Exercises: decimal numbers (mixed)

Solve the following expressions.

$({2.3}^{2} - {1.7}^{2}) : 0.6$

For this task you need the following basic knowledge: Decimal fractions
An adequate knowledge of exponential expressions, of the order of operations (PEMDAS) and of division by decimals is a prerequisite for working out the value of the above expression.
The following steps will guide you to the solution.
1. Work out the value of the exponential expressions.
2. Subtract.
3. Divide the difference by the decimal.
So, let's get going.
1. Work out the value of the exponential expressions.
${2.3}^{2} = 2.3 \cdot 2.3 = 5.29$ .
${1.7}^{2} = 1.7 \cdot 1.7 = 2.89$ .
2. Subtract.
${2.3}^{2} - {1.7}^{2} = 5.29 - 2.89 = 2.4$ .
3. Divide the difference by 0.6.
$({2.3}^{2} - {1.7}^{2}) : 0.6 = 2.4 : 0.6 = 24 : 6 = 4$ .
Done! $({2.3}^{2} - {1.7}^{2}) : 0.6$ evaluates to 4.
$({3.1}^{2} - {0.6}^{2}) : 2.5$

For this task you need the following basic knowledge: Decimal fractions
Like all other numerical expressions in exercise 4, the above contains parentheses and two decimals raised to the power of 2. Hence an adequate knowledge of the order of operations (PEMDAS), exponential expressions and division by a decimal is a prerequisite for evaluating this numerical expression.
Adhering to the following steps will guide you to the solution. This sequence of steps is the same for each numerical expression of exercise 4.
1. Evaluate the exponential expressions.
2. Subtract.
3. Divide.
So, let's get going.

1. Evaluate the exponential expressions.
${3.1}^{2} = 3.1 \cdot 3.1 = 9.61$ .
${0.6}^{2} = 0.6 \cdot 0.6 = 0.36$ .
2. Subtract.
$9.61 - 0.36 = 9.25$ .
3. Divide.
$9.25 : 2.5 = 92.5 : 25 = (75 + 17.5) : 25 = 3.7$ .
Done! So $({3.1}^{2} - {0.6}^{2}) : 2.5 = (9.61 - 0.36) : 2.5 = 9.25 : 2.5 = 3.7$ .
The above numerical expression evaluates to 3.7 .
$({4.7}^{2} - {1.2}^{2}) : 5.9$

For this task you need the following basic knowledge: Decimal fractions
$({4.7}^{2} - {1.2}^{2}) : 5.9$ $=$
↓
Quadriere 4.7 und 1.2
$=$ $(22.09 - 1.44) : 5.9$
↓
Subtrahiere
$=$ $20.65 : 5.9$
↓
Dividiere
$=$ $3.5$
Like all other numerical expressions in exercise 4, the above contains parentheses and two decimals raised to the power of 2. Hence an adequate knowledge of the order of operations (PEMDAS), exponential expressions and division by a decimal is a prerequisite for evaluating this numerical expression.
Adhering to the following steps will guide you to the solution. This sequence of steps is the same for each numerical expression of exercise 4.
1. Evaluate the exponential expressions.
2. Subtract.
3. Divide the difference by the decimal.
So, let's get started.
1. Evaluate the exponential expressions.
${4.7}^{2} = 4.7 \cdot 4.7 = 22.09$ .
${1.2}^{2} = 1.2 \cdot 1.2 = 1.44$ .
2. Subtract.
$22.09 - 1.44 = 20.65$ .
3. Divide the difference by 5.9.
$20.65 : 5.9 = 206.5 : 59 = (177 + 29.5) : 59 = 3.5$ .

Done! So, $({4.7}^{2} - {1.2}^{2}) : 5.9 = (22.09 - 1.44) : 5.9 = 20.65 : 5.9 = 3.5$ .
Hence $({4.7}^{2} - {1.2}^{2}) : 5.9$ evaluates to 3.5 .
$({5.3}^{2} - {1.9}^{2}) : 7.2$

For this task you need the following basic knowledge: Decimal fractions
Like all other numerical expressions in exercise 4, the above contains parentheses and two decimals raised to the power of 2. Hence an adequate knowledge of the order of operations (PEMDAS), exponential expressions and division by a decimal is a prerequisite for evaluating this numerical expression.
Adhering to the following steps will guide you to the solution. This sequence of steps is the same for each numerical expression of exercise 4.
1. Evaluate the exponential expressions.
2. Subtract.
3. Divide the difference by the decimal.
So, let's get going.
1. Evaluate the exponential expressions.
${5.3}^{2} = 5.3 \cdot 5.3 = 28.09$ .
${1.9}^{2} = 1.9 \cdot 1.9 = 3.61$ .
2. Subtract.
$28.09 - 3.61 = 24.48$ .
3. Divide the difference by 7.2 .
$24.48 : 7.2 = 244.8 : 72 = (216 + 28.8) : 72 = 3 + 0.4 = 3.4$ .
Done! So, $({5.3}^{2} - {1.9}^{2}) : 7.2 = (24.48 - 3.61) : 7.2 = 24.48 : 7.2 = 3.4$ .
Hence $({5.3}^{2} - {1.9}^{2}) . 7.2$ evaluates to 3.4 .

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$({4.7}^{2} - {1.2}^{2}) : 5.9$	$=$
	↓	Quadriere 4.7 und 1.2
	$=$	$(22.09 - 1.44) : 5.9$
	↓	Subtrahiere
	$=$	$20.65 : 5.9$
	↓	Dividiere
	$=$	$3.5$