All the solutions provided in **McGraw Hill Math Grade 3 Answer Key PDF Chapter 4 Lesson 6 Use Multiplication to Find Combinations** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 3 Answer Key Chapter 4 Lesson 6 Use Multiplication to Find Combinations

**Math in My World**

Example 1

Amos’ team has 3 jersey colors: green, red, and yellow. They can wear orange or black shorts. Find all of the jersey and short combinations for the team.

1. Color the first jersey m green, the second one red, and the last yellow.

2. Color 1 pair of 43 shorts orange and 1 pair of shorts black below each jersey.

Answer:

Explanation:

Amos’ team has 3 jersey colors: green, red, and yellow

They can wear orange or black shorts

There are 3 jersey colors x 2 shorts colors = 6 jersey and shorts combinations are possible.

1st combination is green jersey and orange shorts, 2nd combination is green jersey and black shorts, 3rd combination is red jersey and orange shorts, 4th combination is red jersey and black shorts, 5th combination is yellow jersey and orange shorts and 6th combination is yellow jersey and black shorts

In this way we will get 6 combinations.

Another way to find combinations is to use a tree diagram.

A tree diagram uses “branches” to show all possible combinations.

Example 2

What are all the possible fruit sorbet combinations if you choose one flavor and one fruit to add in?

Complete the tree diagram.

Check Multiply to find the number of possible combinations.

Answer:

Explanation:

3 fruits X 3 flavors = 9 possible combinations

1st combination is mango and banana, 2nd combination is mango and berries, 3rd combination is mango and peach, 4th combination is strawberry and banana, 5th combination is strawberry and berries, 6th combination is strawberry and peach, 7th combination is vanilla and banana, 8th combination is vanilla and berries and9th combination is vanilla and peach

In this way every fruit will combine with 3 flavors

So, there are 9 possible combinations.

**Guided Practice**

Question 1.

Refer to Example 2. How would the possible number of combinations change if one more flavor was added? Write the multiplication sentence

multiplication sentence:

Answer:

3 fruits X 4 flavors = 12 possible combinations

Explanation:

In example 2, We used 3 flavors and 3 fruits

Here we added 1 flavor

So for example if mango will combine with 4 flavors , we can get 4 combinations

In this way other 2 fruits also combine with 4 flavors

One fruit will get 4 combinations

Here we are using 3 fruits

So, there are 12 possible combinations.

**Talk Math**

Explain how a tree diagram helps you find all the possible combinations without repeating any.

Answer:

A tree diagram is a visual representation of all possible future outcomes and the associated probabilities of a random variable. Tree diagrams are particularly useful when we have several possible outcomes. They can help you record all the possibilities in a clear, uncomplicated manner.

**Independent Practice**

**Find all the possible combinations. Write a multiplication sentence to check.**

Question 2.

Jackie is playing a card game with triangles and circles. Each shape can be blue, red, yellow, or green. How many different cards are there?

Answer:

Explanation:

Multiplication sentence : 2 shapes X 4 color = 8 different card combinations.

So there are 8 different card combinations possible

Here we take 2 shapes and 4 colors

So every shape will combine with 4 cards. Like wise triangle will combine with 4 colors means blue, red, yellow or green

So we get 4 different card combinations they are triangle blue card, triangle red card, triangle yellow card and triangle green card.

In this way if circle also combine with 4 colors, then we get 4 different combinations of cards

Now, if we add triangle combinations and circle combinations together we get 8 different combinations of cards.

List all of the 2-digit numbers that can be made with 3 or 4 as the tens digit and 1, 6, 7, 8, or 9 as the ones digit number

Answer:

Multiplication sentence:2 tens digit numbers X 5 ones digit numbers = 10 two digit numbers .

There are 10 two digit numbers possible

Explanation:

In this problem their are 2 tens digit numbers and 5 ones digit numbers

Here 3 and 4 are tens digit numbers

1, 6, 7, 8, 9 are ones digit numbers

Here both tens digit numbers 3 and 4 will combine with 1, 6, 7, 8, 9 numbers means

If 3 will combine with 1 then we get 31, like wise it will combine with 6, 7, 8, 9 then we get 36 , 37 , 38 ,39 numbers

Number 4 also combine with 1, 6, 7, 8, 9 then we get 41, 46, 47,48, 49 numbers. every tens digit number will combine with these 5 numbers . then we can get 5 combinations with each number. here we have two numbers

So there are 10 two digit numbers possible

The numbers are 31 , 36 , 37 , 38 ,39 , 41 , 46 , 47 , 48 , 49.

**Problem Solving**

**Write a multiplication sentence to solve the problem.**

Question 4.

Madison needs to choose 1 breakfast item and 1 drink. Find the number of possible combinations.

Answer:

Multiplication sentence : 2 break fast items X 2 drinks = 4 possible combinations.

There are 4 possible combinations in breakfast .

Explanation:

Here there are 2 breakfast items and 2 drinks

Every breakfast item will combine with 2 drinks , then we can get 2 different combinations with each breakfast item

Pan cakes and bread toast as breakfast items, milk and juice are drinks

Now we get 2 combinations with pan cakes they are

pancakes and milk , pancakes and juice

Also we get 2 combinations with bread toast they are

bread toast and milk , bread toast and juice

In this way there are 4 possible combinations.

Suppose hot chocolate was added to the drink menu. How would the number of combinations change?

Answer:**
**Multiplication sentence: 2 breakfast items X 3 drinks = 6 possible combinations.

So there are 6 possible combinations.

Explanation:

To the above example if w e add hot chocolate to the drink menu

Every breakfast item will combine with 3 drinks

The combinations are pancakes and milk, pancakes and juice, pancakes and hot chocolate, bread toast and milk, bread toast and juice, bread toast and hot chocolate

In this way the number of possible combinations will be 6.

**HOT Problems**

Question 5.

**Mathematical PRACTICE 5 Use Math Tools** Write a real-world combination problem for the multiplication sentence 4 × 2 = . Ask a classmate to solve with a tree diagram. Then find the unknown.

Answer:

Explanation:

Multiplication sentence: 4 different shapes X 2 different colors = 8 different combinations.

There are 4 different shapes like circle, oval, triangle, square and 2 different colors are blue and pink. So every shape will combine with 2 colors

That is circle with blue and circle with pink, oval with blue and oval with pink, triangle with blue and triangle with pink, square with blue and square with pink. In this way every shape will combine with each color. So, we get 8 possible combinations like blue circle, pink circle, blue oval, pink oval, blue triangle, pink triangle, blue square , pink square

So there are 8 different combinations possible.

Question 6.

**? Building on the Essential Question** How can multiplication help to find combinations?

Answer:

Using multiplication can help us to find the combinations

For example their are two shirts and 4 trousers with John the number of combinations that he can make using them can be found by multiplying them

That is 2 x 4 = 8

Therefore, 8 will the number of combinations that John can make with 2 shirts and 4 trousers.

### McGraw Hill My Math Grade 3 Chapter 4 Lesson 6 My Homework Answer Key

**Practice**

Question 1.

Diana can take 1 pencil and 1 eraser to school. Her choices are shown. How many different pencil and eraser combinations are there? Complete the tree diagram. Write a multiplication sentence.

Answer:

Multiplication sentence : 1 pencil X 1 eraser = 1 possible combination.

Explanation:

Multiplication sentence : 1 pencil X 1 eraser = 1 possible combination.

Here there are 2 items only

If 1 pencil will combine with 1 eraser then the number of possible combinations is only 1

So there is only one possible combination.

Question 2.

**Mathematical PRACTICE 7 Identify Structure** For a snack. Randy can choose from peanuts, carrots, or popcorn. He can have water or juice to drink How many snack and drink combinations are there? Complete the tree diagram. Write a multiplication sentence.

Answer:

Explanation:

Multiplication sentence : 3 snack item X 2 drinks = 6 possible combinations

Here there are 3 snack items like peanuts, carrots, popcorn and 2 drinks like water and juice

If every snack item will combine with each drink

Like peanuts with water and juice , carrots with water and juice , popcorn with water and juice

We get 6 possible combinations like peanuts and water , peanuts and juice , carrots and water , carrots and juice , popcorn and water and popcorn and juice

So there are 6 combinations possible.

**Vocabulary Check**

Question 3.

Write the correct vocabulary word(s) in each space to complete the sentence.

Combination tree diagram

Each branch of a —–** **shows a possible —-** **of items.

Answer:

Each branch of a tree diagram shows a possible combination of items.

**Test Practice**

Question 4.

Amanda bought 4 pairs of shoes and 5 purses. Which number sentence shows the number of different shoes and purse combinations that Amanda can make?

A. 4 + 5 = 9

B. 5 × 8 = 40

C. 4 + 4 + 4 + 4 = 16

D. 4 × 5 = 20

Answers:

D. 4 × 5 = 20

Explanation:

D Is answer because if 4 pairs of shoes will combine with 5 purses then

Multiplication sentence: 4 pairs of shoes X 5 purses = 20 combinations

So there are 20 possible combinations