How to Write and Interpret Numerical Expressions?

Write numerical expressions

What is the Meaning of Numerical Expression?

A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division.

• To simplify a numerical expression that has two or more operations, we perform the PEMDAS rule.
• In PEMDAS rule we have to solve operations like parentheses first, followed by exponents, multiplication, division, addition and then subtraction.

The word PEMDAS stands for:

P → Parentheses

E → Exponents

M → Multiplication

D → Division 

A → Addition

S → Subtraction        

Some examples of numerical expressions:

 4 + 6

134 – 39

56 × 3 + 7

Write Numerical Expression

Example1:

A Cineplex has 500 seats on the first class and 130 in the balcony. Every seat is filled for 3 shows. Write an expression that shows the calculations you could use to determine how many tickets were sold.

Solution:

Step1: Add 500 + 130 to find the total number of seats.

Step2: Multiply the number by 3.

Step3: We need to write a numerical expression that represents:

            “Find 3 times the sum of 500 and 130”.

Step4: Using numbers and symbols to write the numerical expression.

          The sum of 500 and 130: 500 + 130       

             

Step5: 3 times the sum:  3 x (500 + 130)

            The expression 3 x (500 + 130) shows the calculations for the number of tickets sold.

Example 2:

Sonu wants to write an expression to show the calculations he could use to determine the total area of the rectangles.

Solution:     

Step1: Find the area of rectangle.   

            Use l x b formula

            Multiply 18 by 22

Step2: We need to write a numerical expression that represents:

             “Find 3 times the product of 18 and 22.”

Step3: Using numbers and symbols to write the numerical expression.

            The product of 22 and 18: 18 x 22

Step4: 3 times the product:  3 x (18 x 22)

 The expression 3 x (18 x 22) shows the calculations for the total areas of the rectangles.

Example3:   

Write the numerical expression for the following:

Add 98 and 22, and then multiply by 3.     

Solution:

Step1: Add 98 + 22 to find the total number.

Step2: Multiply by number of shows, 3

Step3: We need to write a numerical expression that represents:

            “Find 3 times the sum of 98 and 22”.

Step4: Using numbers and symbols to write the numerical expression.

            The sum of 98 and 22:  98 + 22

             Step5: 3 times the sum:  3 x (98 + 22)

             The expression 3 x (98 + 22) shows the calculations for the number.

Interpret Numerical Expressions.

Example1:   

Robin’s Santa dress costume requires 6/8 + 2/3 + 1 2/4 yards of fabric.

His dad’s matching costume requires 4 x ( 6/8 + 2/3 + 1 2/4).

How much more fabric is required for the dad’s costume to compare the amount required?

Solution:

Step1: Interpret the part of each expression that is the same.

                      6/8 + 2/3 + 1 2/4

4 x (6/8 + 2/3 + 1 2/4)

Step2: Both expressions contain the sum . This amount of     

            fabric is needed for Robin’s costume.

Step3: Interpret the part of each expression that is different.

    6/8 + 2/3 +1 2/4

      4 x ( 6/8 + 2/3 + 1 2/4)

So, dad’s costume requires 4 times as much fabric as Robin’s costume.

Example 2:

Without doing any calculations, describe how expression A compares to expression B.

A) 7 × (30,456)

B) 30,456    

Solution:

Step1: Interpret the part of each expression that is the same.

             A) 7 × (30,456)

              B) 30, 456

Step2: Both expressions contain the numbers 30,456.

Step3: Interpret the part of each expression that is different.

              A) 7 × (30,456)

              B) 30, 456     

Step4: The first expression shows that 30, 456 multiply by 7.

Step5: Now compare the two expressions.

             7 × (30, 456)      >         30, 456.

So, the expression A is 7 times more than expression B.

Concept Map:

Exercise:

1. Add 9 and 7, and then multiply by 3.
2. Add 71, 135 and 17, and then divide by 10.
3. Subtract 59 from the sum of 270 and 20.
4. Sum of 8 and 9 is divided by 3 and then added to 6.
5. Divide 12 by 3, subtract from 12 and then multiply the result by 2.
6. Steffen has 10 chocolate bars. She gives 4 chocolates to her sister, 1 to her friend and eats 2. Later she visits her grandmother, and she (grandmother) offers Steffen 12 more chocolate bars. How many chocolate bars does Steffen have now?
7. Without doing any calculations, describe how expression A compares to expression B.
   A (634 + 14, 897) ÷3
   B 524 + 15, 564
8. Without doing any calculations, write >, <, or =.

a.) (384 + 910) + 30                (385 + 8,816) + 35

b.) 82 + (13,888 – 5,296)            80 + (13,887 – 5,296)  

9. Without doing any calculations, describe how expression A compares to expression B.
A (9684 + 14, 788) ÷5
B 699 + 15, 688

10. At a drawing competition, color pencils were distributed to 20 students. Five of the students got packets that had 10 color pencils, and the other five got packets that had 20 color pencils. How many color pencils were distributed in all?