## Envision Math Accelerated Grade 7 Volume 1 Chapter 5 Generate Equivalent Expressions

**Question. Explain whether sorting the tiles with positive coefficients together and tiles with negative coefficients.**

We need to explain whether sorting the tiles with positive coefficients together and tiles with negative coefficients.

Together help to simplify an expression that involves all the tiles.

The way of sorting the tiles with positive coefficients together and tiles with negative coefficients together will not help much.

Since we only add all the numbers alone and subtract the rest from them.

The main problem here exists with the numbers with variables.

We couldn’t able to do any arithmetic operations on them.

So, this won’t help much.

Sorting the tiles with positive coefficients together and tiles with negative coefficients together help to simplify an expression. That involves all the tiles wouldn’t help much.

**Question. Explain how the properties of operations are used to simplify expressions.**

We need to explain how the properties of operations are used to simplify expressions.

Simplification is the process of rewriting the given expression into its most compact form.

To simplify expressions, we can use the properties of operations such as distributive, commutative, and associative properties.

These properties will help in simplifying the terms by grouping them together.

Also, it combines like terms to get the simplified form.

The properties of operations are used to simplify expressions by grouping and combining the like terms together.

**Question. Simplify the expression -6 – 6f + 7 – 3f – 9.**

We need to simplify the expression − 6 − 6f + 7 − 3f − 9

The given expression is −6−6f +7 − 3f − 9

**Simplifying it we get**

−6−6f + 7 − 3f − 9 = − 6f − 3f − 6 + 7 − 9

= −9f + 1 − 9

= − 9f − 8

The simplified expression is −9f − 8

Simplification is the process of rewriting the given expression into its most compact form.

To simplify expressions, we can use the properties of operations such as distributive, commutative, and associative properties.

These properties will help in simplifying the terms by grouping them together.

Also, it combines like terms to get the simplified form.

We can sort the expressions into two groups.

One having the numbers alone.

The other having both the numbers and variables in it.

We can group each group separately and then do arithmetic operations to simplify it.

We will decide in what way to reorder the terms of an expression. When simplifying it is by looking at the variables and constants and grouping them separately to simplify it.

**Question. Explain how the properties of operations are used to simplify expressions.**

We need to explain how the properties of operations are used to simplify expressions.

Simplification is the process of rewriting the given expression into its most compact form.

To simplify expressions, we can use the properties of operations such as distributive, commutative, and associative properties.

These properties will help in simplifying the terms by grouping them together.

Also, it combines like terms to get the simplified form

The properties of operations are used to simplify expressions by grouping and combining the like terms together.

**Question. Explain why constant terms expressed as different rational number types can be combined.**

We need to explain why constant terms expressed as different rational number types can be combined.

The constant terms expressed as different rational number types can be combined because can be grouped together since they are all like terms.

The constant terms don’t have a variable in them.

So it can be grouped. It can be simplified, grouped, and combined no matter what since they are all like terms.

Constant terms expressed as different rational number types can be combined because they are all like terms.

**Question. Explain how you know when an expression is in its simplest form.**

We need to explain how you know when an expression is in its simplest form.

The expression is in its simplest form when it cannot be simplified further.

We cannot combine or group any further terms if they are simplified.

We cannot use any properties to simplify it further when they are simplified.

An expression is in its simplest form when we cannot group or combine them further.

**Question. Simplify the expression -4b + (-9k) – 6 – 3b + 12.**

We need to simplify the expression −4b + ( −9k)−6 − 3b + 12.

The given expression is −4b + (−9k) −6 −3b + 12

**Simplifying it we get**

−4b + (−9k) − 6 − 3b + 12 = −4b − 9k − 6 − 3b + 12

= −4b − 3b − 9k − 6 + 12

= −7b − 9k + 6

The simplified expression is −7b − 9k + 6

**Question. Simplify the expression -2 + 6.45z – 6 + (-3.25z).**

We need to simplify the expression −2 + 6.45z − 6 + ( −3.25z)

The given expression is −2 + 6.45z − 6 + (−3.25z)

**Simplifying it we get**

−2 + 6.45z − 6 + (−3.25z) =−2 − 6 + 6.45z − 3.25z

= −8 + 3.20z

= 3.2z − 8

The simplified expression is 3.2z − 8

**Question. Simplify the expression **-9 + (\(\frac{-1}{3}y\)) + 6-\(\frac{4}{3}y\).

We need to simplify the expression

− 9 + (\(\frac {-1}{3}y\)) + 6−\(\frac {4}{3}y\)

The given expression is − 9 + (\(\frac {-1}{3}y\)) + 6 −\(\frac {4}{3}y\)

**Simplifying it, we get**

− 9 + (\(\frac{−1}{3}y\))+6−\(\frac{4}{3}y\)

= − 9 + 6 − \(\frac{1}{3}y\) − \(\frac{4}{3}y\)

= −3 + (\(\frac{ −y −4y}{3}\))

= −3 −\(\frac{5}{3}y\)

The simplified expression is − 3 −\(\frac {5}{3}y\)

**Question. Simplify the expression -2.8f + 0.9f – 12 – 4.**

We need to simplify the expression − 2.8f + 0.9f − 12 − 4

The given expression is − 2.8f + 0.9f − 12 − 4

**Simplifying it, we get**

− 2.8f + 0.9f − 12 − 4 = f(−2.8 + 0.9) − 16

= f( −1.9) −16

= −1.9f − 16

The simplified expression is −1.9f − 16

**Question. Simplify the expression 3.2 – 5.1n – 3n + 5.**

We need to simplify the expression 3.2 − 5.1n − 3n + 5

The given expression is 3.2 − 5.1n − 3n + 5

**Simplifying it we get**

3.2 − 5.1n − 3n + 5

= 3.2 + 5 − 5.1n − 3n

= 8.2 − 8.1n

The simplified expression is 8.2 − 8.1n

**Question. Simplify the given expression 2n + 5.5 – 0.9n – 8 + 4.5p.**

We need to simplify the given expression.

The given expression is 2n + 5.5 − 0.9n − 8 + 4.5p

**Combining the like terms together, we get
**

2n + 5.5 − 0.9n − 8 + 4.5p

= 2n − 0.9n + 5.5 − 8 + 4.5p

= n(2 − 0.9) − 2.5 + 4.5p

= 1.1n + 4.5p − 2.5

The simplified expression is 1.1n + 4.5p − 2.5

**Question. Simplify the given expression **12 + (-4)\(-\frac{2}{5}j-\frac{4}{5}j\) + 5.

We need to simplify the given expression.

12 + (−4)\(−\frac{2}{5} j−\frac{4}{5} j\) + 5

**Using the properties and combining the like terms together, we get**

12 + (−4)\(-\frac{2}{5} j-\frac{4}{5} j\) + 5

= 12− 4\(-\frac{2}{5} j−\frac{4}{5} j\) + 5

= 8 + j(\(-\frac{2}{5} −\frac{4}{5} \)) + 5

= 13 + j(\(\frac{−2−4}{5}\))

= 13 + j\(\frac{−6}{5}\)

= 13− j\(\frac{6}{5}\)

The simplified expression is 13−\(\frac{6}{5} j\)

**Question. Simplify the given expression -5v + (-2) + 1 + (-2v) and to find which among the given expression is equal to it.**

We need to simplify the given expression − 5v + ( −2) + 1 + (−2v) and to find which among the given expression is equal to it

**Simplifying it, we get**

−5v + (−2) + 1 + ( −2v) = −5v − 2 + 1 − 2v

= −5v − 2v − 2 + 1

= −7v − 1

The given expression is equal to (C) −7v − 1

**Question. Find which expression is equivalent to **\(\frac{2}{3}x+(-3)+(-2)-\frac{1}{3}x\).

We need to find which expression is equivalent to \(\frac{2}{3}x+(-3)+(-2)-\frac{1}{3}x\)

**Simplifying it, we get**

\(\frac{2}{3}\)x +(−3)+(−2)−\(\frac{1}{3}\)x

= \(\frac{2}{3}\)x −3−2−\(\frac{1}{3}\)x

= \(\frac{2}{3}\)x − \(\frac{1}{3}\)x −5

= \(\frac{2x −x}{3}\) − 5

= \(\frac{x}{3}\) − 5

= (or) \(\frac{1}{3}x\) − 5

The given expression is equivalent to \(\frac{1}{3}x\) − 5

**Question. The dimensions of a garden are shown. We need to write an expression to find the perimeter.**

The dimensions of a garden are shown. We need to write an expression to find the perimeter.

Add all the lengths to find the perimeter.

The perimeter of the rectangle is 2(l+w)

**Here, substituting the given we get**

2(1+w) = 2(\(\frac{1}{2}x\) −7+x)

= 2(\(\frac{1}{2}x\) +x−7)

= 2 (\(\frac{x+2x}{2}−7\))

= 2(\(\frac{3x}{2}\)−7)

= 3x−14

The expression to find the perimeter is 3x−14

**Question. Simplify the given expression 8h + (-7.3d) – 14 + 5d – 3.2h**

We need to simplify the given expression.

The given expression is 8h +(−7.3d) −14 + 5d − 3.2h

**Combining the like terms together, we get**

8h + (−7.3d) − 14 + 5d − 3.2h

= 8h −7.3d −14 + 5d − 3.2h

= 8h − 3.2h − 7.3d + 5d − 14

= 4.8h − 2.3d − 14

The simplified expression is 4.8h − 2.3d − 14

**Question. Simplify the given expression 4 – 2y + (-8y) + 6.2.**

We need to simplify the given expression.

The given expression is 4 − 2y + (−8y) + 6.2

**Combining the like terms together, we get**

4−2y + (−8y) + 6.2 = 4 − 2y − 8y + 6.2

= 4 − 10y + 6.2

= 4 + 6.2 − 10y

= 10.2 − 10y

The simplified expression is 10.2 − 10y

**Question. Simplify the given expression **\(\frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8\).

We need to simplify the given expression.

The given expression is \(\frac{4}{9} z-\frac{3}{9} z+5-\frac{5}{9} z-8\)

**Combining the like terms together, we get**

\(\frac{4}{9}z\)−\(\frac{3}{9}z\) + 5 −\(\frac{5}{9}z\) − 8

= \(\frac{4z−3z}{9}\)+5−\(\frac{5}{9}z\) − 8

= \(\frac{z}{9}\)−\(\frac{5z}{9}\) + 5 − 8

= \(\frac{−4}{9}z\) − 3

The simplified expression is \(\frac{− 4z}{9} − 3\)

**Question. Show that the given two expressions 11t – 4t is equivalent to 4t – 11t.**

We need to explain whether 11t − 4t is equivalent to 4t −11t.

We need to support our answer by evaluating the expression for t = 2.

The expression 11t − 4t is not equivalent to 4t −11t.

**Substitute t = 2 in both cases, we get
**

11t −4t = 7t

= 7 × 2 = 14

4t−11t = − 7t

= − 7 × 2 = −14

Thus, the value differs.

The given two expressions are not equivalent to each other.

**Question. Observe the diagram the signs show the costs of different games at a math festival. Find how much would it cost n people to play Decimal Decisions and Ratio Rage.**

Given that the signs show the costs of different games at a math festival.

We need to find how much would it cost n people to play Decimal Decisions and Ratio Rage.

The cost of playing Decimal decisions will be

12.70 − n + 9

The cost of Ratio Race will be

\(\frac{n}{4}\)The total cost will be

12.70 − n + 9 + \(\frac{n}{4}\)

= 12.7 − n + \(\frac{n}{4}\) + 9

= 12.7 + 9 + \(\frac{−4n+n}{4}\)

= 21.7 − \(\frac{3n}{4}\)

The cost to play Decimal Decisions-and Ratio Rage will be 21.7−\(\frac{3n}{4}\)