## Everyday Mathematics 4th Grade Answer Key Unit 2 Multiplication and Geometry

Exploring Square Numbers

A square number is a number that can be written as the product of a number multiplied by itself. For example, the square number 9 can be written as 3 ∗ 3.

Question 1.
Fill in the missing factors and square numbers.

We will fill the blanks factors and square numbers.

Explanation:
As the square number is a number that can be written as the product of a number multiplied by itself. So, here we will fill the blanks factors and square numbers.

Question 2.
What pattern(s) do you see in the factors? In the products?
The pattern do we see in the factors is Prime Factorization.

Explanation:
Here, in the above table, we have used the Prime Factorization pattern. The Prime Factorization method is defined as a way of  finding prime numbers, which are multipled together to get the original number.

Question 3.
What other pattern(s) do you see in the table?
The other pattern that we have seen in the table is the squares of the numbers.

Question 4.
Write an equation to describe each array.
a.
Equation: ___

The equation will be 4 × 9 = 36.

Explanation:
As we have 36 dots in all and there are 4 rows with 9 dots in each row. So the equation will be 4 × 9 which is 36 dots.

b.
Equation: ___

The equation will be 5 × 5 = 25.

Explanation:
As we have 25 dots in all and there are 5 rows with 5 dots in each row. So the equation will be 5 × 5 which is 25 dots.

Question 5.
a. Which of the arrays above shows a square number? ___________
b. Explain. ________
a. The above arrays that show a square number is array b.
b. As there are 5 rows of 5 dots which is 25 dots.

Explanation:
In the above arrays that show a square number is array b as there are 5 rows of 5 dots which is 25 dots.

Practice

Question 6.
32, 45, 58, ____, ____, ____ Rule: _____
32, 45, 58, 71, 84, 97.

Explanation:
Here, we need to add 13. If we check the difference between 45 and 32 we will get the difference as 13. So, we can see that in the given series, so 13 is added to the given numbers. So the rule is adding 13.

Question 7.
___, ___, ___, 89, 115, 141 Rule: ____
11,37,63,89,115,141
Rule: subtract 26.

Explanation:
Here, we need to subtract 26. If we check the difference between 141 and 115 we will get the difference as 26. So, we can see that in the given series, so 26 is subtracted to the given numbers. So the rule is subtracting 26.

Area of a Rectangle

Question 1.
Draw a rectangle that has length of 9 units and width of 4 units.

Equation: ___
Area = ___ square units
The area of the rectangle is 36 square units.

Explanation:
Here, we have constructed a rectangle that has a length of 9 units and a width of 4 units. And here we need to find the area of the rectangle, so the area of the rectangle is
= 9 × 4
= 36 square units.
So the area of the rectangle is 36 square units.

Question 2.
Draw a rectangle that has a length of 7 units and a width of 8 units.

Equation: ___
Area = ___ square units
The area of the rectangle is 56 square units.

Explanation:
Here, we have constructed a rectangle that has a length of 7 units and a width of 8 units. And here we need to find the area of the rectangle, so the area of the rectangle is
= 7 × 8
= 56 square units.
So the area of the rectangle is 56 square units.

Use the formula A = I ∗ w to find the area of each rectangle.

Question 3.

Equation: ___
Area = ___ square units
The area of the rectangle is 48 square units.

Explanation:
Here, we need to find the area of the rectangle, so the area of the rectangle is
= 8 × 6
= 48 square units.
So the area of the rectangle is 48 square units.

Question 4.

Equation: ___
Area = ___ square units

The area of the rectangle is 48 square units.

Explanation:
Here, we need to find the area of the rectangle, so the area of the rectangle is
= 8 × 6
= 48 square units.
So the area of the rectangle is 48 square units.

Question 5.
Riley’s dining room tabletop is 9 feet long and 6 feet wide. What is the area of the tabletop?
Equation: _____
Area = ___ square feet

The area of the tabletop is 54 square feet.

Explanation:
Riley’s dining table top is 9 feet long and width is 6 feet, so the area of the tabletop is
Area = length × width
= 9 × 6
= 54 square feet.
So the area of the tabletop is 54 square feet.

Practice

Question 6.
368 – 59 = ____
The subtraction of two numbers is 309.

Explanation:
By subtracting the given numbers 368 – 59 we will get the result as 309.

Question 7.
194 – 147 = ___
The subtraction of two numbers is 47.

Explanation:
By subtracting the given numbers 194 – 147 we will get the result as 47.

Question 8.
____ = 1,729 – 623
The subtraction of two numbers is 1,106.

Explanation:
By subtracting the given numbers 1,729 – 623 we will get the result as 1,106.

Working with Factor Pairs

Write equations to help you find all the factor pairs of each number below. Use dot arrays, if needed.

Practice

Question 2.
356 + 433 = ___
The addition of two numbers is 789.

Explanation:
The addition of the two given numbers 356 + 433 is 789.

Question 3.
___ = 2,167 + 696
The addition of two numbers is 2,863.

Explanation:
The addition of the two given numbers 2,167 + 696 is 2,863.

Question 4.
___ = 4,578 – 2,232
The subtraction of two numbers is 2,346

Explanation:
The subtraction of the two given numbers 4,578 – 2,232 is 2,346.

Question 5.
3,271 – 1,089 = ___
The subtraction of two numbers is 2,182.

Explanation:
The subtraction of the two given numbers 4,578 – 2,232 is 2,182.

Finding Multiples

Question 1.
List the first 5 multiples of 4. ____________
4 × 1 = 4,
4 × 2 = 8,
4 × 3 = 12,
4 × 4 = 16,
4 × 5 = 20.

Explanation:
The first 5 multiples of 4 are:
4 × 1 = 4,
4 × 2 = 8,
4 × 3 = 12,
4 × 4 = 16,
4 × 5 = 20.

Question 2.
List the first 10 multiples of 2. _______________
2 × 1 = 2,
2 × 2 = 4,
2 × 3 = 6,
2 × 4 = 8,
2 × 5 = 10,
2 × 6 = 12,
2 × 7 = 14,
2 × 8 = 16,
2 × 9 = 18,
2 × 10 = 20.

Explanation:
The first 10 multiples of 2 is
2 × 1 = 2,
2 × 2 = 4,
2 × 3 = 6,
2 × 4 = 8,
2 × 5 = 10,
2 × 6 = 12,
2 × 7 = 14,
2 × 8 = 16,
2 × 9 = 18,
2 × 10 = 20.

Question 3.
a. List the first 10 multiples of 3. _________

3 × 1 = 3,
3 × 2 = 6,
3 × 3 = 9,
3 × 4 = 12,
3 × 5 = 15,
3 × 6 = 18,
3 × 7 = 21,
3 × 8 = 24,
3 × 9 = 27,
3 × 10 = 30.

Explanation:
The first 10 multiples of 3 is
3 × 1 = 3,
3 × 2 = 6,
3 × 3 = 9,
3 × 4 = 12,
3 × 5 = 15,
3 × 6 = 18,
3 × 7 = 21,
3 × 8 = 24,
3 × 9 = 27,
3 × 10 = 30.

b. List the first 10 multiples of 5. _________

5 × 1 = 5,
5 × 2 = 10,
5 × 3 = 15,
5 × 4 = 20,
5 × 5 = 25,
5 × 6 = 30,
5 × 7 = 35,
5 × 8 = 40,
5 × 9 = 45,
5 × 10 = 50.

Explanation:
The first 10 multiples of 5
5 × 1 = 5,
5 × 2 = 10,
5 × 3 = 15,
5 × 4 = 20,
5 × 5 = 25,
5 × 6 = 30,
5 × 7 = 35,
5 × 8 = 40,
5 × 9 = 45,
5 × 10 = 50.

c. List the multiples of 3 that are also multiples of 5. ________
Multiples of 3 that are also multiples of 5 are 15, 30, 45, 60, 75, 90.

Explanation:
The multiples of 3 that are also multiples of 5 are 15, 30, 45, 60, 75, 90.

Question 4.
Is 28 a multiple of 7? ___ Explain. ______
Yes, 28 is a multiple of 7.

Explanation:
Yes, 28 is a multiple of 7. As 28 is divisible by 7 and when we divide 28 by 7 we will get the reminder as zero. So 28 is a multiple of 7.

Question 5.
Is 35 a multiple of 6? __ Explain. _____
No, 35 is not a multiple of 6.

Explanation:
No, 35 is not a multiple of 6. As 35 is not divisible by 6 and when we divide 35 by 6 we will not get the reminder as zero. So 35 is not divisible by 6.

Question 6.
a. List the factors of 15. List the multiples through 15 of each factor.

b. Is 15 a multiple of each of its factors? Explain.
Yes, 15 is a multiple of each of its factors.

Explanation:
Yes, 15 is a multiple of each of its factors. As 15 is divisible by 1, 3, 5, 15, and by dividing we will get the reminder as zero. So 15 is a multiple of each of its factors.

Practice

Question 7.
24, ____, 48, ___, 72, ___ Rule: ____
24, 36, 48, 72, 84.

Explanation:
Here, we will add 12 to the given number 24 then we will get 36 and then we will add 12 to the number 36 then we will get 48 and we will continue until we will get the last number. So here the rule is adding 12.

Question 8.
___, 108, 162, ___, 270, ___ Rule: ____
54, 108, 162, 216, 270, 324.

Explanation:
Here, we need to add 54. If we check the difference between 162 and 108 we will get the difference as 54. So, we can see that in the given series, so 54 is added to the given numbers. So the rule is adding 54.

Question 9.
86, ___, 52, ___, 18, Rule: ___
86, 69, 52, 35, 18, 1.
Rule: The difference between consecutive numbers is 17. 86, 69, 52, 35, 18, 1.

Explanation:
Here, we will subtraction 17 between the consecutive numbers.

Question 10.
425, ___, 339, ____, 253, ____ Rule: ___
425, 382, 339, 296, 253, 210.
Rule: The difference between each pair of numbers is 43.

Explanation:
Here, the difference between each pair of the numbers is 43. So 425, 382, 339, 296, 253, 210.

Prime and Composite Numbers

A prime number is a whole number that has exactly two different factors—1 and the number itself. A composite number is a whole number that has more than two different factors. For each number:

• List all of its factors.
• Write whether the number is prime or composite.
• Circle all of the factors that are prime numbers.

Practice
Solve.

Question 10.
841 + 527 = _____
841 + 527 = 1,368.

Explanation:
The addition of the given two numbers 841 + 527 is 1,368.

Question 11.
____ = 3,263 + 5,059
8,322 = 3,263 + 5,059

Explanation:
The addition of the given two numbers 3,263 + 5,059 is 8,322.

Question 12.
7,461 + 2,398 = _____
7,461 + 2,398 = 9,859

Explanation:
The addition of the given two numbers 7,461 + 2,398 is 9,859.

Question 13.
___ = 4,172 – 3,236
936 = 4,172 – 3,236

Explanation:
The difference between the given numbers 4,172 – 3,236 is 936.

Question 14.
8,158 = 5,071 + __
The missing number is 3,087.

Explanation:
Let the missing number be x and we will replace the missing number with x, then 8,158 = 5,071 + x. So x is
x = 8,158 – 5,071
= 3,087.

Question 15.
3,742 – 3,349 = ___
3,742 – 3,349 = 393.

Explanation:
The difference between the given numbers 3,742 – 3,349 is 393.

Using Multiplication

Home Market sells 3 grapefruits for $2. Question 1. Darius spent$6 on grapefruits. How many did he buy? Use words, numbers, or diagrams to show your reasoning.
Darius bought 9 grapefruits.

Explanation:
As Darius spent $6 on grapefruits, here home market sells 3 grapefruits for$2. So the number of grapefruits did Darius bought for $6 is 3 + 3 + 3 which is 9. So Darius bought 9 grapefruits. Question 2. Jana bought 15 grapefruits. How much did she spend? Use words, numbers, or diagrams to show your reasoning. Answer: Jana spends$10.

Explanation:
As Jana bought 15 grapefruits. here home market sells 3 grapefruits for $2. So the number of grapefruits did Darius bought for$6 is 2 + 2 + 2 + 2 + 2 which is 10. So Jana spends $10. Question 3. On the back of this page, write a multiplication number story about buying grapefruits at Home Market. Show how to solve your number story. Answer: Explanation: Practice Write these numbers using words. Question 4. 12,309 _________________ Answer: Twelve thousand three hundred and nine. Explanation: I have written the given numbers using words which is Twelve thousand three hundred and nine. Question 5. 30,041 _________ Answer: Thirty Thousand and forty-one. Explanation: I have written the given numbers using words which is Thirty Thousand and forty-one. Question 6. 600,780 _________ Answer: Six hundred thousand seven hundred eighty. Explanation: I have written the given numbers using words which is Six hundred thousand seven hundred eighty. Question 7. 9,090,506 ________ Answer: Ninety Lakh Ninety Thousand Five hundred Six. Explanation: I have written the given numbers using words which is Ninety Lakh Ninety Thousand Five hundred Six. ### Everyday Math Grade 4 Home Link 2.6 Answer Key Converting Units of Time Use the measurement scales to fill in the tables and answer the questions. Question 1. Answer: Filled the table with minutes for the given hours using the measurement scales. Explanation: Here, we have filled the table with minutes for the given hours using the measurement scales. Question 2. Answer: Filled the table with minutes for the given hours using the measurement scales. Explanation: Here, we have filled the table with seconds for the given minutes using the measurement scales. Question 3. Zac worked on his spelling for 9 minutes last night and 8 minutes this afternoon. How many seconds did he work? Answer: seconds Answer: Zac worked 1,020 seconds. Explanation: Here, Zac worked on his spelling for 9 minutes last night and 8 minutes this afternoon, so the total number of minutes did Zac worked is 9 + 8 which is 17 minutes. Now we will convert minutes to seconds 17 × 60 which is 1,020 seconds. So Zac worked 1,020 seconds. questions 4. Eton’s baby sister took a nap for 2 hours and 22 minutes yesterday and 1 hour and 35 minutes today. How many more minutes did she sleep yesterday than today? Answer: ___ minutes Answer: Eton’s baby sister took a nap yesterday then today is 47 minutes. Explanation: Here, Eton’s baby sister took a nap for 2 hours and 22 minutes yesterday, so the total number of minutes 120 + 22 which is 142 minutes. And 1 hour and 35 minutes today, so the total number of minutes 60 + 35 is 95 minutes. And the total number of minutes did Eton’s baby sister took a nap yesterday then today is 142 – 95 = 47 minutes. Try This Question 5. How many seconds did Eton’s baby sister sleep all together? Answer: ___ seconds Answer: The total number of seconds did Eton’s sister sleeps is 14,220 seconds. Explanation: Eton’s baby sister sleeps all together 142 + 95 which is 237 minutes and we need to convert minutes to seconds 237 × 60 = 14,220 seconds. So the total number of seconds did Eton’s sister sleeps is 14,220 seconds. Practice Question 6. 945 + 1,055 = ___ Answer: 945 + 1,055 = 2000 Explanation: Add the two given numbers to get the resultant sum. Hence the answer is 2000. Question 7. 2,953 + 4,471 = ___ Answer: 2,953 + 4,471 = 7424 Explanation: Add the two given numbers to get the resultant sum. Hence the answer is 7424. Question 8. 4,552 + 4,548 = ___ Answer: 4,552 + 4,548 = 9100 Explanation: Add the two given numbers to get the resultant sum. Hence the answer is 9100. Question 9. 3,649 + 3,649 = ___ Answer: 3,649 + 3,649 = 7298 Explanation: Add the two given numbers to get the resultant sum. Hence the answer is 7298. ### Everyday Math Grade 4 Home Link 2.8 Answer Key Multiplicative Comparisons Family Note In this lesson students used comparison statements and equations to represent situations in which one quantity is a number of times as much as another quantity. For example: José saved$5 over the summer. His sister saved 3 times as much. How much money did José’s sister save? In this number story students compare the amount of money José saved to the amount his sister saved. Students write the equation 3 ∗ 5 = 15 to represent this comparison and solve the problem:
José’s sister saved \$15. Because these comparison statements and equations involve multiplication, they are called multiplicative comparisons.

Complete the problems below. Write an equation with a letter for the unknown and solve.

Question 1.
What number is 7 times as much as 9?
Equation with unknown:
n = 7 × 9
63

Explanation:
The number which is 7 times as much as 9 is 63 and the equation is 7 × 9 which is 63.

Question 2.
What number is 5 times as much as 6?
Equation with unknown:
n = 5 * 6
30

Explanation:
The number which is 5 times as much as 6 is 30 and the equation is 5 × 6 which is 30.

Question 3.
32 is 4 times as much as what number?
a. Equation with unknown: ___
n = 32 * 4
128

Explanation:
The number which is 32 times as much as 4 is 128 and the equation is 32 × 4 which is 128.

Question 4.
Write an equation to represent this situation and solve.
Ameer worked 3 times as many hours as Simi each week during the summer.
If Simi worked 10 hours each week, how many hours did Ameer work each week?
a. Equation with unknown: ____
The number of hours did Ameer work each week is 30 hours.

Explanation:
Here, Ameer worked 3 times as many hours as Simi each week during the summer and Simi worked 10 hours each week. So the number of hours did Ameer work each week 3 × 10 which is 30 hours. So the number of hours did Ameer work each week is 30 hours.

Practice

Question 5.
7,482 – 7,083 = ___
7,482 – 7,083 = 399

Explanation:
By subtracting the given numbers 7,482 – 7,083 the answer we get is 399.

Question 6.
7,702 – 3,581 = ___
7,702 – 3,581 = 4121

Explanation:
By subtracting the given numbers 7,702 – 3,581 the answer we get is 4121.

Question 7.
5,201 – 3,052 = ___
5,201 – 3,052 = 2149

Explanation:
By subtracting the given numbers 5,201 – 3,052 the answer we get is 2149.

Question .8
8,002 – 5,403 = ____
8,002 – 5,403 = 2599

Explanation:
By subtracting the given numbers 8,002 – 5,403 the answer we get is 2599.

Solving Multiplicative Comparison Number Stories

Make a diagram or drawing and write an equation to represent the situation. Then find the answer.

Question 1.
Judith collected 9 marbles. Swen has 6 times as many. How many marbles does Swen have?
Diagram or drawing:
Equation with unknown: ____
54 marbles

Explanation:
Here the Swen has 54 marbles. As Judith collected 9 marbles and Swen has 6 times as many as Judith it means the Swen has 9 * 6 = 54 marbles.

Question 2.
Sol ran 4 times as many minutes as Jerry. Jerry ran 12 minutes. How many minutes did Sol run?
Diagram or drawing:
Equation with unknown: ____
48 minutes

Explanation:
Here, Sol ran 4 times as many minutes as Jerry and Jerry ran 12 minutes. So the number of minutes did Sol ran 12 × 4 which 48 minutes.

Insert quantities into the number story. Make a diagram and write an equation to represent the story.

Question 3.
Lola picked apples. Eilene picked apples. Eilene picked times as many apples as Lola.
Diagram or drawing:
Equation with unknown: _____

Practice

Write these numbers in expanded form.

Question 4.
3,830 _________
3000 + 800 + 30

Question 5.
56,037 ________
50,000 + 6000 + 30 + 7

Question 6.
800,700 __
800000 + 700

Question 7.
716,305 _____
700,000 + 10,000 + 6000 + 300 + 5

Identifying Triangles

Write the letter or letters that match each statement.

Question 1.
Has perpendicular line segments
C, D

Explanation:
The perpendicular line segments in the given question are C, D

Question 2.
Has an obtuse angle
E, F

Explanation:
E and F are the triangles which are obtuse angle.

Question 3.
Has right angles
C, D

Explanation:
C and D are the right angles.

Question 4.
Has acute angles
A, B

Explanation:
A and B are the acute angles given in the question.

Question 5.
Has more than one kind of angle
C, D, E, F

Explanation:
C, D, E, and F are the one kind of angle that is given in the question.

Question 6.
Has only one kind of angle
A, B

Explanation:
A and B are the only kind of angle.

Question 7.
Does NOT have any right angles
A, B, E, F

Explanation:
A, B, E, and F do not have any right angles in the given question.

Question 8.
Is a right triangle
C, D

Explanation:
C and D is the right triangle in the given question.

Practice

Question 9.
List all the factors of 12.
1, 2, 3, 4, 6, 12

Explanation:
The factors of 12 are 1, 2, 3, 4, 6, 12 because each of those divides 12 without leaving a remainder.

Question 10.
Name the next 4 multiples of 7. 35, _____, _____, ___, ____
42, 49, 56, 63.

Explanation:
The next 4 multiples of 7 are 42, 49, 56, 63.

Question 1.
A parallelogram is a quadrilateral that has 2 pairs of parallel sides. Draw a parallelogram.

I have drawn a parallelogram that has 2 pairs of parallel sides.

Explanation:
As asked in the question I have drawn a parallelogram below.

Question 2.
a. Can a parallelogram have right angles? Explain.
b. Could a quadrilateral have 4 obtuse angles? Explain.
c. Name a quadrilateral that has at least 1 pair of parallel sides.
a.
b. No, all the four angles of a quadrilateral cannot be obtuse. As the sum of the angles of a quadrilateral is 360∘, they may have a maximum of three obtuse angles.
c. Trapezoids
Trapezoids have only one pair of parallel sides.

Question 3.

Draw a quadrilateral that has at least 1 right angle.

Question 4.
Draw a quadrilateral that has 2 separate pairs of equal length sides but is NOT a parallelogram.
This is called a ____.

Practice

Question 5.
5 ∗ 30 = ___
150

Explanation:
By multiplying the given numbers the answer we get is 150.

Question 6.
__ = 40 ∗ 3
120

Explanation:
By multiplying the given numbers the answer we get is 120.

Question 7.
___ = 80 ∗ 6
480

Explanation:
By multiplying the given numbers the answer we get is 480.

Question 8.
6 ∗ 70 = ____
420

Explanation:
By multiplying the given numbers the answer we get is 420.

Drawing Lines of Symmetry

Question 1.
Draw the other half of each picture to make it symmetrical. Use a straightedge to form the line of symmetry.

Question 2.
Draw a line of symmetry for each figure.

Question 3.
List four items in your home that are symmetric. Pick one item and draw it below, including at least one line of symmetry.
Item: __ Item: ___ Drawing:
Item: __ Item: ___

Practice

Question 4.
___ = 2,767 + 3,254
6021

Explanation:
Add the two given numbers to get the resultant sum. Hence the answer is 6021.

Question 5.
193 + 6,978 = ___
7171

Explanation:
Add the two given numbers to get the resultant sum. Hence the answer is 7171.

Question 6.
7,652 − 5,388 = ___
5674

Explanation:
By subtracting the given numbers the answer we get is 5674.

Question 7.
___ = 4,273 − 1,678
2595

Explanation:
By subtracting the given numbers the answer we get is 2595.

Identifying Patterns

Question 1.
Complete.

What patterns do you see?
The pattern is multiples of 9.

Explanation:
The pattern is multiples of 9 in which 2 is in and 18 is out and that series continuous till the number 6.

Question 2.
Complete.

What patterns do you see?

Explanation:
The pattern is adding 11 in which 11 is in and 22 is out and that series continuous till the number 55.

Question 3.
Study the pattern
a. Draw the next step in the pattern. What patterns do you notice?
b. How many circles will be in the 6th step? __ In the 10thstep? ___
c. How did you figure out how many circles will be in the 10th step?
a. In this question the number of circles is odd and increases by 2 every time.

Explanation:
I have drawn the next step in the pattern below.

b. 11; 19

Explanation:
There will be 11 circles in the 6th step. And 19 circles in the 10th step.

c. In this, each step is the next odd number so I skip counted from 1 by 2 until I got to the 10th step.

Explanation:
We can figure it out by observing each step given in the pattern. As in each step, the next one is an odd number so we can skip counted from 1 by 2 until we got to the 10th step.

Practice

Question 4.
800,000 + 90 = ___
800,090

Explanation:
Add the two given numbers to get the resultant sum. Hence the answer is 800,090.

Question 5.
200,000 + 50,000 + 4 = ___