Question 1.
Mark each number on the number line. The first one is done for you.  Explanation:
Marked each number on the number line as
30.72 marked in between 30.7 and 30.8,
31.05 marked in between 31.0 and 31.1,
29.94 marked in between 29.9 and 30.0 and
30.38 marked in between 30.3 and 30.4 as shown above.

Question 2.
Round the area of each country to the nearest tenth of a square mile.  Explanation:
Rounded the area of each country to the nearest
tenth of a square mile as
1. Vatican city from 0.17 mi2≈ 0.2 mi2,
2. Monaco from 0.75 mi2≈ 0.8 mi2,
3. Nauru from 8.11 mi2≈ 8.1 mi2,
4. Tuvalu from 10.04 mi2≈ 10.0 mi2,
5. San Marino from 23.63 mi2≈ 23.6 mi2,
6. Liechtenstein from 61.78 mi2≈ 61.8 mi2,
7. St. Kitts and Nevis from 100.77 mi2≈ 100.8 mi2,
8. Maldives from 115.83 mi2≈ 115.8 mi2,
9. Malta from 122.01 mi2≈ 122.0 mi2,
10. Grenada from 132.82 mi2≈ 132.8 mi2 respectively.

Practice
Write the following expressions in standard notation.
Question 3.
8 ∗ 103 = ___8,000_______
8 ∗ 103 = 8,000,

Explanation:
The standard notation of 8 ∗ 103 is
8 X 10 X 10 X 10 = 8,000.

Question 4.
23 ∗ 105 = ___2,300,000__
23 ∗ 105 = 2,300,000,

Explanation:
The standard notation of 23 ∗ 105 is
23 X 10 X 10 X 10 X 10 X 10 = 2,300,000.

Write the following numbers using exponential notation.
Question 5.
400 = 4 ∗ ___102 _____
400 = 4  X  102,

Explanation:
The exponential notation of 400 is
4 X 10 X 10 = 4  X  102.

Question 6.
15,000 = 15 ∗ ___103 ______
15,000 = 15 X 103,

Explanation:
The exponential notation of 15,000 is
15 X 10 X 10 X 10 = 15  X  103.

Plotting Points to Create an Outline Map

Question 1.
a. Plot the following points on the grid:
(21, 14) (17, 11) (17, 13) (15, 14) (2, 16)
(1, 11) (2, 8) (3, 6) (7, 5) (11, 3) (13, 4) Explanation:
Plotted the points
(21, 14) (17, 11) (17, 13) (15, 14) (2, 16)
(1, 11) (2, 8) (3, 6) (7, 5) (11, 3) (13, 4)
on the grid as shown above.

b. Connect all the points in the order listed. Then connect (13, 4) to (17, 5) and (21, 14) to (22, 15). You should see an outline map of the United States.  Explanation:
Connected all the points in the order listed
(21, 14) (17, 11) (17, 13) (15, 14) (2, 16)
(1, 11) (2, 8) (3, 6) (7, 5) (11, 3) (13, 4) and
then connected (13, 4) to (17, 5) and (21, 14) to (22, 15)
as shown above I could see an outline map of the United States.

Question 2.
Write the coordinates of each city.
a. Chicago, Illinois __(15,11)______
b. Dallas, Texas ____(12,6)______
c. Atlanta, Georgia ___(17,7)_______
a. Chicago, Illinois  is (15,11),
b. Dallas, Texas is (12,6),
c. Atlanta, Georgia is (17,7),

Explanation:
From the grid the coordinates of each city of
a. Chicago, Illinois  is (15,11),
b. Dallas, Texas is (12,6),
c. Atlanta, Georgia is (17,7),
d. Denver, Colorado is (8,9) respectively.

Question 3.
Plot each city on the grid and write the city name.
a. Billings, Montana (7, 13)
b. Salt Lake City, Utah (5, 10) Explanation:
Plotted each city on the grid and wrote the city names of
a. Billings, Montana at (7, 13)
b. Salt Lake City, Utah at (5, 10) as shown above.

Practice
Use the clues to write the mystery number.
Then read each decimal to someone at home.
Question 4.
Write 0 in the tenths place.
Write 7 in the ones place.
Write 3 in the thousandths place.
Write 5 in the hundredths place.
__7____. ___0___ ___5___ ___3___
The myster number is 7.053,

Explanation:
Wrote 0 in the tenths place means 0.0,
Wrote 7 in the ones place means 7,
Wrote 3 in the thousandths place means 0.003 and
Wrote 5 in the hundredths place means 0.05,
therfore the myster number is 7.053.

Question 5.
Write 5 in the hundredths place.
Write 1 in the tenths place.
Write 4 in the ones place.
Write 9 in the thousandths place.
___4___. __1____ ___5___ ___9___
The myster number is 4.159,

Explanation:
Wrote 5 in the hundredths place means 0.05,
Wrote 1 in the tenths place means 0.1,
Wrote 4 in the ones place means 4 and
Wrote 9 in the thousandths place means 0.009,
Therefore the myster number is 4.159.

Treasure Steps

Play a coordinate grid game, Treasure Steps,
with someone at home or by yourself.
The treasure is marked with a ∗. Make a spinner with a paper clip and a pencil. To play with a partner:

• Take turns. When it is your turn, spin.
This is the first number in your ordered pair.
Spin again. This is the second number in your ordered pair.
Plot the point on the gameboard.
• Count the number of “steps” from your point to the treasure.
Stay on the grid lines as you count.
Record your ordered pair and the number of steps.
• After 5 rounds, find your total number of steps.
The player with the smaller total wins.

To play by yourself:
The goal is to get as close to 30 steps as you can.
would if you were playing with a partner.
Record the ordered pairs and step s.
After 5 rounds, find the total number of steps.
How close did you get to 30? Explanation:
Round 1: ( 6, 8),
Round 2: ( 8, 5),
Round 3: (4, 5),
Round 4: (8, 2),
Round 5: (9, 5) repectively as shown above,
Total number of steps are 16, 14 less steps to 30.

Practice
Question 1.
Put an X by the expressions that show 3.245 in expanded form.  Explanation:
Kept an X by the expressions that show
3.245 in expanded form, Expression 1 : 3 ones +
2 tenths + 4 hundredths + 5 thousandths and
(3 X 1) + ( 2 X 1/10) + (4 X 1/100) + (5 X 1/1,000).

Question 2.
Write 0.605 in expanded form. Use any version of
expanded form you wish.
0.605 = 0 X 1 + 0.1 X 6 + 0.01 X 0 + 0.001 X 5,

Explanation:
Given to write 0.605 in expanded form as
0.605 = 0 X 1 + 0.1 X 6 + 0.01 X 0 + 0.001 X 5.

Plotting Figures on a Coordinate Grid

Question 1.
Plot any three points and connect them to make a triangle on the grid below. Label the points A, B, and C. List the coordinates of your points.
A: (___9___, __9____)
B: (___6___, ___4___)
C: (___12___, ___4___) Explanation:
Plotted three points and connected them to make a
triangle on the grid below. Label the points A, B, and C.
Listed the coordinates of my points as A(9,9),
B(6,4) and C(12,4) respectively.

Question 2.
Plot four points and connect them to make a quadrilateral on the grid below. The quadrilateral may overlap the triangle. Label the points as M, N, O, and P. List the coordinates of your points.
M: (___5___, __12____)
N: (__15____, __12____)
O: (__2____, __7____)
P: (__11____, __7____)  Explanation:
Plotted four points and connected them to make
a quadrilateral on the grid below.
The quadrilateral may overlap the triangle.
Labeled the points as M, N, O, and P.
Listed the coordinates of my points as shown above as
M: (5, 12)
N: (15, 12)
O: (2, 7)
P: (11, 7) respectively.

Practice
Write <, >, or = to make true number sentences.
Question 3.
0.3 __>____ 0.25
0.3 > 0.25,

Explanation:
As 0.3 is greater than 0.25, So 0.3 > 0.25.

Question 4.
0.76 __<___ 0.8
0.76 < 0.8,

Explanation:
As 0.76 is less than 0.8, So 0.76 < 0.8.

Question 5.
0.1 ___=___ 0.10
0.1 = 0.10,

Explanation:
As 0.1 is equal to 0.10, So 0.1 = 0.01.

Question 6.
0.785 ___<___ 0.79
0.785 < 0.79,

Explanation:
As 0.78 is less than 0.79, So 0.78 < 0.79.

Question 7.
4.03 ___=___ 4.030
4.03 = 4.030,

Explanation:
4.03 is equal to 4.030, So 4.03 = 4.030.

Question 8.
1.512 ___>___ 1.499
1.512 > 1.499,

Explanation:
1.512 > 1.499,

Explanation:
As 1.512 is greater than 1.499, So 1.512 > 1.499.

Solving Problems on a Coordinate Grid

Clay reads the same amount of a book each day.
The table below shows how many chapters of the
book he has read at the end of each day.
Write the data from the table as ordered pairs.
Plot the points on the grid and connect them in a line.
Use the graph to answer the questions.  Explanation:
Given Clay reads the same amount of a book each day.
The table showed how many chapters of the
book he has read at the end of each day.
Wrote the data from the table as ordered pairs as
(1,3), (2,6), (3,9), (4,12), (5,15) and
Plotted the points on the grid and
connected them in a line as shown above.

Question 1.
Between which two days did Clay finish reading Chapter 5 in the book?
Between days _____1_____ and ____2____
Clay finished reading Chapter 5 in the book
between days 1 and 2,

Explanation:
By seeing the table data it is clear that Chapter 5
comes in between Chapter 3 and Chapter 5, So
Clay finished reading Chapter 5 in the book
between days 1 and 2.

Question 2.
through the fourth day (Day 3$$\frac{1}{2}$$)?
Number of chapters did Clay read half-way through
the fourth day (Day 3$$\frac{1}{2}$$) is 10 or 11,

Explanation:
By seeing the table data it is clear that
number of chapters Clay read half-way through
the fourth day (Day 3$$\frac{1}{2}$$) is in
between 9 and 12 so 10 or 11.

Question 3.
If the book has 17 chapters, on what day would
Clay complete the book?
Some time on the sixth day,

Explanation:
By seeing the table data it is clear that
If the book has 17 chapters, the day Clay would
complete the book would be some time on the sixth day.

Question 4.
By calculating using the given table data,

Explanation:
By seeing the table data it is clear that from
End of Day 1 completed chapters are 3,
Day 2 it is 3 + 3 = 6, Day 3 it is 6 + 3 = 9,
Day 4 it is 9 + 3 = 12 and Day 5 it is 12 +3 = 15,
means everyday it is 3 chapters,
So If the book has 17 chapters, the day Clay would
complete the book would be some time on the sixth day.

Practice
Round the following numbers to the nearest hundredth.
Question 5.
0.546 ___0.55_____
0.546 to the nearsest hundreth is 0.55,

Explanation:
Given 0.546, We know the hundredths place is
the second digit to the right of the decimal point.
So the nearest hundreth to 0.546 is 0.55.

Question 6.
3.971 ____3.97____
3.971 to the nearsest hundreth is 3.97,

Explanation:
Given 3.971, We know the hundredths place is
the second digit to the right of the decimal point.
So the nearest hundreth to 3.971 is 3.97.

Question 7.
84.099 ____84.10____
84.099 to the nearsest hundreth is 84.10,

Explanation:
Given 84.099, We know the hundredths place is
the second digit to the right of the decimal point.
So the nearest hundreth to 84.099 is 84.10.

Question 8.
0.008 ____0.01______
0.008 to the nearsest hundreth is 0.01,

Explanation:
Given 0.008, We know the hundredths place is
the second digit to the right of the decimal point.
So the nearest hundreth to 0.008 is 0.01.

Using a Coordinate Grid

Eva made a drawing of her house on a coordinate grid.
She said that the real house looks like it is about twice
as wide as it is high. Her brother said she should change
her picture to look more like their real house. Question 1.
Write a rule that Eva can use to make the drawing
of the house look more like her real house.
Rule is (2x,2y),

Explanation:
Given Eva made a drawing of her house on a coordinate grid.
She said that the real house looks like it is about twice
as wide as it is high, So the rule that Eva can use to make
the drawing of the house look more like her real house is
(2x,2y).

Question 2.
Use your rule to write the new coordinates.  Explanation:
Using my rule (2x, 2y) to write the new coordinates are
(0,4) as (0, 8)
(0, 0) as (0, 0),
(4, 0) as (8, 0),
(4, 4) as (8, 8),
(0, 4) as (0, 8),
(2, 6) as (4, 12) and
(4, 4) as (8, 8) respectively as shown above.

Decimal Addition and Subtraction with Grids

Question 1.
a. Shade this grid to show 0.61.  Explanation:
Shaded the grid to show as 0.61 above.

b. Shade this grid to show 0.34.  Explanation:
Shaded the grid to show 0.34 as above.

c. Shade this grid to show 0.61 + 0.34.  Explanation:
Shaded the grid to show 0.61 + 0.34 as above.

d. Write an addition number sentence to represent
what you did in Parts a–c.
0.61 + 0.34 = 0.95,

Explanation:
In parts a to c is first shading 0.61 then shading part b
as 0.34 then in part c shading 0.61 + 0.34, So
the addition number sentence to represent part a – c is
0.61 + 0.34 = 0.95.

Question 2.
a. Shade the grid at the right to show 0.4.  Explanation:
Shaded the grid at the right to show 0.4 as shown above.

shade 0.15 darker, or cross out 0.15. Explanation:
shaded 0.15 darker as shown above.

c. Write a subtraction number sentence to show what you did.
Subtraction number sentence : 0.4 – 0.15 = 0.25,

Explanation:
as 0.15 on 0.4, So the subtraction number sentence
is 0.4 – 0.15 = 0.25.

Practice
Make an estimate. Then solve using U.S. traditional multiplication.
Question 3.  Explanation:
Estimated 27 X 31 = 837 and solved using
U.S. traditional multiplication as shown above.

Question 4.  Explanation:
Estimated 308 X 56 = 17,248 and solved using
U.S. traditional multiplication as shown above.

Question 5.  Explanation:
Estimated 412 X 176 = 72,512 and solved using
U.S. traditional multiplication as shown above.

For Problems 1–3, make an estimate. Write a
number sentence to show how you estimated.
Then solve the problem using partial-sums addition,
Question 1.
2.4 + 9.3 = ? 2.4 + 9.3 = __11.7_______ 2.4
+ 9.3
11.7

Explanation:
Wrote a number sentence as 2.4 + 9.3 = 11.7,
then solved the problem using column addition as
shown above the answer is reasonable
as estimate is same to the solved one 11.7.

Question 2.
5.8 + 3.36 = ? 5.8 + 3.36 = ___9.16_______ 5.8
+3.36
9.16

Explanation:
Wrote a number sentence as 5.8 + 3.36 = 9.16,
then solved the problem using column addition as
shown above the answer is reasonable
as estimate is same to the solved one 9.16.

Question 3.
12.07 + 6.98 = ? 12.07 + 6.98 =___19.05_____ 1 1
12.07
+6.98
19.05
Explanation:
Wrote a number sentence as 12.07 + 6.98 = 19.05,
then solved the problem using column addition as
shown above the answer is reasonable
as estimate is same to the solved one 19.05.

For Problems 4 and 5, write a number model with a letter for the unknown. Then solve.
Question 4.
At the 2012 Summer Olympics in London, Usain Bolt
won the men’s 100-meter race with a time of 9.63 seconds and
the men’s 200-meter race with a time of 19.32 seconds.
How long did it take the sprinter to run the two races combined? ___28.95_______ seconds 28.95 econds it will the sprinter to run the two races combined,

Explanation:
Given at the 2012 Summer Olympics in London,
Usain Bolt won the men’s 100-meter race with a time of
9.63 seconds and the men’s 200-meter race with a
time of 19.32 seconds.
So long did it take the sprinter to run the two races
combined are 100-meter + 200-meter is
9.63 sec + 19.32 sec = 28.95 seconds.

Question 5.
In July 2006, the smallest living horse was 44.5 cm tall, from the ground to its back. In May 2006, the smallest living dog was 10.16 cm tall, from the ground to the top of its head. How far from the ground would the dog’s head be if it stood on the horse’s back? ___54.66_______ cm 54.66 cm far from the ground would the dog’s head
be if it stood on the horse’s back,

Explanation:
Given in July 2006, the smallest living horse was 44.5 cm tall,
from the ground to its back. In May 2006, the smallest living
dog was 10.16 cm tall, from the ground to the top of its head.
So far from the ground would the dog’s head be if it stood
on the horse’s back is 44.5 cm  + 10.16 cm = 54.66 cm.

Practice
Question 6.
What is $$\frac{1}{2}$$ of 12?
6

Explanation:
Given to find $$\frac{1}{2}$$ of 12 means
$$\frac{1}{2}$$ X 12 = 6.

Question 7.
What is $$\frac{1}{2}$$ of 11?
$$\frac{11}{2}$$ or 5$$\frac{1}{2}$$,

Explanation:
Explanation:
Given to find $$\frac{1}{2}$$ of 11 means
$$\frac{1}{2}$$ X 11 = $$\frac{11}{2}$$ or as
numerator is greater than denominatore on further s
implification we write in mixed fraction as (2 X 5 + 1 = 11 by 2 ),
So $$\frac{11}{2}$$ = 5$$\frac{1}{2}$$.

Question 8.
What is $$\frac{1}{5}$$ of 11?
$$\frac{11}{5}$$ or 2$$\frac{1}{5}$$,

Explanation:
Explanation:
Given to find $$\frac{1}{5}$$ of 11 means
$$\frac{1}{5}$$ X 11 = $$\frac{11}{5}$$ or as
numerator is greater than denominatore on further s
implification we write in mixed fraction as (5 X 2 + 1 = 11 by 5),
So $$\frac{11}{5}$$ = 2$$\frac{1}{5}$$.

Subtracting Decimals

For Problems 1–3, make an estimate. Write a
number sentence to show how you estimated.
Then solve the problem using trade-first subtraction,
counting-up subtraction, or U.S. traditional subtraction.
Question 1.
10.6 – 3.9 = ? 10.6 – 3.9 = ___6.7____ 10.6
-3.9
6.7

Explanation:
Wrote a number sentence as 10.6 – 3.9 = 6.7,
then solved the problem using U.S. traditional subtraction
as shown above the answer is reasonable
as estimate is same to the solved one 6.7.

Question 2.
8.97 – 4.22 = ? 8.97 – 4.22 = __4.75_______ 8.97
-4.22
4.75

Explanation:
Wrote a number sentence as 8.97 – 4.22 = 4.75,
then solved the problem using U.S. traditional subtraction
as shown above the answer is reasonable
as estimate is same to the solved one 4.75.

Question 3.
24.29 – 13.37 = ? 24.29 – 13.37 = ___10.92______ 24.29
-13.37
10.92

Explanation:
Wrote a number sentence as 24.29 – 13.37 = 10.92,
then solved the problem using U.S. traditional subtraction
as shown above the answer is reasonable
as estimate is same to the solved one 10.92.

For Problems 4 and 5, write a number model
with a letter for the unknown. Then solve.
Question 4.
At the 2012 Summer Olympics in London, swimmer Michael Phelps won the gold medal in the men’s 100-meter butterfly with a time of 51.21 seconds. The eighth-place swimmer finished in 52.05 seconds. How much faster was Phelps?
Number model: ____52.05 – 51.21 = 0.84_____
_____0.84______ second
Number Model : 52.05 – 51.21 = 0.84
Phelps was 0.84 seconds faster than the eighth-place,

Explanation:
Given at the 2012 Summer Olympics in London,
swimmer Michael Phelps won the gold medal in
the men’s 100-meter butterfly with a time of 51.21 seconds.
The eighth-place swimmer finished in 52.05 seconds.
Therefore faster was Phelps than  is 52.05 – 51.21 = 0.84 seconds.

Question 5.
In May 2009, the longest dog tongue ever measured was 11.43 cm long. In February 2009, the longest human tongue ever measured was 9.8 cm long. How much longer was the dog tongue than the human tongue?
Number model: ___11.43 – 9.8 = __1.63 cm____
____1.63_______ cm
1.63 longer was the dog tongue than the humn tongue,

Explanation:
Given in May 2009, the longest dog tongue ever
measured was 11.43 cm long. In February 2009,
the longest human tongue ever measured was 9.8 cm long.
Longer is the dog tongue than the human tongue is
11.43 – 9.8 = 1.63 cm.

Practice
Give the value of the 9 in each decimal.
Question 6.
4.897 ____0.09_____
The value of the 9 in the decimal 4.897 is 0.09,

Explanation:
Given to find the value of the 9 in each decimal,
so the value of the 9 in the decimal 4.897 is 0.09.

Question 7.
0.981 ____0.9_____
The value of the 9 in the decimal 0.981 is 0.9,

Explanation:
Given to find the value of the 9 in each decimal,
so the value of the 9 in the decimal 0981 is 0.9.

Question 8.
49.772 _____9____
The value of the 9 in the decimal 49.772 is  9,

Explanation:
Given to find the value of the 9 in each decimal,
so the value of the 9 in the decimal 49.772 is 9.

Question 9.
6.019 ______0.009___
The value of the 9 in the decimal 6.019 is 0.009,

Explanation:
Given to find the value of the 9 in each decimal,
so the value of the 9 in the decimal 6.019 is 0.009.

Question 10.
496.12 ____90_____
The value of the 9 in the decimal 496.12 is 90,

Explanation:
Given to find the value of the 9 in each decimal,
so the value of the 9 in the decimal 496.12 is 90.

Question 11.
72.497 ____0.09_____
The value of the 9 in the decimal 72.497 is 0.09,

Explanation:
Given to find the value of the 9 in each decimal,
so the value of the 9 in the decimal 72.497 is 0.09.

Number Stories with Money

For each number story, write a number model
with a letter for the unknown. Then solve.
Show your work on the back of this paper.
Question 1.
You buy a loaf of fresh bread for $1.49 and a bottle of honey for$1.99. How much do you spend in all?  Explanation:
Given I buy a loaf of fresh bread for $1.49 and a bottle of honey for$1.99. So total amount spend in all is
$1.49 +$1.99 = $3.48. Question 2. Your grocery bill comes to$17.37. You pay with
a $20.00 bill. How much change do you get? Answer: Explanation: Given my grocery bill comes to$17.37.
I pay with a $20.00 bill. So change I got is$20.00 – $17.37 =$2.63.

Question 3.
A pound of strawberries costs $2.49. A pound of apples costs$1.99. How much more money per pound
do the strawberries cost than the apples?  Explanation:
Given a pound of strawberries costs $2.49. A pound of apples costs$1.99.
More money per pound the strawberries cost
than the apples is $2.49 –$1.99 = $0.50. Question 4. One granola bar costs 88 cents. How much do two granola bars cost? Answer: Explanation: Given one granola bar costs 88 cents. So for two granola bars cost 88 cents X 2 =176 cents as 1 cent = 0.01 so 176 cents =$1.76.

Practice
Question 5.
Make an estimate. Then divide using
partial-quotients division. Write your remainder as a fraction.
812 ÷ 17 = ?
Estimate: ___47_______
812 ÷ 17 =47$$\frac{13}{17}$$,

Explanation:
Given to solve 812 ÷ 17 =
47 R13
17)812(
68
132
119
13
Therefore, 812 ÷ 17 =47$$\frac{13}{17}$$.

Question 6.
Draw an area model to match your solution in Problem 5.
Area (Dividend): _____812_____  So 812 ÷ 17 = 47$$\frac{13}{17}$$ as shown above and