- Subtraction of fractions can be done by following the given steps:

**Step 1: **Make sure that the numbers are in fraction form. If they are not, then convert them into fraction form as follows:

**Case 1**. If the number is a whole number, convert it into a fraction by putting it over \(1\).

**For example:** \(2-\dfrac{1}{3}\)

Here, \(2=\dfrac{2}{1}\)

Thus, \(\dfrac{2}{1}-\dfrac{1}{3}\)

**Case 2. **If the number is a mixed number, convert it into an improper fraction.

**For example:** \(1\dfrac{1}{3}-\dfrac{1}{2}\)

Here, \(1\dfrac{1}{3}=\dfrac{4}{3}\)

Thus, \(\dfrac{4}{3}-\dfrac{1}{2}\)

**Step 2: **Make sure that the denominators are equal. If they are not, convert them into like fractions.

**For example:** \(\dfrac{3}{4}-\dfrac{2}{7}\)

LCM of \(4\) and \(7=28\)

Now, LCM becomes the least common denominator.

So, \(\dfrac{3}{4}×\dfrac{7}{7}=\dfrac{21}{28}\)

\(\dfrac{2}{7}×\dfrac{4}{4}=\dfrac{8}{28}\)

Thus, \(\dfrac{21}{28}\) and \(\dfrac{8}{28}\) are like fractions.

**Step 3: **Subtract the like fractions.

In the above example,

\(\dfrac{21}{28}-\dfrac{8}{28}=\dfrac{21-8}{28}\)

\(=\dfrac{13}{28}\)

**Step 4: **Simplify the result.

In the above example, \(13\) and \(28\) do not have any common factor other than \(1.\)

\(\therefore\) \(\dfrac{13}{28}\) is in its simplest form.

A \(\dfrac{771}{5}\) pounds

B \(\dfrac{621}{5}\) pounds

C \(145\dfrac{7}{5}\) pounds

D \(154\dfrac{2}{5}\) pounds

- Multiplication of fractions can be done by following the given steps:

**Step 1: **Make sure that the numbers are in fraction form. If they are not, convert them into fraction form as follows:

**Case 1: **If the number is a whole number, convert it into a fraction by putting it over \(1\).

**For example:** \(5×\dfrac{1}{6}\)

Here \(5=\dfrac{5}{1}\)

Thus, \(\dfrac{5}{1}×\dfrac{1}{6}\)

**Case 2: **If the number is a mixed number, convert it into an improper fraction.

**For example:** \(\dfrac{3}{7}×2\dfrac{1}{5}\)

Here \(2\dfrac{1}{5}=\dfrac{11}{5}\)

Thus, \(\dfrac{3}{7}×\dfrac{11}{5}\)

**Step 2: **Multiply the numerator by numerator and denominator by denominator.

**For example:** \(\dfrac{5}{9}×\dfrac{3}{8}\)

\(\dfrac{5×3}{9×8}=\dfrac{15}{72}\)

**Step 3. **Simplify the result.

In the above example: \(\dfrac{15}{72}\)

The Greatest Common Factor (GCF) of \(15\) and \(72\) is \(3\).

\(\therefore \;\;\;\;\dfrac{15\div3}{72\div3}=\dfrac{5}{24}\)

Thus, \(\dfrac{5}{24}\) is in its simplest form.

A \($108\)

B \($109.5\)

C \($120.2\)

D \($102\)

- Addition of fractions can be done by following the given steps:

**Step 1: **Make sure that the numbers are in fraction from. If they are not, convert them into fraction form as follows:

**Case 1: **If the number is a whole number, then convert it into a fraction by putting it over \(1\).

**For example:** \(3+\dfrac{1}{2}\)

\(3=\dfrac{3}{1}\)

Thus, \(\dfrac{3}{1}+\dfrac{1}{2}\)

**Case 2: **If the number is a mixed number, convert it into an improper fraction.

**For example:** \(3\dfrac{2}{3}+\dfrac{4}{5}\)

\(3\dfrac{2}{3}=\dfrac{11}{3}\)

Thus, \(\dfrac{11}{3}+\dfrac{4}{5}\)

**Step 2: **Make sure that the denominators are equal, if they are not, convert them into like fraction.

**For example:** \(\dfrac{2}{3}+\dfrac{4}{5}\)

LCM of \(3\) and \(5\;=\;15\)

Now, LCM becomes the least common denominator (LCD).

So, \(\dfrac{2}{3}×\dfrac{5}{5}=\dfrac{10}{15}\) and

\(\dfrac{4}{5}×\dfrac{3}{3}=\dfrac{12}{15}\)

Thus, \(\dfrac{10}{15}\, \text{and }\dfrac{12}{15}\) are like fractions.

**Step 3. **Add the like fractions.

In the above example,

\(\dfrac{10}{15}+\dfrac{12}{15}=\dfrac{10+12}{15}=\dfrac{22}{15}\)

**Step 4. **Simplify the result.

In the above example,

\(22\) and \(15\) do not have any common factor other than \(1\).

\(\therefore\) \(\dfrac{22}{15}\) is in its simplest form.

A \(\text{Alex is right}.\)

B \(\text{Kevin is right}.\)

C \(\text{Jose is right}.\)

D \(\text{Both Kevin and Jose are right}.\)

- Dividing a fraction by another fraction is same as multiplying by its reciprocal.
- To understand it, consider an example.

\(\dfrac{5}{4}\div\dfrac{2}{3}\)

**Step 1: **Find the reciprocal of the divisor.

Here, divisor \(=\dfrac{2}{3}\) and dividend \(=\dfrac{5}{4}\)

So, reciprocal of \(\dfrac{2}{3}\) is \(\dfrac{3}{2}\).

**Step 2: **Multiply the dividend by the reciprocal of divisor.

\(\dfrac{5}{4}×\dfrac{3}{2}\)

\(=\dfrac{5×3}{4×2}\)

\(=\dfrac{15}{8}\)

**Step 3: **Simplify the result.

\(15\) and \(8\) do not have any common factor other than \(1\).

\(\therefore\) \(\dfrac{15}{8}\) is in its simplest form.

Thus, \(\dfrac{5}{4}\div\dfrac{2}{3}=\dfrac{15}{8}\)

**Note: **Convert the mixed number into an improper fraction.

**For example:** \(2\dfrac{5}{7}=\dfrac{19}{7}\)

A solution of a problem can be achieved by following steps:

1. Identify the keywords

2. Apply appropriate operation to solve the problem.

**Example:** A bank charges an overdraft fee on a standard current account when the balance falls below zero at any point of time. Mr. Watson had a balance of \($4500\) in his account. He withdrew \(\dfrac{6}{5}\) of the account balance for business purposes. The bank charged \(\dfrac{1}{20}\) of the overdrawn balance. Next day, he deposited \($3000\) into the bank account. Calculate the current balance of his bank account.

**Solution**: Original balance in bank account \(=$4500\)

Fraction of amount withdrew \(=\dfrac{6}{5}\) of the account balance

\(=\dfrac{6}{5}\) of \(4500\)

\(=\dfrac{6}{5}×4500\)

**\(=\dfrac{6×4500}{5×1}=5400\)**

Now, the overdrawn amount \(=\text{Total withdrawal }-\text{Original deposit}\)

\(=5400-4500\)

\(=$900\)

Thus, the overdrawn amount is \($900\).

Now, the overdrawn fees \(=\dfrac{1}{20}\text{ of Total overdrawn amount}\)

\(=\dfrac{1}{20}\text{ of }(900)\)

\(=\dfrac{1}{20}×(900)\)

\(=\dfrac{1×(900)}{20×1}=$45\)

Overdrawn amount and fee is taken as negative amount as bank takes away this amount.

So, the total amount taken away by bank

\(=900+45\\=$945\)

Now, the total amount deposited by Mr. Watson \(=$3000\)

So, the current balance of the bank account

\(\text{=Total amount deposited after withdrawal - Total amount taken away by bank}\\=$3000 \;-\;$945\\=$2055\)

A \(\dfrac{2}{3}\) miles

B \(\dfrac{3}{4}\) miles

C \(\dfrac{4}{5}\) miles

D \(\dfrac{5}{6}\) miles