Students can use the **Spectrum Math Grade 3 Answer Key Chapter 4 Posttest** as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 3 Chapter 4 Posttest Answers Key

Multiply.

Question 1.

a.

Answer:

Explanation:

Any number multiplied by 1 gives the same number itself, hence 1 × 5 = 5.

b.

Answer:

Explanation:

By mental computation,

As the number to be added is 9 and the integral number value is 9, so to find the value we need to add 9 for 9 times, 9 × 9 = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = 81, hence 9 × 9 = 81.

c.

Answer:

Explanation:

By mental computation,

As the number to be added is 3 and the integral number value is 2, so to find the value we need to add 3 for 2 times, 3 × 2 = 3 + 3 = 6, hence 3 × 2 = 6.

d.

Answer:

Explanation:

By mental computation,

As the number to be added is 5 and the integral number value is 4, so to find the value we need to add 5 for 4 times, 5 × 4 = 5 + 5 + 5 + 5 = 20, hence 3 × 2 = 6.

e.

Answer:

Explanation:

By mental computation,

As the number to be added is 6 and the integral number value is 3, so to find the value we need to add 6 for 3 times, 6 × 3 = 6 + 6 + 6 = 18, hence 6 × 3 = 18.

f.

Answer:

Explanation:

Any number multiplied by 0 gives the product as 0, hence 8 × 0 = 0.

Question 2.

a.

Answer:

Explanation:

By mental computation,

As the number to be added is 9 and the integral number value is 7, so to find the value we need to add 9 for 7 times, 9 × 7 = 9 + 9 + 9 + 9 + 9 + 9 + 9 = 63, hence 9 × 7 = 63.

b.

Answer:

Explanation:

By mental computation,

As the number to be added is 5 and the integral number value is 2, so to find the value we need to add 5 for 2 times, 5 × 2 = 5 + 5 = 10, hence 5 × 2 = 10.

c.

Answer:

Explanation:

Any number multiplied by 1 gives the same number itself, hence 6 × 1 = 6.

d.

Answer:

Explanation:

By mental computation,

As the number to be added is 8 and the integral number value is 2, so to find the value we need to add 8 for 2 times, 8 × 2 = 8 + 8 = 16, hence 8 × 2 = 16.

e.

Answer:

Explanation:

By mental computation,

As the number to be added is 5 and the integral number value is 7, so to find the value we need to add 5 for 7 times, 5 × 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35, hence 5 × 7 = 35.

f.

Answer:

Explanation:

By mental computation,

As the number to be added is 3 and the integral number value is 4, so to find the value we need to add 3 for 4 times, 3 × 4 = 3 + 3 + 3 + 3 = 12, hence 3 × 4 = 12.

Question 3.

a.

Answer:

Explanation:

By mental computation,

As the number to be added is 6 and the integral number value is 5, so to find the value we need to add 6 for 5 times, 6 × 5 = 6 + 6 + 6 + 6 + 6 = 30, hence 6 × 5 = 30.

b.

Answer:

Explanation:

By mental computation,

As the number to be added is 8 and the integral number value is 3, so to find the value we need to add 8 for 3 times, 8 × 3 = 8 + 8 + 8 = 24, hence 8 × 3 = 24.

c.

Answer:

Explanation:

By mental computation,

As the number to be added is 4 and the integral number value is 3, so to find the value we need to add 4 for 3 times, 4 × 3 = 4 + 4 + 4 = 12, hence 4 × 3 = 12.

d.

Answer:

Explanation:

Any number multiplied by 0 gives the product as 0, hence 0 × 8 = 0.

e.

Answer:

Explanation:

By mental computation,

As the number to be added is 6 and the integral number value is 2, so to find the value we need to add 6 for 2 times, 6 × 2 = 6 + 6 = 12, hence 6 × 2 = 12.

f.

Answer:

Explanation:

By mental computation,

As the number to be added is 4 and the integral number value is 7, so to find the value we need to add 4 for 7 times, 4 × 7 = 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28, hence 4 × 7 = 28.

Question 4.

a.

Answer:

Explanation:

Step 1: Multiply the integral value 2 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 2 × 0 = 0.

Step 2: Multiply the integral value 2 with the number in tens place, any number multiplied by 1 gives the same number itself, hence 2 × 1 = 2.

Therefore, 10 × 2 = 20.

b.

Answer:

Explanation:

Step 1: Multiply the integral value 4 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 4 × 0 = 0.

Step 2: Multiply the integral value 4 with the number in tens place,

By mental computation,

As the number to be added is 2 and the integral number value is 4, so to find the value we need to add 2 for 4 times, 2 × 4 = 2 + 2 + 2 + 2 = 8, hence 2 × 4 = 8.

Therefore, 20 × 4 = 80.

c.

Answer:

Explanation:

Step 1: Multiply the integral value 5 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 5 × 0 = 0.

Step 2: Multiply the integral value 5 with the number in tens place, any number multiplied by 1 gives the same number itself, hence 5 × 1 = 5.

Therefore, 10 × 5 = 50.

d.

Answer:

Explanation:

Any number multiplied by 1 gives the same number itself, hence 40 × 1 = 40.

e.

Answer:

Explanation:

Any number multiplied by 0 gives the product as 0, hence 10 × 0 = 0.

f.

Answer:

Explanation:

Any number multiplied by 0 gives the product as 0, hence 20 × 0 = 0.

Question 5.

a.

Answer:

Explanation:

Step 1: Multiply the integral value 2 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 2 × 0 = 0.

Step 2: Multiply the integral value 2 with the number in tens place,

By mental computation,

As the number to be added is 5 and the integral number value is 2, so to find the value we need to add 5 for 2 times, 5 × 2 = 5 + 5 = 10, hence 5 × 2 = 10.

Therefore, 50 × 2 = 100.

b.

Answer:

Explanation:

Step 1: Multiply the integral value 2 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 2 × 0 = 0.

Step 2: Multiply the integral value 2 with the number in tens place,

By mental computation,

As the number to be added is 4 and the integral number value is 2, so to find the value we need to add 4 for 2 times, 4 × 2 = 4 + 4 = 8, hence 4 × 2 = 8.

Therefore, 40 × 2 = 80.

c.

Answer:

Explanation:

Step 1: Multiply the integral value 3 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 3 × 0 = 0.

Step 2: Multiply the integral value 3 with the number in tens place, any number multiplied by 1 gives the same number itself, hence 3 × 1 = 3.

Therefore, 10 × 3 = 30.

d.

Answer:

Explanation:

Step 1: Multiply the integral value 2 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 2 × 0 = 0.

Step 2: Multiply the integral value 2 with the number in tens place,

By mental computation,

As the number to be added is 3 and the integral number value is 2, so to find the value we need to add 3 for 2 times, 3 × 2 = 3 + 3 = 6, hence 3 × 2 = 6.

Therefore, 30 × 2 = 60.

e.

Answer:

Explanation:

Step 1: Multiply the integral value 5 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 5 × 0 = 0.

Step 2: Multiply the integral value 5 with the number in tens place,

By mental computation,

As the number to be added is 2 and the integral number value is 5, so to find the value we need to add 2 for 5 times, 2 × 5 = 2 + 2 + 2 + 2 + 2 = 10, hence 2 × 5 = 10.

Therefore, 20 × 5 = 100.

f.

Answer:

Explanation:

Step 1: Multiply the integral value 3 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 3 × 0 = 0.

Step 2: Multiply the integral value 3 with the number in tens place,

By mental computation,

As the number to be added is 2 and the integral number value is 3, so to find the value we need to add 2 for 3 times, 2 × 3 = 2 + 2 + 2 = 6, hence 2 × 3 = 6.

Therefore, 20 × 3 = 60.

Question 6.

a.

Answer:

Explanation:

Step 1: Multiply the integral value 2 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 2 × 0 = 0.

Step 2: Multiply the integral value 2 with the number in tens place,

By mental computation,

As the number to be added is 2 and the integral number value is 2, so to find the value we need to add 2 for 2 times, 2 × 2 = 2 + 2 = 4, hence 2 × 2 = 4.

Therefore, 20 × 2 = 40.

b.

Answer:

Explanation:

Step 1: Multiply the integral value 3 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 3 × 0 = 0.

Step 2: Multiply the integral value 3 with the number in tens place,

By mental computation,

As the number to be added is 5 and the integral number value is 3, so to find the value we need to add 5 for 3 times, 5 × 3 = 5 + 5 + 5 = 15, hence 5 × 3 = 15.

Therefore, 50 × 3 = 150.

c.

Answer:

Explanation:

Step 1: Multiply the integral value 5 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 5 × 0 = 0.

Step 2: Multiply the integral value 2 with the number in tens place,

By mental computation,

As the number to be added is 4 and the integral number value is 5, so to find the value we need to add 4 for 5 times, 4 × 5 = 4 + 4 + 4 + 4 + 4 = 20, hence 4 × 5 = 20.

Therefore, 40 × 5 = 200.

d.

Answer:

Explanation:

Step 1: Multiply the integral value 3 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 3 × 0 = 0.

Step 2: Multiply the integral value 3 with the number in tens place,

By mental computation,

As the number to be added is 4 and the integral number value is 3, so to find the value we need to add 4 for 3 times, 4 × 3 = 4 + 4 + 4 = 12, hence 4 × 3 = 12.

Therefore, 40 × 3 = 120.

e.

Answer:

Explanation:

Any number multiplied by 1 gives the same number itself, hence 70 × 1 = 70.

f.

Answer:

Explanation:

Step 1: Multiply the integral value 2 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 2 × 0 = 0.

Step 2: Multiply the integral value 2 with the number in tens place,

By mental computation,

As the number to be added is 6 and the integral number value is 2, so to find the value we need to add 6 for 2 times, 6 × 2 = 6 + 6 = 12, hence 6 × 2 = 12.

Therefore, 60 × 2 = 120.

Question 7.

a.

Answer:

Explanation:

Step 1: Multiply the integral value 3 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 3 × 0 = 0.

Step 2: Multiply the integral value 3 with the number in tens place,

By mental computation,

As the number to be added is 7 and the integral number value is 3, so to find the value we need to add 7 for 3 times, 7 × 3 = 7 + 7 + 7 = 21, hence 7 × 3 = 21.

Therefore, 70 × 3 = 210.

b.

Answer:

Explanation:

Step 1: Multiply the integral value 5 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 5 × 0 = 0.

Step 2: Multiply the integral value 5 with the number in tens place,

By mental computation,

As the number to be added is 6 and the integral number value is 5, so to find the value we need to add 6 for 5 times, 6 × 5 = 6 + 6 + 6 + 6 + 6 = 30, hence 6 × 5 = 30.

Therefore, 60 × 5 = 300.

c.

Answer:

Explanation:

Step 1: Multiply the integral value 4 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 4 × 0 = 0.

Step 2: Multiply the integral value 4 with the number in tens place,

By mental computation,

As the number to be added is 3 and the integral number value is 4, so to find the value we need to add 3 for 4 times, 3 × 4 = 3 + 3 + 3 + 3 = 12, hence 3 × 4 = 12.

Therefore, 30 × 4 = 120.

d.

Answer:

Explanation:

Step 1: Multiply the integral value 8 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 8 × 0 = 0.

Step 2: Multiply the integral value 8 with the number in tens place,

By mental computation,

As the number to be added is 2 and the integral number value is 8, so to find the value we need to add 2 for 8 times, 2 × 8 = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16, hence 2 × 8 = 16.

Therefore, 20 × 8 = 160.

e.

Answer:

Explanation:

Step 1: Multiply the integral value 5 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 5 × 0 = 0.

Step 2: Multiply the integral value 5 with the number in tens place,

By mental computation,

As the number to be added is 3 and the integral number value is 5, so to find the value we need to add 3 for 5 times, 3 × 5 = 3 + 3 + 3 + 3 + 3 = 15, hence 3 × 5 = 15.

Therefore, 30 × 5 = 150.

f.

Answer:

Explanation:

Step 1: Multiply the integral value 9 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 9 × 0 = 0.

Step 2: Multiply the integral value 9 with the number in tens place, any number multiplied by 1 gives the same number itself, hence 9 × 1 = 9.

Therefore, 10 × 9 = 90.

Question 8.

a.

Answer:

Explanation:

Step 1: Multiply the integral value 4 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 4 × 0 = 0.

Step 2: Multiply the integral value 4 with the number in tens place,

By mental computation,

As the number to be added is 4 and the integral number value is 4, so to find the value we need to add 4 for 4 times, 4 × 4 = 4 + 4 + 4 + 4 = 16, hence 4 × 4 = 16.

Therefore, 40 × 4 = 160.

b.

Answer:

Explanation:

Step 1: Multiply the integral value 2 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 2 × 0 = 0.

Step 2: Multiply the integral value 2 with the number in tens place,

By mental computation,

As the number to be added is 9 and the integral number value is 2, so to find the value we need to add 9 for 2 times, 9 × 2 = 9 + 9 = 18, hence 9 × 2 = 18.

Therefore, 90 × 2 = 180.

c.

Answer:

Explanation:

Step 1: Multiply the integral value 4 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 4 × 0 = 0.

Step 2: Multiply the integral value 4 with the number in tens place,

By mental computation,

As the number to be added is 7 and the integral number value is 4, so to find the value we need to add 7 for 4 times, 7 × 4 = 7 + 7 + 7 + 7 = 28, hence 7 × 4 = 28.

Therefore, 70 × 4 = 280.

d.

Answer:

Explanation:

Step 1: Multiply the integral value 8 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 8 × 0 = 0.

Step 2: Multiply the integral value 8 with the number in tens place,

By mental computation,

As the number to be added is 5 and the integral number value is 8, so to find the value we need to add 5 for 8 times, 5 × 8 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 40, hence 5 × 8 = 40.

Therefore, 50 × 8 = 400.

e.

Answer:

Explanation:

Step 1: Multiply the integral value 3 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 3 × 0 = 0.

Step 2: Multiply the integral value 3 with the number in tens place,

By mental computation,

As the number to be added is 3 and the integral number value is 3, so to find the value we need to add 3 for 3 times, 3 × 3 = 3 + 3 + 3 = 9, hence 3 × 3 = 9.

Therefore, 30 × 3 = 90.

f.

Answer:

Explanation:

Step 1: Multiply the integral value 7 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 7 × 0 = 0.

Step 2: Multiply the integral value 7 with the number in tens place,

By mental computation,

As the number to be added is 2 and the integral number value is 7, so to find the value we need to add 2 for 7 times, 2 × 7 = 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14, hence 2 × 7 = 14.

Therefore, 20 × 7 = 140.

Question 9.

a.

Answer:

Explanation:

Step 1: Multiply the integral value 6 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 6 × 0 = 0.

Step 2: Multiply the integral value 6 with the number in tens place,

By mental computation,

As the number to be added is 2 and the integral number value is 6, so to find the value we need to add 2 for 6 times, 2 × 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12, hence 2 × 6 = 12.

Therefore, 20 × 6 = 120.

b.

Answer:

Explanation:

Step 1: Multiply the integral value 3 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 3 × 0 = 0.

Step 2: Multiply the integral value 3 with the number in tens place,

By mental computation,

As the number to be added is 6 and the integral number value is 3, so to find the value we need to add 6 for 3 times, 6 × 3 = 6 + 6 + 6 = 18, hence 6 × 3 = 18.

Therefore, 60 × 3 = 180.

c.

Answer:

Explanation:

Step 1: Multiply the integral value 4 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 4 × 0 = 0.

Step 2: Multiply the integral value 4 with the number in tens place, any number multiplied by 1 gives the same number itself, hence 4 × 1 = 4.

Therefore, 10 × 4 = 40.

d.

Answer:

Explanation:

Step 1: Multiply the integral value 5 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 5 × 0 = 0.

Step 2: Multiply the integral value 5 with the number in tens place,

By mental computation,

As the number to be added is 3 and the integral number value is 5, so to find the value we need to add 3 for 5 times, 3 × 5 = 3 + 3 + 3 + 3 + 3 = 15, hence 3 × 5 = 15.

Therefore, 30 × 5 = 150.

e.

Answer:

Explanation:

Step 1: Multiply the integral value 9 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 9 × 0 = 0.

Step 2: Multiply the integral value 9 with the number in tens place, any number multiplied by 1 gives the same number itself, hence 9 × 1 = 9.

Therefore, 10 × 9 = 90.

f.

Answer:

Explanation:

Step 1: Multiply the integral value 5 with the number in ones place, any number multiplied by 0 gives the product as 0, hence 5 × 0 = 0.

Step 2: Multiply the integral value 5 with the number in tens place,

By mental computation,

As the number to be added is 8 and the integral number value is 5, so to find the value we need to add 8 for 5 times, 8 × 5 = 8 + 8 + 8 + 8 + 8 = 40, hence 8 × 5 = 40.

Therefore, 80 × 5 = 400.

**Make a mental computation first. Then, solve each problem.**

Question 10.

Kin has 10 friends. She gave each friend 2 apples. How many apples did Kin have?

Mental computation: ______

Kin had __________ apples.

Answer:

Mental computation: 20 apples,

Kin had 20 apples,

Explanation:

Number of friends Kin has = 10, Number of apples she gave to each friend = 2, Number of apples Kin has :

By mental computation:

Number of apples Kin has = 2 × 10 = 2+2+2+2+2+2+2+2+2+2 = 20 apples or

10 × 2 = 10 + 10 = 20 apples,

By multiplication:

Number of apples Kin has = Number of friends Kin has × Number of apples she gave to each friend = 10 × 2 = 20 apples.

Question 11.

Each of Mr. Black’s 4 daughters needs new shoes. Each pair of shoes will cost 30 dollars. How much money will Mr. Black spend on all 4 pairs of shoes?

Mental computation: ______

Mr. Black will spend _____ dollars on the 4 pairs of shoes.

Answer:

Mental computation: 120 dollars,

Mr. Black will spend 120 dollars on the 4 pairs of shoes,

Explanation:

Number of daughters Mr. Black has = 4, Cost of each pair of shoes = 30 dollars, Amount spent on all the four pairs of shoes :

By mental computation:

Amount spent on all the four pairs of shoes = 30 × 4 = 30+30+30+30 = 120 dollars

By multiplication:

Amount spent on all the four pairs of shoes = Cost of each pair of shoes × Number of daughters Mr. Black has = 30 × 4 = 120 dollars.

**Solve each problem.**

Question 12.

There are 30 students in each classroom. If there are 5 classrooms, how many total students are there?

There are a total of __________ students.

Answer:

There are total of 150 students,

Explanation:

Number of students in each classroom = 30, Number of classrooms = 5, Total number of students = Number of students in each classroom × Number of classrooms = 30 × 5 = 150.

Question 13.

There are 7 friends that each have 2 dollars. How much money do the 7 friends have?

The friends have a total of __________ dollars.

Answer:

The friends have total of 14 dollars,

Explanation:

Number of friends = 7, Number of dollars each friend has = 2, Total money friends have = Number of friends × Number of dollars each friend has = 7 × 2 = 14 dollars.

Question 14.

There are a total of 20 students in Ms. Walker’s class, If each student receives papers, how many papers are there?

There are _____ papers in all.

Answer:

There are 20 papers in all,

Explanation:

Total number of students in the class = 20, Number of papers each student got = 1, Total number of papers Ms. Walker got = Total number of students in the class × Number of papers each student got = 20 × 1 = 20.