Exercises: decimal numbers (mixed)

Compute

$17.17 + 0.3$

For this task you need the following basic knowledge: Addition and subtraction of decimal fractions
$17.17 + 0.3$
Use the written addition to add the two decimal fractions. You must insert an additional zero as the second decimal place for the $0.3$ .
$\begin{array}{l} 17.17 \\ + 0.30 \\ 17.47 \end{array}$
Alternative way
Convert the decimal numbers to fractions and bring them to a common denominator.
$17.17 + 0.3$ $=$ $\frac{1717}{100} + \frac{30}{100}$
↓
Add the fractions.
$=$ $\frac{1747}{100}$
↓
Convert into a decimal number.
$=$ $17.47$
$18.7 - 1.87$

For this task you need the following basic knowledge: Addition and subtraction of decimal fractions
$18.7 - 1.87$
Subtract the two decimal fractions using written subtraction. You must insert an additional zero as a decimal place.
$\begin{array}{l} 1 \overset{7}{8} . \overset{\overset{16}{6}}{7} \overset{10}{0} \\ - 1. 8 7 \\ 1 6. 8 3 \end{array}$
Alternative way
Convert into decimal fractions.
$18.7 - 1.87$ $=$ $\frac{1870}{100} - \frac{187}{100}$
↓
Subtract fractions.
$=$ $\frac{1683}{100}$
↓
Convert into a decimal number.
$=$ $16.83$
$1.2 \cdot 0.12$

For this task you need the following basic knowledge: Multiplying decimal fractions
$1.2 \cdot 0.12$
Apply written multiplication to the decimal fractions.
$\begin{array}{r} 1.2 \cdot 0.12 \\ 24 \\ 120 \\ 0.144 \end{array}$
Alternative way
Convert into decimal fractions.
$1.2 \cdot 0.12$ $=$ $\frac{12}{10} \cdot \frac{12}{100}$
↓
Multiply the fractions.
$=$ $\frac{144}{1000}$
↓
Convert into a decimal number.
$=$ $0.144$
$0.8 : 0.32$

For this task you need the following basic knowledge: Division of decimal fractions
$0.8 : 0.32 = 80 : 32$
Multiplying by 100 in the denominator and the enumerator does not change the value of the fraction. Use the written division.
$\begin{array}{l} 80 : 32 = 2.5 \\ - 64 \\ 160 \\ - 160 \\ 0 \end{array}$
Alternative way
$0.8 : 0.32$ $=$
↓
Form a fraction.
$=$ $\frac{\frac{8}{10}}{\frac{32}{100}}$
↓
Divide by $\frac{32}{100}$ .
$=$ $\frac{8}{10} \cdot \frac{100}{32}$
↓
Multiply by the reciprocal fraction.

$=$ $\frac{800}{320}$
↓
Convert into a decimal number.
$=$ $2.5$

$0.32 : 0.6$

$0.5 3$
$5. 3$
1.875

$0.0123 : 1000$

For this task you need the following basic knowledge: Decimal fractions
$0.0123 : 1000$
When dividing by 1000, the decimal point is shifted by 3 places to the left.
$= 0.0000123$
Alternative way
$0.0123 : 1000$ $=$
↓
Convert into fractions.
$=$ $\frac{\frac{123}{10000}}{\frac{1000}{1}}$
↓
Divide by $\frac{1000}{1}$ .
$=$ $\frac{123}{10000} \cdot \frac{1}{1000}$
↓
Multiply by the reciprocal fraction.

$=$ $\frac{123}{10000000}$
↓
Convert into a decimal number.
$=$ $0.0000123$
$0.0123 \cdot 100$

For this task you need the following basic knowledge: Decimal fractions
$0.0123 \cdot 100$
When multiplying by 100, move the decimal point two places to the right.
$= 1.23$
Alternative way
$0.0123 \cdot 100$ $=$
↓
Convert the decimal numbers into fractions.
$=$ $\frac{123}{10000} \cdot \frac{100}{1}$
↓
Multiply the fractions.
$=$ $\frac{12300}{10000}$
↓
Shorten the fractions.
$=$ $1.23$

$5.5 \cdot 0.12 : 0.1$

$(2.08 + 9.2) - 6.99$

$(9 \cdot 0.8 - 0.70) : (0.6 + 0.5)$

$5. 90$
$0.0 18$
$0. 81$

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$17.17 + 0.3$	$=$	$\frac{1717}{100} + \frac{30}{100}$
	↓	Add the fractions.
	$=$	$\frac{1747}{100}$
	↓	Convert into a decimal number.
	$=$	$17.47$

$18.7 - 1.87$	$=$	$\frac{1870}{100} - \frac{187}{100}$
	↓	Subtract fractions.
	$=$	$\frac{1683}{100}$
	↓	Convert into a decimal number.
	$=$	$16.83$

$1.2 \cdot 0.12$	$=$	$\frac{12}{10} \cdot \frac{12}{100}$
	↓	Multiply the fractions.
	$=$	$\frac{144}{1000}$
	↓	Convert into a decimal number.
	$=$	$0.144$

$0.8 : 0.32$	$=$
	↓	Form a fraction.
	$=$	$\frac{\frac{8}{10}}{\frac{32}{100}}$
	↓	Divide by $\frac{32}{100}$ .
	$=$	$\frac{8}{10} \cdot \frac{100}{32}$
	↓	Multiply by the reciprocal fraction.
	$=$	$\frac{800}{320}$
	↓	Convert into a decimal number.
	$=$	$2.5$

$0.32 : 0.6$	$=$	$\frac{\frac{32}{100}}{\frac{60}{100}}$
	↓	Convert the decimal numbers into fractions.
	$=$	$\frac{32}{100} \cdot \frac{100}{60}$
	↓	Multiply by the reciprocal fraction.
	$=$	$\frac{3200}{6000}$
	↓	Shorten by 100.
	$=$	$\frac{8}{15}$
	↓	You may still be able to convert the fraction to a periodic decimal fraction.
	$=$	$0.5 3$

$0.0123 : 1000$	$=$
	↓	Convert into fractions.
	$=$	$\frac{\frac{123}{10000}}{\frac{1000}{1}}$
	↓	Divide by $\frac{1000}{1}$ .
	$=$	$\frac{123}{10000} \cdot \frac{1}{1000}$
	↓	Multiply by the reciprocal fraction.
	$=$	$\frac{123}{10000000}$
	↓	Convert into a decimal number.
	$=$	$0.0000123$

$0.0123 \cdot 100$	$=$
	↓	Convert the decimal numbers into fractions.
	$=$	$\frac{123}{10000} \cdot \frac{100}{1}$
	↓	Multiply the fractions.
	$=$	$\frac{12300}{10000}$
	↓	Shorten the fractions.
	$=$	$1.23$

$5.5 \cdot 0.12 : 0.1$	$=$
	↓	Convert into fractions.
	$=$	$\frac{\frac{550}{100} \cdot \frac{12}{100}}{\frac{10}{100}}$
	↓	Divide by $\frac{10}{100}$ .
	$=$	$\frac{550}{100} \cdot \frac{12}{100} \cdot \frac{100}{10}$
	↓	Multiply the fractions.
	$=$	$\frac{660000}{100000}$
	↓	Shorten the fraction.
	$=$	$\frac{66}{10}$
	↓	Convert into a decimal number.
	$=$	$6.6$

$(2.08 + 9.2) - 6.99$	$=$
	↓	First, compute $2.08 + 9.2$ .
	$=$	$11.28 - 6.99$
	$=$	$4.29$

$(2.08 + 9.2) - 6.99$	$=$
	↓	Convert the decimal numbers into fractions.
	$=$	$\frac{208}{100} + \frac{92}{10} - \frac{699}{100}$
	↓	Get everything on a common denominator.
	$=$	$\frac{208}{100} + \frac{920}{100} - \frac{699}{100}$
	↓	Compute.
	$=$	$\frac{429}{100}$
	↓	Convert into a decimal number.
	$=$	$4.29$

$(9 \cdot 0.8 - 0.70) : (0.6 + 0.5)$	$=$
	↓	Pay special attention to the operator hierarchy. Calculate first $9 \cdot 0.8$ .
	$=$	$(7.2 - 0.70) : (0.6 + 0.5)$
	↓	Add/subtract the numbers in the parentheses.
	$=$	$6.5 : 1.1$
	↓	The value does not change when the numerator and denominator are multiplied by 10. Now use the written method of division.
	$=$	$65 : 11$

$(9 \cdot 0.8 - 0.70) : (0.6 + 0.5)$	$=$
	↓	Convert decimal numbers into fractions.
	$=$	$(\frac{9}{1} \cdot \frac{8}{10} - \frac{70}{100}) : (\frac{6}{10} + \frac{5}{10})$
	↓	Multiply and add the fractions.
	$=$	$(\frac{72}{10} - \frac{70}{100}) : \frac{11}{10}$
	↓	Get everything on a common denominator; subtract.
	$=$	$(\frac{720 - 70}{100}) : \frac{11}{10}$
	↓	Divide the fractions.
	$=$	$\frac{650}{100} \cdot \frac{10}{11}$
	$=$	$\frac{6500}{1100}$
	↓	Shorten the fraction.
	$=$	$\frac{65}{11}$
	↓	You may still convert the fraction into a periodic decimal number.
	$=$	$5. 90$

Exercises: decimal numbers (mixed)

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