Multi-step Multiplication of Two-digit Numbers (Definition, Types and Examples) - BYJUS

# Multi-step Multiplication of Two-digit Numbers

Multiplication is one of the four basic operations in math. Multiplication simplifies problems that include repeated addition, and it can be used to solve several maths problems. Some math problems cannot be solved in a single step. Learn how to solve multi-step math problems using multiplication....Read MoreRead Less

## What are Multi-step Problems?

Some math problems can be solved in a single step and these problems are usually direct and easy. There are also certain math problems that can only be solved in multiple steps. We need to apply a different strategy while dealing with such problems.

Here is an example of a single step multiplication problem:

There are 20 students in a classroom. Each student owns two pens. Find the total number of pens brought by the students to the classroom.

We can find the solution to this problem in a single multiplication step.

Here is an example of a multi-step multiplication problem:

There are 20 students in a classroom. Each student brings 3 notebooks to the classroom. If all notebooks have 200 pages and weigh 2 ounces, find the total weight of all the notebooks that the students bring to the classroom.

This math problem cannot be solved in a single step easily. We usually break down such problems into multiple steps.

## Solving a Multi-step Multiplication Problem

We need to use special strategies while solving multi-step problems. In general, the steps involved in solving multi-step problems are as follows:

• Step 1: Understand the problem.

The first thing to do is to read the problem thoroughly to analyze the little details. Here, we get to pick out the information provided to us and what we need to find with the provided information.

• Step 2: Make a plan.

After having a clear idea about the information we have in hand and what we need to do with it, we need to decide how we are going to solve the problem. We take in the necessary information and discard the rest.

• Step 3: Solve

The problem is solved in multiple steps.

Let’s solve the problem mentioned above using this strategy.

Question: There are 20 students in a classroom. Each student brings 3 notebooks to the classroom. If all notebooks have 200 pages and weigh 2 ounces, find the total weight of all the notebooks that the students bring to the classroom.

Solution:

Step 1: Understand the problem.

 What do you know?There are 20 students.Each student brings 3 notebooks.Each notebook weighs 2 ounces.Each notebook has 200 pages.

What do you need to find?

• Weight of all the notebooks in the classroom

Step 2: Make a plan.

 How will you solve it?Multiply 20 by 3 to find the total number of notebooks.Multiply the product by 2 to find the total weight of all notebooks.The number of pages in a notebook is irrelevant to this problem.

Step 3: Solve

 Step 1: How many notebooks are there in the classroom? Total number of notebooks = Number of students × Number of notebooks owned by each student           20 × 3 = a a is the unknown product.                   20                  × 3                 ___                  60 a = 60 There are 60 notebooks in the classroom. Step 2: Use a to find the total weight of all the notebooks. Total weight of notebooks = Weight of notebook × Number of notebooks            2 oz. × a = b            2 oz. × 60 = b b is the unknown product.                        60                      × 2                     ___                     120 b = 120 Therefore, the total weight of all notebooks is 120 oz.

We always start by analyzing the information provided in the question. To solve such problems, we need to find the relationship between the known values and the unknown values and form an equation. The goal is always to find the unknown value in the equation with the help of the provided information.

## Solved Examples

Example 1: Which expression can be used to solve the following problem?

In a basketball match, all five players of Team A scored a 2-pointer. All five players of Team B scored a 3-pointer. Find the number of points scored in the basketball match.

1. (5 + 5)$$\times$$(2 + 3)
2. (5 + 2)$$\times$$(5 + 3)
3. (5$$\times$$2) + (5$$\times$$3)

Solution:

We use the expression (5$$\times$$2) + (5$$\times$$3) to solve this math problem as this gives the right relationship between the values provided in the question. Since 5 players of Team A scored 2 pointers and the other 5 players of Team B scored 3 pointers, the total number of points scored is the sum of the points scored by each team.

Points scored by Team A = 5$$\times$$2

Points scored by Team B = 5$$\times$$3

So, the correct expression is (5$$\times$$2) + (5$$\times$$3)

Example 2: Jan drinks 2 cups of coffee every day. If a cup of coffee costs $5, how much money did she spend on coffee in April 2022? Solution: Step 1: Understand the problem.  What do you know?Jan drinks 2 cups of coffee every day.A cup of coffee costs$5.The month is April.The year is 2022. What do you need to find?Total amount Jan spent on coffee in April 2022

Step 2: Make a plan.

 How will you solve it?Multiply 2 with 5 to find the total money spent on coffee every day.Multiply the product by 30 (number of days in April).The year is irrelevant as April has 30 days every year.

Step 3: Solve

 Step 1: How much does Jan spend on coffee in a day?Amount spent on coffee every day = Price of 1 cup of coffee × Number of cups of coffee consumed in a day          5$$\times$$2 = aa is the unknown product.                        5                     × 2                     ___                       10a = 10Jan spends $10 on coffee every day. Step 2: Use a to find the total amount she spends in the month of April.Total money spent on coffee in April = Number of days in April × Amount spent on coffee in a day 30$$\times$$a = b 30$$\times$$$10 = bb is the unknown product.                           30                         × 10                          ___                          300b = 300Therefore, Jan spent $300 on coffee in April 2022. Example 3: Ryan kept 5 full decks of playing cards on a table. Each deck has 52 cards. Two of these decks are kept face up, and the rest of the decks are kept face down. How many cards have their face down? Solution: Step 1: Understand the problem.  What do you know?Ryan kept 5 full decks of cards on a table.Each deck has 52 cards2 decks are kept face up and the rest are kept face down. What do you need to find?Total number of cards that are facing down Step 2: Make a plan.  How will you solve it?Find the number of decks that are placed face down.Multiply the number of decks by 52 (number of cards in a deck) Step 3: Solve  Step 1: How many decks are placed face downNumber of decks kept face down = Total number of decks – Number of decks kept face up 5 – 2 = aa is the unknown product. 5 – 2 ___ 3a = 33 decks of cards are kept face down. Step 2: Use a to find the total number of cards that are facing down.Total number of cards kept face down = Number of cards in a deck × Number of decks kept face up. 52$$\times$$a = b 52$$\times$$3 = bb is the unknown product. 52 × 3 ___ 156b = 156 Therefore, 156 cards are kept face down. Example 4: A donut shop sells donuts in boxes of dozens and each donut costs$2. The shop serves 20 customers every day, and each customer buys two boxes of donuts. Find the total money earned by the shopkeeper on a Monday.

Solution:

Step 1: Understand the problem.

 What do you know?A shop serves 20 customers in a day.Each customer buys 2 boxes of donuts.A box contains a dozen (12) donuts.Each donut costs $2It’s Monday. What do you need to find?Total money earned by the shopkeeper. Step 2: Make a plan.  How will you solve it?Multiply 20 by 2 to find the number of boxes of donuts sold in a day. Multiply the product by 12 to find the number of donuts sold in a day. Multiply the product by 2 to find the total money earned in a day. The day the sale was made is irrelevant to the question as the shop sells the same number of donuts every day. Step 3: Solve  Step 1: How many boxes of donuts does the shop sell in a day? Number of boxes sold in a day = Number of customers served × Number of boxes purchased by each customer 20$$\times$$2 = aa is the unknown product. 20 × 2 ___ 40a = 40 The shop sells 40 boxes of donuts in a day. Step 2: How many donuts does the shop sell in a day? Total number of donuts sold in a day = Number of donuts in a box × Number of boxes sold in a day 12$$\times$$a = b 12$$\times$$40 = bb is the unknown product. 40 ×12 ____ 80+ 400 ____ 480b = 480The shop sells 480 donuts in a day Step 3: How much money does the shopkeeper earn in a day? Total amount earned in a day = Cost of 1 donut × Total number of donuts solds in a day$2$$\times$$b = c         $24$$\times$$80 = cc is the unknown product. 480 × 2 _____ 960c = 960Therefore, the shopkeeper earns$960 in a day.