Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Lesson 7.3 Simplifying Algebraic Expressions to score better marks in the exam.

## Math in Focus Grade 6 Course 1 A Chapter 7 Lesson 7.3 Answer Key Simplifying Algebraic Expressions

### Math in Focus Grade 6 Chapter 7 Lesson 7.3 Guided Practice Answer Key

**Simplify each expression. Then state the coefficient of the variable In the expression.**

Question 1.

x + x + x + x + x

Answer:

5x

Explanation:

x is the variable or constant,

add all the variables, we get 5x.

So, 5 is the coefficient of the variable x.

Question 2.

y + y + 6

Answer:

2y + 6

Explanation:

y is the variable, add all the variables

y + y + 6

2y + 6

So, 25 is the coefficient of the variable y

Question 3.

m + m + m + 5 + 4

Answer:

3m + 9

Explanation:

3 is the coefficient of the variable m,

add of the variables.

m + m + m + 5 + 4

3m+9

Question 4.

n + n + n + n + n + n + 12 – 8

Answer:

6n + 4

Explanation:

n is the variable, add all the variables at first.

n + n + n + n + n + n + 12 – 8

6n + 4

6 is the coefficient of the variable 2

**Solve.**

Question 5.

A square has sides of length x centimeters. Find the perimeter of the square in terms of x.

The perimeter of the square is centimeters.

Answer:

4x

Explanation:

x + x + x + x = 4x

The perimeter of the square is 4x centimeters.

Question 6.

The figure shows a trapezoid. The length of each side is given as shown. Find the perimeter of the trapezoid in terms of w.

10cm

The perimeter of the trapezoid is centimeters.

Answer:

3w + 10 cm

Explanation:

The perimeter of the trapezoid is 3w + 10 centimeters.

**Hands-On Activity**

Materials:

- paper
- ruler
- scissors

RECOGNIZE SIMPLIFIED EXPRESSIONS ARE EQ UIVALENT)

Work in pairs.

STEP 1: Make the following set of paper strips.

Let the length of the shortest strip be m units. Make and label 5 such strips.

Make and label 4 more strips of lengths 2m units, 3m units, 4m units, and 5m units.

STEP 2: Take one of the longer strips and place it horizontally.

STEP 3: Ask your partner to use the pieces of the shortest strips to match the length of the chosen strip in STEP 2.

Example

STEP 4: Write an algebraic expression to describe the number of short strips used, and simplify it. For example in STEP 3, write m + m + m = 3m.

STEP 5: Repeat the activity with other lengths of strips.

Activity 1:

m + m + m + m = 4m

Activity 2:

m + m + m + m + m = 5m

**Math Journal** How do the lengths of the strips show that the expressions are equivalent?

Answer:

We use the fraction strips to show differences between different fractions.

Explanation:

For example;

We start with halves and quarters.

Ask each student to pull out a 1/2 foot strip.

Now ask them to clear their desks of everything but the 1/4 pieces and the one 1/2 strip.

Then ask them to put down enough quarter pieces to make the same length as the half piece.

We can show the lengths of the strips are equivalent with expressions.

**Complete.**

Question 7.

Simplify x + 8x.

x + 8x =

Answer:

9x

Explanation:

We use the fraction strips to show differences between different fractions.

**Simplify each expression.**

Question 8.

3r + 2r

Answer: 5r

Explanation:

r is the variable in the given expression

3r + 2r

= r + r + r + r + r

= 5r

5 is the coefficient of the variable r.

Question 9.

5y + 6y

Answer:

11y

Explanation:

y is the variable in the given expression.

y + y + y + y + y + y +y + y + y + y + y = 11y

11 is the coefficient of the variable y.

**State whether each pair of expressions are equivalent.**

Question 10.

3a and a + a + a

Answer:

YES, pair of expressions are equivalent.

Explanation:

3a can be expanded as a + a + a = 3a

a + a + a = 3a

So, the given statement is correct.

Question 11.

2h + 2h and 4h

Answer:

YES, pair of expressions are equivalent.

Explanation:

2h can be expanded as h + h

2h + 2h = 4h

h + h + h + h = 4h

Question 12.

2k + 5 and (k + k) • 5

Answer:

NO, pair of expressions are not equivalent.

Explanation:

2k + 5 and (k + k) • 5

2k + 5 is not equal to 2k.5

2k + 5 is not equal to 10k

Question 13.

6z + 4z and 10 + 2z

Answer:

NO, pair of expressions are notequivalent.

Explanation:

6z + 4z = 10z

10 + 2z is another expression

10z not equal to 10 + 2z

Question 14.

1p + 3p and 13p

Answer:

NO, pair of expressions are not equivalent.

Explanation:

1p + 3p = 4p

4p is not equal to 13p

Question 15.

3n + 2 + 4n and 2 + 7n

Answer:

YES, pair of expressions are equivalent.

Explanation:

both are equal

3n + 2 + 4n

= 3n + 4n + 2

= 7n + 2

**Complete**

Question 16.

Simplify 4s – s

4s – s =

Answer:

3s

Explanation:

We use the fraction strips to show differences between different fractions.

**Simplify each expression.**

Question 17.

12z – 7z

Answer:

5z

Explanation:

Subtract 12 from 7

12z – 7z = 5z

Question 18.

3p – 3p

Answer:

0

Explanation:

Subtracting 3p from 39 we get 0

3p – 3p = 0

**State whether each pair of expressions are equivalent.**

Question 19.

f – 6 and 6 – f

Answer:

NO, pair of expressions are not equivalent.

Explanation:

f- 6 is positive if f > 6

6-f is negative for the above f value.

Question 20.

5c – 5c and a – a

Answer:

YES, pair of expressions are equivalent.

Explanation:

5c – 5c = 0

a – a = 0

both are correct.

**Simplify each expression.**

Question 21.

(j + 3j) + 2j = + 2j

=

Answer:

6j

Explanation:

(j + 3j) + 2j

= 4j + 2j

= 6j

Question 22.

4j + 5j + 2j

Answer:

11j

Explanation:

4j + 5j + 2j

= 9j + 2j

= 11j

Question 23.

9t – 3t – 4t

Answer:

2t

Explanation:

9t – 3t – 4t

= 6t – 4t

= 2t

Question 24.

5t – t – 4t

Answer:

0

Explanation:

5t – t – 4t

= 4t – 4t = 0

Question 25.

8w – 6w + 3w

Answer:

5w

Explanation:

8w – 6w + 3w

= 2w + 3w

= 5w

Question 26.

7w + 2w – 6w

Answer:

3w

Explanation:

7w + 2w – 6w

= 9w – 6w = 3w

**Complete.**

Question 27.

The figure shows a quadrilateral. Find the perimeter of the quadrilateral.

6x + 6 + 2x + 2 = 6x + 2x + 6 + 2

= +

The perimeter of the quadrilateral is units.

Answer:

8x + 8 units

Explanation:

6x + 6 + 2x + 2

= 6x + 2x + 6 + 2

= 8x + 8 units

The perimeter of the quadrilateral is 8x + 8 units.

**Simplify each expression.**

Question 28.

4x – 3 + 3x

Answer:

7x – 3

Explanation:

4x – 3 + 3x

= 4x + 3x – 3

= 7x – 3

Question 29.

5y + 4 = 2y

Answer:

3y + 4 =0

Explanation:

5y + 4 = 2y

5y – 2y + 4

3y + 4 = 0

Question 30.

8y – 7 – 4y

Answer:

4y – 7

Explanation:

8y – 7 – 4y

subtract the variables first,

= 4y – 7

Question 31.

7z + 9 – 2z – 2

Answer:

5z + 7

Explanation:

7z + 9 – 2z – 2

Bring all the variables and coefficients to one side.

= 7z – 2z +9 – 2

= 5z + 7

Question 32.

5 + 11 z – 4 + 6z

Answer:

1 + 17z

Explanation:

5 + 11 z – 4 + 6z

Bring all the variables and coefficients to one side.

= 5 – 4 + 11 z + 6z

= 1 + 17z

Question 33.

8g + 10 – 3g + 7

Answer:

5g + 17

Explanation:

8g + 10 – 3g + 7

Bring all the variables and coefficients to one side.

=8g – 3g + 10 + 7

=5g + 17

Question 34.

12 + 6g – 5 – 4g

Answer:

7 – 2g

Explanation:

12 + 6g – 5 – 4g

Bring all the variables and coefficients to one side.

=12 – 5 + 6g – 4g

=7 – 2g

Question 35.

27 + 3r – 9 + 15r

Answer:

18 +18r

Explanation:

27 + 3r – 9 + 15r

Bring all the variables and coefficients to one side.

=27 – 9 +3r + 15r

=18 +18r

### Math in Focus Course 1A Practice 7.3 Answer Key

**Simplify each expression. Then state the coefficient of the variable in each expression.**

Question 1.

u + u + u + u

Answer:

4u

Explanation:

Add all the variable to get the sum

u + u + u + u = 4u

Question 2.

v + v + 5 – 2

Answer:

2v + 3

Explanation:

v + v + 5 – 2

Add all the variable at first,

then subtract the coefficient.

Finally, write an algebraic expression.

= 2v + 5 – 2

= 2v + 3

Question 3.

w + w + w + w + w + w + 15 – 7

Answer:

6w + 8

Explanation:

Add all the variable at first,

then subtract the coefficient.

Finally, write an algebraic expression.

w + w + w + w + w + w + 15 – 7

= 6w + 15 – 7

= 6w + 8

**Simplify each expression.**

Question 4.

3p + p

Answer:

4p

Explanation:

3p + p

Expand the variables at first, then add.

= p + p + p + p

= 4p

Question 5.

4p + 5p

Answer:

9p

Explanation:

4p + 5p

Expand the variables at first, then add.

p + p + p + p + p + p + p + p + p

= 9p

Question 6.

7p – 2p

Answer:

5p

Explanation:

7p -2 p

Expand the variables at first, then subtract.

= (p + p + p + p + p + p + p) – (p + p)

= 5p

Question 7.

3p – 2p + 5p

Answer:

6p

Explanation:

3p – 2p + 5p

3p – 2p = 1p

1p + 5p = 6p

Question 8.

2p + 3p + 4p + 5p – 6p – 7p

Answer:

p

Explanation:

2p + 3p + 4p + 5p – 6p – 7p

14p – 13p = p

**State whether each pair of expressions are equivalent.**

Question 9.

5x and x + x + 3x

Answer:

YES, pair of expressions are equivalent.

Explanation:

x + x + 3x = 5x

So, 5x and x + x + 3x are equivalent.

Question 10.

4y + 2y + y and 5y + y

Answer:

NO, pair of expressions are not equivalent.

Explanation:

4y + 2y + y and 5y + y

4y+2y+y = 7y

5y+y=6y

7y is not equal to 6y

Question 11.

2z + 5 and z + 8 + z – 3

Answer:

YES, pair of expressions are equivalent.

Explanation:

2z + 5 and z + 8 + z – 3

2z + 5

z + 8 + z – 3 = 2z+5

both are equal

Question 12.

2w – 5 and 5 – 2w

Answer:

No, pair of expressions are not equivalent.

Explanation:

2w – 5 and 5 – 2w

2w – 5, here coefficient is negative and variable is positive.

-2w + 5, here coefficient is positive and variable is negative.

Question 13.

11u – 4u and 11 – 4 + u

Answer:

No, pair of expressions are not equivalent.

Explanation:

11u – 4u and 11 – 4 + u

11u – 4u = 7u

11 – 4 + 4 = 7 + u

7 + u is not 7u

Question 14.

3v + v and \(\frac{12v}{3}\)

Answer:

Yes, pair of expressions are equivalent.

Explanation:

3v + v and \(\frac{12v}{3}\)

3v + v = 4v

\(\frac{12v}{3}\) = 4v

4v is equal \(\frac{12v}{3}\)

**Simplify each expression.**

Question 15.

3x + 5 + 4x + 6

Answer:

7x + 11

Explanation:

3x + 5 + 4x + 6

Add all the variables and coefficients.

= 3x + 4x + 5 + 6

= 7x + 11

Question 16.

3x + 2x + 3x + 2

Answer:

8x + 2

Explanation:

3x + 2x + 3x + 2

Add all the variables at first,

= 8x + 2

Question 17.

17 + 4w – 12 – w

Answer:

5 + 3w

Explanation:

17 + 4w – 12 – w

= 17 -12 + 4w – w

= 5 + 3w

Question 18.

9 + 5u + 6u – 7 – 8u + 4

Answer:

6 + 3u

Explanation:

9 + 5u + 6u – 7 – 8u + 4

= 9 – 7 + 4 + 5u + 6u – 8u

= 6 + 3u

**Solve.**

Question 19.

A book has a length of (b + 2) inches and a width of b inches. Write a simplified expression for the perimeter of the book.

Answer:

4b + 4 inches

Explanation:

A book has a length of (b + 2) inches and a width of b inches.

Perimeter = 2(length + width)

= b + 2 + b + b + 2 + b

Add all the variables and coefficients to write an equation.

= 4b + 4 inches is the perimeter of the book.

Question 20.

The figure shows a quadrilateral. The length of each side is given as shown. Find the perimeter of the quadrilateral in terms of z.

Answer:

3z + 15 cm

Explanation:

The length of each side is given as shown.

The perimeter of the quadrilateral in terms of z.

p = z + 8 + z + 3 + z + 4

= 3z + 15 cm

Question 21.

Anne is currently h years old. Bill is currently 2h years old and Charles is currently 8 years old. Find an expression for each person’s age after h years. Then find an expression for the sum of their ages after h years.

Answer:

8 + h years

Explanation:

Anne h years

Bill is 2h years

Charles is 8 years

an expression for each person’s age after h years

Anne h + h = 2h years

Bill is 2h + h = 3h years

Charles is 8 + h years

Question 22.

There are 18 boys in a class. There are w fewer boys than girls. How many students are there in the class?

Answer:

36 – w

Explanation:

Boys = 18

Girls = 18 – w

Total number of students = 18 + 18 – w

= 36 – w

Question 23.

A rectangular garden has a length of (y + 2) yards and a width of (4y – 1) yards. Find the perimeter of the garden in terms of y.

Answer:

10y + 2

Explanation:

A rectangular garden has a length of (y + 2) yards and a width of (4y – 1) yards.

The perimeter of the garden in terms of y.

p = y + 2 + 4y – 1 + y + 2 + 4y – 1

p = 10y + 2

the perimeter of the garden in terms of y is = 10y + 2

Question 24.

Kayla had 64b dollars. She gave \(\frac{1}{8}\) of it to Luke and spent $45. How much money did Kayla have left? Express your answer in terms of b.

Answer:

\(\frac{520b -360} {8}\)

Explanation:

Kayla had 64b dollars.

She gave \(\frac{1}{8}\) of it to Luke and spent $45.

64b- \(\frac{1}{8}\) -45

= \(\frac{64b x 8 + 8b -45 x 8} {8}\)

= \(\frac{520b – 360} {8}\)

Question 25.

A rectangle has a length of (2m + 1) units and a width of (10 – m) units. A square has sides of length \(\frac{2 m+1}{2}\) units.

a) Find the perimeter of the rectangle.

Answer:

2m + 22

Explanation:

length of (2m + 1) units and a width of (10 – m) units

the perimeter of the rectangle is

= 2m + 1 + 10 – m + 2m + 1 + 10 – m

= 2m + 22

b) Find the perimeter of the square.

Answer:

4 x \(\frac{2 m+1}{2}\) units

Explanation:

length \(\frac{2 m+1}{2}\) units

Perimeter of a square =4 x \(\frac{2 m+1}{2}\) units

c) Find the sum of the perimeters of the two figures if m = 6.

Answer:

26 units

Explanation:

the perimeters of the two figures if m = 6

Perimeter of a square = 4 x \(\frac{2 m+1}{2}\) units

= 4 x \(\frac{2 x 6+1}{2}\) units

= 4 x \(\frac{13}{2}\) units

= 26 units

the perimeter of the rectangle is = 2m + 22 units

=2 x 9 + 22

= 18 + 22

= 40 units

d) If m – 6, the perimeter of the rectangle is greater than the perimeter of the square. Find how many units greater the rectangle’s perimeter is than the square’s perimeter.

Answer:

40 units

Explanation:

the perimeters of the two figures if m = 6

Perimeter of a square = 26 units

the perimeter of the rectangle is = 40 units

Question 26.

**Math Journal** Rita simplified the expression 10w – 5w + 2w in this way:

Is Rita’s answer correct? If not, explain why it is incorrect.

Answer:

Is Rita’s answer Wrong

Explanation:

In the above math journal of Rita,

she wrote the express as -5w + 2w = – 7

where as the correct express is 10w – 5w = 5w

5w + 2w = 7w