 # Numerical Expressions Involving Fractional Numbers | Simplification of Numerical Expressions with Fractional Numbers

Numerical Expressions Involving Fractional Numbers: A group of numbers and symbols that shows a mathematical relationship is known as the expression. In the previous articles, we have discussed in detail numerical expressions involving whole numbers and decimal numbers. In this article, we are going to learn about numerical expressions involving fractional numbers.

So, the students of 5th grade are suggested to read this page thoroughly and learn deeply about numerical expressions with fractional numbers. You will know how to evaluate the expressions involving fractional numbers with solved problems here. Hence make use of our articles and score the maximum marks in the exams.

Do Refer:

## Simplification of Numerical Expressions

A numerical expression is a mathematical statement with different fundamental operations such as addition, subtraction, multiplication, and division. To simplify the numerical expression with different operations we use brackets to make the calculation easy. There is a trick to remember the concept of numerical expressions i.e, BODMAS Rule.
B – Brackets
O – of means
D – Division
M – Multiplication
S – Subtraction

### How to Simplify Numerical Expressions involving Fractions?

Follow the steps listed below while evaluating numerical expressions involving fractions. They are along the lines

1. Write the given expression and perform the operations inside parentheses.
2. Simplify the values in the bracket.
3. Write the results of the performed operations like addition, subtraction, multiplication, and division.
4. Next, simplify the expressions from the left.
5. Now apply all the required operations of all the results and simplify the fractional numbers.

### Evaluating Numerical Expressions Involving Fractional Numbers Questions

The concept of Numerical Expressions Involving Fractional Numbers is explained in detail with examples from the below section.

Example 1.
Simplify the numerical expression involving fractional numbers of equation is 19/4 + 5/2 ÷ 7/2 – 3/2
Solution:
Given that,
19/4 + 5/2 ÷ 7/2 – 3/2
=19/4 + 5/2 × 7/2 – 3/2( first step: divide 5/2 × 7/2 = 5/7)
=19/4 + 5/7 – 3/2( second step: add 19/4 + 5/7 = 65/28)
=65/28 – 3/2( third step: subtract 65/28 – 3/2 = 23/28
= 23/28
Therefore 19/4 + 5/2 ÷ 7/2 – 3/2 = 23/28

Example 2.
Simplify the numerical expression involving fractional numbers of equation is 7/2 + 12/7 × 2/3 – 1/4 ÷ 4
Solution:
7/2 + 12/7 × 2/3 – 1/4 ÷ 4
7/2 + 12/7 × 2/3 – 1/4 × 1/4(first step: divide 1/4 by 4 = 1/4 × 1/4)
= 7/2 + 12/7 × 2/3 – 1/16(second step: 1/4 × 1/4 = 1/16)
= 7/2 + 8/7 – 1/16( third step: multiply 12/7 × 2/3 = 8/7)
= 4 – 1/6( fourth step: add 7/2 + 8/7 = 4)
= 23/6( fiveth step: subtract 4 – 1/6 = 23/6)
Therefore 7/2 + 12/7 × 2/3 – 1/4 ÷ 4 = 23/6.

Example 3.
Simplify the numerical expression involving fractional numbers of equation is 7/3 – {5/2 ÷ (9/5 – 1/2)}
Solution:
Given that,
7/3 – {5/2 ÷( 9/5 – 1/2)}
Subtract 9/5 – 1/2 = 13/10
=7/3 – { 5/2 ÷ 13/10}
Divide 5/2 ÷ 13/10 = 1/12
=7/3 – 1/12
Subtract 7/3 – 1/12 = 9/4
=9/4
Therefore 7/4 – {5/2 ÷ (9/5 – 1/2)} = 9/4

Example 4.
Simplify the numerical expression involving fractional numbers of equation is 11/7 + 25/8 ÷ 5/4 – 7/3
Solution:
Given that,
11/7 + 25/8 ÷ 5/4 – 7/3
=11/7 + 25/8 × 5/4 – 7/3( first step: multiply 25/8 × 5/4 = 5/2)
= 11/7 + 5/2 – 7/3(second step: add 11/7 + 5/2 = 57/14)
= 57/14 – 7/3( third step: subtract 57/14 – 7/3 =74/42)
= 74/42
Therefore 11/7 + 25/8 ÷ 5/4 – 7/3 = 74/42

Example 5.
Simplify the numerical expression involving fractional numbers of equation is 7/4 + 21/8 × 1/3 – 1/2 ÷ 2
Solution:
Given that,
7/4 + 21/8 × 1/3 – 1/2 ÷ 2(divide 1/2 by 2 = 1/2 × 1/2)
= 7/4 + 21/8 × 1/3 – 1/2 × 1/2( multiply 1/2 × 1/2 = 1/4
= 7/4 + 21/8 × 1/3 – 1/4( multiply 21/8 × 1/3 = 21/32)
= 7/4 + 21/32 – 1/4( add 7/4 + 21/32 = 77/32)
= 77/32 – 1/4( subtract 77/32 – 1/4 = 69/32)
= 69/32
Therefore 7/4 + 21/8 × 1/3 – 1/2 ÷ 2 = 69/32.

### FAQs on Numerical Expressions Involving Fractional Numbers

1. How do you do numerical expressions with fractions?

1. Perform operations inside parentheses.
2. Evaluate exponents.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.

2. What is mean by numeric expression?

A numeric expression is a combination of numeric elements such as numbers, variables, and functions, and operators that evaluate a numeric value.

3. Is 27 a numerical expression?

No, there is no other additional operation to the given number. Thus, 27 is not a numerical expression.

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