- Converting Decimals to Fractions
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- Converting a decimal to a mixed number and an improper fraction in simplest form: Basic
- Exponents and fractions
- Order of operations with fractions: Problem type 1

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# Order of operations with fractions: Problem type 1

We combine the order operations (PEMDAS) with adding, subtracting, multiplying, and dividing fractions.

**Rules for Order of Operations with Fractions**

First, we simplify any parentheses if any in the expression.

Next, we simplify any exponents if present in the expression.

We do multiplication and division before addition and subtraction.

We do multiplication and division based on order of appearance from left to right in the problem.

Next, we do addition and subtraction based on order of appearance from left to right in the problem.

Consider the following problems involving PEMDAS with adding, subtracting, multiplying, and dividing fractions.

Evaluate $\frac{4}{5}[17-32\left ( \frac{1}{4} \right )^{2}]$

### Solution

**Step 1:**

As per the PEMDAS rule of operations on fractions we simplify the brackets or the parentheses first.

**Step 2:**

Within the brackets, the first we simplify the exponent as $\left ( \frac{1}{4} \right )^{2} = \frac{1}{16}$

**Step 3:**

Within the brackets, next we multiply as follows

$17-32\left ( \frac{1}{4} \right )^2 = 17-32 \times \frac{1}{16} = 17 - 2$

**Step 4:**

Within the brackets, next we subtract as follows

17 - 2 So, $[17-32\left ( \frac{1}{4} \right )^2] = 15$

**Step 5:**

$\frac{4}{5}[17-32\left ( \frac{1}{4} \right )^2] = \frac{4}{5}[15] = \frac{4}{5} \times 15$

So, simplifying we get

$\frac{4}{5} \times 15 = 4 \times 3 = 12$

**Step 6:**

So, finally $\frac{4}{5}[17-32\left ( \frac{1}{4} \right )^2] = 12$

Evaluate $\left ( \frac{36}{7} - \frac{11}{7}\right ) \times \frac{8}{5} - \frac{9}{7}$

### Solution

**Step 1:**

As per the PEMDAS rule of operations on fractions we simplify the brackets or the parentheses first.

Within the brackets, the first we subtract the fractions as follows

**Step 2:**

Next, we multiply as follows

$\left ( \frac{36}{7} - \frac{11}{7}\right ) \times \frac{8}{5} - \frac{9}{7} = \frac{25}{7} \times \frac{8}{5} - \frac{9}{7} = \frac{40}{7} - \frac{9}{7}$

**Step 3:**

We then subtract as follows

$\frac{40}{7} - \frac{9}{7} = \frac{(40-9)}{7} = \frac{31}{7}$

**Step 4:**

So, finally $\left ( \frac{36}{7} - \frac{11}{7} \right ) \times \frac{8}{5} - \frac{9}{7} = \frac{31}{7} = 4\frac{3}{7}$