- What is Multiplicative Comparison?
- How do We Write a Comparison Sentence for a Multiplication Equation?
- How do We Write a Multiplication Equation for a Comparison Sentence?
- How do We Write a Comparison Sentence for an Addition Equation?
- How can We Write an Addition Equation for a Comparison Sentence?
- Solved Examples
- Frequently Asked Questions
What is multiplicative comparison?
Multiplicative comparison is an interpretation which involves comparing two quantities in such a way that when a number is multiplied by another number, we get a different product. For example, Thomas is three times Ben’s age.
The multiplication equation for this multiplicative comparison is:
3 × 20.
So, we can say that when we compare two quantities that need to be multiplied, it is called a multiplicative comparison.
Some commonly used phrases for multiplicative comparison are:
1) times as many
2) times as much
3) times more
4) times as large
Multiplicative comparisons are written as word problems with the following structure:
Statement, Statement, Question.
Example: Statement: 24 days is 6 times more than 4 days.
Multiplication equation: 24 = 6 × 4.
Example: Daniel has 6 footballs. David has 5 times more footballs than Daniel. Find out how many footballs David has?
Answer : We know that Daniel has 6 footballs.
Hence, the total number of balls David will have: 6 × 5 = 30.
How do we write a comparison sentence for a multiplication equation
To write comparison sentences, find the relationship between the two numbers that are being multiplied by each other. We can write two comparison sentences for a multiplication equation.
Example: 9 × 3 = 27
It can be written as: 27 is 9 times as many as 3.
We know that the commutative property of multiplication states that changing the order of numbers that are being multiplied does not alter the result of the multiplication. This can be represented as:
a × b = b × a.
By using the commutative property, it can be written as: 27 is 3 times as many as 9 because 9 × 3 = 27 = 3 × 9.
How do we write a multiplication equation for a comparison sentence
We can interpret a multiplication sentence as a multiplication equation. Hence, a mathematical equation can be formed for any comparison sentence. Multiplication sentences always form a relation between the two numbers.
Example: The lemon tree in George’s yard is 20 feet tall. The lemon tree is twice as tall as George. How tall is George?
Answer: It is mentioned that the lemon tree is twice as tall as George.
2 × George’s eight = 20
2 × 10 = 20
Hence, George is 10 feet tall.
How do we write a comparison sentence for an addition equation
We know that multiplication operations can be interpreted as repeated addition. Hence, addition can also be used for the comparison of two numbers. This is known as an additive comparison. For this, we need an additive equation of two numbers.
Example : 2 + 6 = 8
It can be written as: 8 is 6 more than 2.
Another way to write this as: 6 + 2 = 8.
The comparison sentence is: 8 is 2 more than 6.
How can we write an addition equation for a comparison sentence
An addition comparison sentence gives the relationship between the three numbers, which can be interpreted in the form of a mathematical equation.
Example: 25 is 10 more than 15.
So, 25 = 15 + 10 is the addition equation.
Solved Examples
Example 1: Compare the height of the man and the cupboard.
Answer: The man’s height = 6 feet
Height of the cupboard = 3 feet
Since 6 = 3 × 2.
6 is 2 times as many as 3.
Hence, the man’s height is twice the height of the cupboard.
Example 2: Earthworms have 10 times as many hearts as humans. How many hearts do earthworms have?
Answer: As we know, humans have only one heart.
So, the number of hearts earthworms have: 10 × 1 = 10 .
Hence, earthworms have 10 hearts.
Example 3: Write the comparison statement in equation form.
84 is 12 times as many as 7.
Answer: It can be written in the form of an equation as:
84 = 12 × 7.
Example 4: Write an equation for the comparison sentence.
1. 78 is 13 times as many as 6.
Answer :
The multiplication equation is: 78 = 13 × 6
So, 78 = 13 × 6 is the multiplication equation.
2. 63 is 35 more than 28.
Answer:
So, 63 = 28 + 35 is the addition equation.
The following phrases can be used for multiplicative comparisons:
1) times as many
2) times as much
3) times more
4) times as large
The expression “Interpret a multiplication equation as a comparison” means expressing the result of the equation or the product in terms of the other two numbers or factors of the equation in a comparative sentence.
For example, 78 = 13 × 6 can be interpreted as: 78 is 13 times as many as 6.