Addition and Multiplication Using Counters & Bar-Diagrams

Introduction:

We can find the solution to the word problem by solving it.

Here, in this topic, we can use 3 methods to find the solution.

1. Add using counters

2. Use factors to get the product

3. Write equations to find the unknown.

Addition Equation: 8+8+8 =?

Multiplication equation: 3×8=?

Example 1:

Andrew has his friends over for the game night. So, he decided to prepare snacks and games.

He started by making mini sandwiches. If he has 4 friends coming over and he made 3 sandwiches for each one of them, how many sandwiches did he make?

Solution:

Andrew prepared 3 sandwiches for each friend.

The number of friends who came to his home is 4.

 The number of sandwiches he has to prepare is,

Step 1:

The number of sandwiches he has to prepare is,

We can use addition to join an equal group.

3 + 3 + 3 + 3 = 12

Step 2:

We can define multiplication as an operation that gives the total number when you join equal groups. 

Factors are the numbers that are being multiplied.

The product is the answer to the multiplication problem.

Step 3:

We can write the equation to solve the problem.

An unknown is a symbol that stands for a number in an equation.

The required addition equation is,

3 + 3 + 3 + 3 =?

3 + 3 + 3 + 3 = 12

The required multiplication equation is,

3 × 4 =?

3 × 4 = 12

Example 2:

A flashlight requires 2 batteries to function. How many batteries in all would 7 such flashlights require?

Solution:

A flashlight requires 2 batteries to function.

7 such flashlights require batteries = 2 × 7 = 14.

Therefore, 7 such flashlights require 14 batteries.

Example 3:

Norah uses an ounce of butter to bake 9 cookies. How many cookies can she bake with 8 ounces of butter?

Solution:

Norah uses an ounce of butter to bake 9 cookies.

With 8 ounces of butter, the number of cookies she can bake is,

The required equation is,

9 × 8 = 72

Therefore, with 8 ounces of butter, the number of cookies she can bake is 72.

Example 4:

A small-time tour operator owns a fleet of 8 cars of the same make. Each car is filled with 2 liters of engine oil. How many liters in all have been filled in the cars?

Solution:

A small-time tour operator owns a fleet of 8 cars of the same make.

Each car is filled with 2 liters of engine oil.

The amount of engine oil filled in 8 cars is,

2 + 2 + 2 +2 + 2 + 2 + 2 + 2 = 16

Therefore, the amount of engine oil filled in 8 cars is liters.

Exercise:

1. Joan has 9 blue balloons. Sandy has 3 times more blue balloons than Joan. How many blue balloons does Sandy have now?
2. A restaurant sold 6 hamburgers every day for a week. How many hamburgers were sold during the week?
3. Alyssa, Joan, and Fred each have 8 pencils. How many pencils do they have in all?
4. The roof is 8 feet above the floor. To support it, John needs 2 sets of metal bars. If each set has 7 metal bars, how many metal bars are there in all?
5. Mike worked 4 hours for 6 days. How many hours did he work in total?
6. Alyssa goes fishing with Tom. Alyssa catches 5 trout. Tom catches twice as many trout as Alyssa. How many trout did Tom catch?
7. A CD contains 4 music tracks. How many music tracks would 8 such CDs contain?
8. Jessica was at the beach for five days and found 9 seashells every day. How many seashells did Jessica find during the beach trip?
9. Mary goes out to lunch with Benny and Sally. Each person orders the lunch special. Mary agrees to pay the bill. How much will she have to pay?
10. There was a total of 5 football games a month. The season is played for 3 months. How many football games are in the season?

Concept Summary: