Rational numbers are a part of Real Numbers but the only necessary condition is that, they need to be represented in the form of $\frac{p}{q}$, where p and q are integers and q $\neq$ 0.
Real world problems on Rational Numbers are those problems which represent a real life situation and we need to solve them. It basically involves some equations and expressions involving rational numbers.
Now, let
$\frac{4}{5}$ = $\frac{y}{100}$
4 $\times$ 100 = 5y
y = 80
To solve this problem, let the required number be n.
On simplifying, we obtain n
Now, let ’t’ hours is the time to complete the car job. So, $\frac{1}{t}$ job will be completed per hour,
Equating the two expressions, we get:
As they work for 2 hours, 2 $\frac{7}{24}$ = $\frac{14}{24}$ part of job will be done.
If they work together, then they will complete $\frac{1}{10}$ + $\frac{1}{x}$ work per hour which equals $\frac{1}{6.5}$. Now, equating the two expressions we obtain,
$\frac{1}{10}$ + $\frac{1}{x}$ = $\frac{1}{6.5}$ It will take 18.57 hours for Robin to lay a foundation. |

Rational numbers can include operations like addition, subtraction, multiplication and division.

Some of the solved examples of word problems with Rational Numbers are given below:

### Solved Examples

**Question 1:**If Sachin covers $\frac{3}{4}$ km distance by foot and then, he covers $\frac{11}{3}$ km distance by bus, while he was going to school, how far is his house from the school?

**Solution:**

Distance covered by him by Bus = $\frac{11}{3}$ km

Total distance covered to reach school = $\frac{3}{4}$ + $\frac{11}{3}$ = $\frac{9}{12}$ + $\frac{44}{12}$ = $\frac{53}{12}$ km

So, the house is 4.42km far from Sachin's school.

**Question 2:**If Shobha has a red ribbon with length $\frac{25}{9}$ m and a piece of $\frac{5}{7}$ m is cut from it and gave to Seema. Find how much long ribbon is left with her?

**Solution:**

Part of ribbon given to seema = $\frac{5}{7}$ m

So, the length of the ribbon left =$\frac{25}{9}$ - $\frac{5}{7}$ = $\frac{175}{63}$ - $\frac{45}{63}$ = $\frac{130}{63}$ m

So, the ribbon left with Shobha is 2.06m

**Question 3:**What should be multiplied with -$\frac{3}{5}$ to make 1?

**Solution:**

So, -$\frac{3}{5}$ * x = 1

x = -$\frac{5}{3}$

**Question 4:**If a basket has $\frac{35}{6}$ kg of grapes and if it is to be distributed among 7 children equally, how much grapes will the each child get?

**Solution:**

Number of students to which it is to be distributed equally = 7

So, each child gets grapes = $\frac{35}{6}$ divided by 7 = $\frac{35}{6}$ $\times$ $\frac{1}{7}$ = $\frac{5}{6}$ kg

So, each child gets 0.83 kg of grapes.