Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 5 Practice 3 Simplifying Algebraic Expressions to finish your assignments.

## Math in Focus Grade 5 Chapter 5 Practice 3 Answer Key Simplifying Algebraic Expressions

**Simplify each expression.**

Example

c + c + c + c = 4c

Question 1.

6p + 3 p =

Answer:

6p + 3 p = **9p**

Explanation:

The given expression is 6p + 3p. Add 6p with 3p the sum is 9p.

Question 2.

b + 3 b + 5b =

Answer:

**b + 3b + 5b = 9b**

Explanation:

The given expression is b + 3b + 5b. Add b with 3b and 5b the sum is 9b.

Question 3.

10k – 3k =

Answer:

**10k – 3k = 7k**

Explanation:

The given expression is 10k – 3k. Subtract 3k from 10k the difference is 7k.

Question 4.

12p – 12p =

Answer:

**12p – 12p = 0**

Explanation:

The given expression is 12p – 12p. Subtract 12p from 12p the difference is 0.

Question 5.

6p – 2p – 3p =

Answer:

**6p – 2p – 3p = 6p – 5p = 1p**

Explanation:

The given expression is 6p – 2p – 3p. First add 2p and 3p the sum is 5p. Subtract 5p from 6p the difference is 1p.

Question 6.

10a – a + 2a =

Answer:

**10a – a + 2a = 9a + 2a = 11a**

Explanation:

The given expression is 10a – a + 2a. First subtract a from 10a the difference is 9a. Now add 9a with 2a the sum is 11a.

Question 7.

4c + c – 5c =

Answer:

**4c + c – 5c = 5c – 5c = 0**

Explanation:

The given expression is 4c + c – 5c. First add 4c with c the sum is 5c. Subtract 5c from 5c the difference is 0.

Question 8.

10f – 4f + f =

Answer:

**10f – 4f + f = 6f + f = 7f**

Explanation:

The given expression is 10f – 4f + f. First subtract 4f from 10f the difference is 6f. Add 6f with f the sum is 7f.

**Simplify each expression.**

Example

5x + 2x + 4 = 7x + 4

Question 9.

x + 5x – 9 =

Answer:

x + 5x – 9 = **6x – 9**

Explanation:

The given expression is x + 5x – 9. Add x with 5x the sum is 6x. The simplified expression is 6x – 9.

Question 10.

2m + 4 + 6m =

Answer:

2m + 4 + 6m = **8m + 4**

Explanation:

The given expression is 2m + 4 + 6m. Add 2m with 6m the sum is 8m. The simplified expression is 8m + 4.

Question 11.

10p – 4p – 5 =

Answer:

10p – 4p – 5 = **6p – 5**

Explanation:

The given expression is 10p – 4p – 5. Subtract 4p from 10p the difference is 6p. The simplified expression is 6p – 5.

Question 12.

4 + 5k – 4k =

Answer:

4 + 5k – 4k =** 4 + k**

Explanation:

The given expression is 4 + 5k – 4k . Subtract 4k from 5k the difference is k. The simplified expression is 4 + k.

Question 13.

2 + 6b – 1 + 4b =

Answer:

2 + 6b – 1 + 4b = **1 +10b**

Explanation:

The given expression is 2 + 6b – 1 + 4b. Subtract 1 from 2 the difference is 1. Add 6b with 4b the sum is 10b. The simplified expression is 1 + 10b.

Question 14.

5c + 3 – 2c + 5 =

Answer:

5c + 3 – 2c + 5 = **3c + 8**

Explanation:

The given expression is 5c + 3 – 2c + 5. Subtract 2c from 5c the difference is 3c. Add 3 with 5 the sum is 8. The simplified expression is 3c + 8.

Question 15.

9e – 2e + 3 + 5e =

Answer:

9e – 2e + 3 + 5e = 7e + 5e + 3 = **12e + 3**

Explanation:

The given expression is 9e – 2e + 3 + 5e. Subtract 2e from 9e the difference is 7e. Add 7e with 5e the sum is 12e. The simplified expression is 12e + 3.

Question 16.

6h + 12 + 2h – 6 =

Answer:

6h + 12 + 2h – 6 = **8h + 6**

Explanation:

The given expression is 6h + 12 + 2h – 6. Subtract 6 from 12 the difference is 6. Add 6h with 2h the sum is 8h. The simplified expression is 8h + 6.

**Write an algebraic expression for each situation.**

Question 17.

The length of a piece of fabric is 8y yards. London cuts 7 yards from it to make some cushion covers. He then cuts another 3y yards to make a curtain. The remaining material is cut into 4 equal pieces. How long is each piece?

Answer:

The length of a piece of fabric is 8y yards. London cuts 7 yards from it to make some cushion covers.

(8y – 7) yards

He then cuts another 3y yards to make a curtain.

(8y – 7 – 3y) yards

The remaining material is cut into 4 equal pieces.

(8y – 7 – 3y)/4 yards

**(5y – 7)/4 yards**

Question 18.

Ling has 4m pounds of flour. She buys another 2 packages of flour, each weighing m pounds. How much flour does Ling have now in terms of m?

Answer:

The algebraic expression is** 4m + 2m = 6m**.

Explanation:

Ling has 4m pounds of flour. She buys another 2 packages of flour, each weighing m pounds. The 2 packages of flour is represented as 2m. Add 4m with 2m the sum is 6m. Ling have 6m pounds of flour.

Question 19.

On Monday, Linus made 5k paper cranes and gave 2k paper cranes to his friends. On Tuesday, he made another 4k paper ‘ cranes. His friend gave him 5 paper cranes. How many paper cranes does he have now in terms of k?

Answer:

On Monday, Linus made 5k paper cranes and gave 2k paper cranes to his friends.

5k – 2k = **3k**

On Tuesday, he made another 4k paper ‘ cranes. His friend gave him 5 paper cranes.

4k + 5k = **9k**

**3k + 9k = 12k**

Now, he have 12k paper cranes.

Question 20.

At the market, a pear costs b cents and an apple costs 7 cents less than a pear. Randy buys 4 pears and an apple. How much does Randy pay in terms of b?

Answer:

The cost of pears is **b cents**.

The cost of an apple is 7 cents less than a pear =** b – 7**

Randy buys 4 pears and an apple.

4b + b – 7 = **5b – 7**

At the market, Randy pays 5b -7.