## Complicated and Big Multiplication Word Problems Solving Techniques

Solving word problems is an essential part of mathematics as with it, the students understand and practise the concepts they learned. This article contains various ways of solving the master multiplication word problems and understanding all the concepts well using some examples.

### Multiplication Basic

Multiplication is the basic concept used very frequently in various maths problems. The foundation for the topic starts in the junior classes. It is also referred to as among the four elementary mathematical arithmetic operations apart from addition, subtraction, and division.

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On performing multiplication, the acquired result is a product of the given numbers or quantities.

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### Master Multiplication Word Problems Using Repetition

Repetition is the first way of solving the multiplication word problems that a student must understand well. Here is how to solve this type of problems, along with a related example:

Example:

Anna has five cartons of eggs. Each of the cartons contains 12 eggs. How many eggs does he have in all?

Solution Steps:

The number of sets = Anna has five cartons of eggs.

The number of items in each set = each of the cartons has 12 eggs.

Question about total items in all sets = How many ages does Anna have in all?

For solving this type of word problems, as we know that each carton has 12 eggs and Anna has five cartons, thus we add 12 for five times, i.e., 12+12+12+12+12.

The resultant is as follows:

12+12+12+12+12 = 12*5 = 60

Therefore, Anna has a total of 60 eggs.

### Big Multiplication Word Problems Using One-Step Comparisons –

In this type of multiplication word problem-solving technique, we compare one quantity with the bigger or smaller. Here are the example and its step-wise solution:

Example:

To buy a gift for their father, John saved 10$ and Patricia saved three times the money that John has. How much money did Patricia save?

Solution Steps:

The number expressing one quantity = John saved 10$.

The number that expresses comparisons between second and first quantities = Patricia saved three times the money that John has.

Question regarding the second quantity = How much money did Patricia have?

For solving this type of problem, since Patricia saved three times the money that John has, we multiple John’s amounts with 3. The solution is as follows:

Patricia’s amount = John’s amount * 3 = 10*3

= 30$

Therefore, Patricia has 30$ in all.

### Master Multiplication Word Problem Using One-Step Formulas –

In this type of Multiplication word problem, we will have to consider some formulas. Here is an example with the solution for it:

Example:

Justin drives a bus. He told us that if he does not stop and continues driving the bus at the same speed of 80 miles per hour, he will complete his route in precisely 2 hours. How many miles does Justin have to cover in his route?

Solution Steps:

Speed = Justin must maintain a speed of 80 miles per hour.

Time to be taken = He should cover the distance in 2 hours.

Question about distance = How many miles do Justin need to cover?

To solve this type of word problem, as we know that if Justin maintains 80 miles per hour, then he will 80 miles in an hour. Now, as he travels for 2 hours, the total distance that he covers is:

80*2 = 160

Therefore, Justin covers 160 miles in 2 hours.

### Big Multiplication Word Problems Using Cartesian Product or Combination

In this form of the multiplication word problem, we find two or more sets of some items or people. These sets are then combined, forming all the pairs possible. Here is the example and solution for this type:

Example:

Today we went to have dinner in an Italian restaurant that specializes in Pasta. It was very confusing to order any dish as they had over nine types of Pasta and 11 types of sauces available on the menu. The restaurant allows the customers to combine any pasta and sauce. How many different pasta combinations can I choose?

Solution Steps:

The number of elements in the first set = 9 types of Pasta.

The number of elements in the second set = 11 types of sauces.

Question referring to total possible combinations = How many different pasta combinations can I choose?

To solve such word problems, we must combine each set of Pasta with 11 types of sauces. Therefore, just with the first type of Pasta, we get 11 different types of dishes. The same goes for the second type of Pasta, the third type, and so on. Thus,

We get the available dishes as 9*11 = 99 different pasta dishes.

1. Explain Multiplication and Mention the Techniques For Solving Multiplication Word Problems.

Ans. The word ‘multiply’ comes from a Latin word ‘multus’, meaning ‘multi’ and ‘plex’, meaning ‘fold’. Multiplication is the elementary mathematical arithmetic that repeatedly adds some numbers, sets, or items to get a resultant, known as a product. Multiplication is an essential operation and is widely used in several mathematical problems of a more challenging level and daily lives. For example, we need multiplication while doing grocery shopping and paying the combined fee, and for much more purposes. We represent multiplication as ‘x’ or a *, depending on our needs and usage scenario. There are four primary ways of solving multiplication problems, which are as follows:

By repetition

By one-step comparison

By one-step formula

By Cartesian product or Combination

2. What are the Commutative and Associative Properties of Multiplication?

Ans. Multiplication over any number is commutative and associative. These are two properties of arithmetic operations, as described below:

**Commutative Property of Multiplication –**This means the order of numbers does not matter while doing a multiplication. For example: a * b = b * a. Say, 3 * 5 = 15 = 5 * 3. Thus, both the answers are the same.**Associative Property of Multiplication –**This means that the grouping of numbers do not matter while performing multiplication. For example: a * (b * c) = (a * b) * c, say, (2 * 3) * 5 = 6 * 5 = 30 and 2 * (3 * 5) = 2 * 15 = 30. Thus both the answers are same.