Spectrum Math Grade 6 Chapter 5 Lesson 4 Answer Key Equivalent Expressions (2024)

Go through the Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.4 Equivalent Expressionsand get the proper assistance needed during your homework.

Spectrum Math Grade 6 Chapter 5 Lesson 5.4 Equivalent Expressions Answers Key

Equivalent expressions are created by simplifying values and combining terms.
4(6x – 5) = 24x – 20 Multiply each value by 4 to create an equivalent expression.
3(4³ + 7x) = 3(64 + 7x) First, calculate the value of the exponents.
3(64 + 7x) = 192 + 21x Then, use the distributive property to create the equivalent expression.
t + t + t = 3t Use multiplication in place of repeated addition.

Create expressions equivalent to the ones below.

Question 1.
7(4z + 8b) ____________
Answer:
Given term is 7(4z + 8b)
Multiply the every given term with 7 as shown below
= 7x 4z + 1 x 8b
= 28z + 8b
Hence the Equivalent Expression for 7(4z + 8b) is 28z + 8b.

Question 2.
8(2x + 3²) ____________
Answer:
Given term is 8(2x + 3²)
1. First calculate the Exponent value of 3² = 9
= 8(2x + 9)
2. Multiply the every given term with 8 as shown below
= 8(2x)+ 8(9)
= 16x + 72
Hence the Equivalent Expression for 8(2x + 3²) is 16x + 72.

Question 3.
4(r + r + r + r) ____________
Answer:
Given term is 4(r + r + r + r)
Multiply the every given term with 4 as shown below
= 4r + 4r + 4r + 4r
= 16r
Hence the Equivalent Expression for 4(r + r + r + r) is 16r.

Question 4.
9(3 + 8x) ____________
Answer:
Given term is 9(3 + 8x)
Multiply the every given term with 9 as shown below
= 9(3) + 9(8x)
= 27 + 72x
Hence the Equivalent Expression for 9(3 + 8x) is27 + 72x.

Question 5.
4²(3 + 6t) ________
Answer:
Given term is 8(2x + 3²)
1. First calculate the Exponent value of 4² = 16
= 16(3 + 6t)
2. Multiply the every given term with 16 as shown below
= 16 x 3+ 16 x 16t
= 48 + 256t
Hence the Equivalent Expression for 4²(3 + 6t) is 48 + 256t.

Question 6.
\(\frac{t+t+t}{4}\) ____________
Answer:
Given term \(\frac{t+t+t}{4}\)
Add the given 3 literals then the result obtained is 3t
Then , substitute the 3t i.e. \(\frac{3t}{4}\).
Therefore the \(\frac{t+t+t}{4}\) value is \(\frac{3t}{4}\).

Question 7.
2(4s³ + 2) ________
Answer:
Given term is 2(4s³ + 2)
Multiply the every given term with 16 as shown below
= 2 x 4s³ + 2 x 2
= 8s³ + 4
Hence the Equivalent Expression for 2(4s³ + 2) is 8s³ + 4.

Question 8.
30(3x + 4) ____________
Answer:
Given term is 30(3x + 4)
Multiply the every given term with 30 as shown below
= (30).(3x) +(30).(4)
= 90x + 120
Hence the Equivalent Expression for 30(3x + 4) is 90x + 120.

Question 9.
6(5a + 9b) ________
Answer:
Given term is 6(5a + 9b)
Multiply the every given term with 6 as shown below
= 6 x 5a +6 x 9b
= 30a + 54b
Hence the Equivalent Expression for 6(5a + 9b) is 30a + 54b.

Question 10.
9(3x + 5⁴) ________
Answer:
Given term is 9(3x + 5⁴)
1. First calculate the Exponent value of 5⁴ = 625
= 9(3x +625)
2. Multiply the every given term with 6 as shown below
= (9).(3x) + 9.(625)
= 27x + 5625
Hence the Equivalent Expression for 9(3x + 5⁴) is 27x + 5625.

Question 11.
7(c + c + c) ________
Answer:
Given term is 7(c + c + c)
Multiply the every given term with 7 as shown below
= 7c + 7c + 7c
= 21c
Hence the Equivalent Expression for 7(c + c + c) is 21c.

Question 12.
9(2 + 7f) _________________
Answer:
Given term is 9(2 + 7f)
Multiply the every given term with 9 as shown below
= (9. 2) + (9.7f)
= 18 + 63f
Hence the Equivalent Expression for 9(2 + 7f) is 18 + 63f.

Question 13.
7⁵(4g – 8d) ________
Answer:
Given term is 7⁵(4g – 8d)
1. First calculate the Exponent value of 7⁵ = 16807
2. Multiply the every given term with 16807 as shown below
= (16807).(4g) + 16807.(8d)
= 67228 g +134456d
Hence the Equivalent Expression for 7⁵(4g – 8d) is 67228 g +134456d.

Question 14.
\(\frac{e+e+e}{5}\) ____________
Answer:
Given term \(\frac{e+e+e}{5}\)
Add the given three e literals the result obtained is 3e
Then , substitute the 3e in \(\frac{e+e+e}{5}\)
Therefore the \(\frac{e+e+e}{5}\) value is \(\frac{3e}{5}\).

Question 15.
5(3z⁶ + 3) _____
Answer:
Given term is 5(3z⁶ + 3)
Multiply the every given term with 5 as shown below
= 5 x 3z⁶ + 5 x3.
= 15 z⁶+ 15
Hence the Equivalent Expression for 5(3z⁶ + 3) is15 z⁶+ 15.

Question 16.
10(y + 2) _________
Answer:
Given term is 10(y + 2)
Multiply the every given term with 10 as shown below
= (10).(y) + (10.2)
= 10y+ 20
Hence the Equivalent Expression for10(y + 2) is 10y+ 20.

Create expressions equivalent to the ones below.

Question 1.
4(a + b) _________________
Answer:
Given term is 4(a + b)
Multiply the every given term with 4 as shown below
= (4).(a) + (4.b)
= 4a+ 4b
Hence the Equivalent Expression for 4(a + b) is 4a+4.

Question 2.
3(9a + 8b) ____________
Answer:
Given term is 3(9a + 8b)
Multiply the every given term with 3 as shown below
= (3).(9a) + (3.8b)
= 27a+ 24b
Hence the Equivalent Expression for3(9a + 8b) is 27a+ 24b.

Question 3.
9(x + 2y) ____________
Answer:
Given term is 9(x + 2y)
Multiply the every given term with 9 as shown below
= (9).(x) + (9).(2y)
= 9x+ 2y
Hence the Equivalent Expression for9(x + 2y) is 9x+ 2y.

Question 4.
2(9x + 3²) ____________
Answer:
Given term is 2(9x + 3²)
1. First calculate the Exponent value of 3²= 9
Then 2(9x + 3²) = 2(9x+ 9)
2. Multiply the every given term with 2 as shown below
= (2).(9x) + 2.(9)
= 18x +18
Hence the Equivalent Expression for 2(9x + 3²)is18x +18.

Question 5.
5³(2 + 4c) ____________
Answer:
Given term is 5³(2 + 4c)
1. First calculate the Exponent value of 5³= 125
Then 5³(2 + 4c)= 125(2+ 4c)
2. Multiply the every given term with 125 as shown below
= (125).(2) + (125).(4c)
= 250 +500c
Hence the Equivalent Expression for 5³(2 + 4c) is 250 +500c.

Question 6.
\(\frac{x+x}{3}\) ____________
Answer:
Given term \(\frac{x+x}{3}\)
First Add the given two x literals the result obtained is 2x
Then, substitute the 2x in \(\frac{2x}{3}\)
Therefore the \(\frac{x+x}{3}\) value is \(\frac{2x}{3}\)

Question 7.
4²( 12 + 5c) _________
Answer:
Given term is 4²( 12 + 5c)
1. First calculate the Exponent value of 4²= 16
Then 4²( 12 + 5c) = 16(12+ 5c)
2. Multiply the every given term with 16 as shown below
= (16).(12) + (16).(5c)
= 192 + 80c
Hence the Equivalent Expression for 4²( 12 + 5c) is 192 + 80c.

Question 8.
17(14r + 3³) – 7r ________
Answer:
Given term is 17(14r + 3³) – 7r
1. First calculate the Exponent value of 3³= 27
Then 17(14r + 3³) – 7r = 17(14r + 27) – 7r
2. Multiply the every given term with 17 as shown below
= (17).(14r) + (17).(27) – 17r
= 238r + 459 – 17r
= 221r + 459
Hence the Equivalent Expression for 17(14r + 3³) – 7r is 221r + 459.

Question 9.
6(c – f) ____________
Answer:
Given term is 6(c – f)
Multiply the every given term with 6 as shown below
= (6).(c) + (6).(f)
= 6c -6f
Hence the Equivalent Expression for 6(c – f) is 6c -6f .

Question 10.
4(10b – 10c) _______________
Answer:
Given term is 4(10b – 10c)
Multiply the every given term with 4 as shown below
= (4).(10b) – (4).(10c)
= 40b – 40c
Hence the Equivalent Expression for 4(10b – 10c) is 40b – 40c .

Question 11.
8(g – 3d) _________
Answer:
Given term is 8(g – 3d)
Multiply the every given term with 8 as shown below
= (8).(g) + (8).(3d)
= 8g -24d
Hence the Equivalent Expression for 8(g – 3d) is 8g -24g.

Question 12.
3(7h + 4²) __________
Answer:
Given term is 3(7h + 4²)
1. First calculate the Exponent value of 4²= 16
Then 3(7h + 4²) = 3(7h + 16)
2. Multiply the every given term with 3 as shown below
= (3).(7h) + (3).(16)
= 21h + 48
Hence the Equivalent Expression for 3(7h + 4²) is 21h + 48.

Question 13.
4⁵(3 + 5t) ________
Answer:
Given term is 3(7h + 4²)
1. First calculate the Exponent value of 4⁵ = 1024
Then 4⁵(3 + 5t) = 1024
2. Multiply the every given term with 1024 as shown below
= ().(3) + ().(5t)
= 3072 + 5120t
Hence the Equivalent Expression for 4⁵(3 + 5t) is 3072 + 5120t.

Question 14.
\(\frac{d+d}{10}\) ____________
Answer:
Given term \(\frac{d+d}{10}\)
First Add the given two d literals which gives as 2d
Then substitute the 2d i.e. \(\frac{2d}{10}\)
\(\frac{d}{5}\)
Therefore the \(\frac{d+ d}{10}\) value is \(\frac{d}{5}\).

Question 15.
6⁴(25 + t) ________
Answer:
Given term is 6⁴(25 + t)
1. First calculate the Exponent value of 6⁴ = 1296
Then 6⁴(25 + t) = 1296(25 + t)
2. Multiply the every given term with 1296 as shown below
= (1296).(25) + (1296).(t)
= 32400 + 1296t
Hence the Equivalent Expression for 6⁴(25 + t) is 32400 + 1296t.

Question 16.
19(20f – w⁴) + 3f _______________
Answer:
Given term is 19(20f – w⁴) + 3f
Multiply the given term19(20f – w⁴) with 19 as shown below
= (19).(20f)- (19).(w⁴)+ 3f
= 380f – 19w⁴ + 3f
Hence the Equivalent Expression for19(20f – w⁴) + 3f is 380f – 19w⁴ + 3f.