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Simplify: 7 8 + 6.4 .

Solution

7 8 + 6.4
Change 7 8 to a decimal. . 0.875 + 6.4
Add. 7.275
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Simplify: 3 8 + 4.9 .

5.275

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Simplify: 5.7 + 13 20 .

6.35

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Order decimals and fractions

In Decimals , we compared two decimals and determined which was larger. To compare a decimal to a fraction, we will first convert the fraction to a decimal and then compare the decimals.

Order 3 8 __ 0.4 using < or >.

Solution

3 8 __ 0.4
Convert 3 8 to a decimal. 0.375 __ 0.4
Compare 0.375 to 0.4 0.375 < 0.4
Rewrite with the original fraction. 3 8 < 0.4
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Order each of the following pairs of numbers, using < or >.

17 20 __ 0.82

>

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Order each of the following pairs of numbers, using < or >.

3 4 __ 0.785

<

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When ordering negative numbers, remember that larger numbers are to the right on the number line and any positive number is greater than any negative number.

Order −0.5 ___ 3 4 using < or >.

Solution

−0.5 ___ 3 4
Convert 3 4 to a decimal. −0.5 ___ −0.75
Compare −0.5 to −0.75 . −0.5 > −0.75
Rewrite the inequality with the original fraction. −0.5 > 3 4
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Order each of the following pairs of numbers, using < or >:

5 8 __ −0.58

<

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Order each of the following pairs of numbers, using < or >:

−0.53 __ 11 20

>

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Write the numbers 13 20 , 0.61 , 11 16 in order from smallest to largest.

Solution

13 20 , 0.61 , 11 16
Convert the fractions to decimals. 0.65 , 0.61 , 0.6875
Write the smallest decimal number first. 0.61 , ____ , _____
Write the next larger decimal number in the middle place. 0.61 , 0.65 , _____
Write the last decimal number (the larger) in the third place. 0.61 , 0.65 , 0.6875
Rewrite the list with the original fractions. 0.61 , 13 20 , 11 16
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Write each set of numbers in order from smallest to largest: 7 8 , 4 5 , 0.82 .

4 5 , 0.82 , 7 8

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Write each set of numbers in order from smallest to largest: 0.835 , 13 16 , 3 4 .

3 4 , 13 16 , 0.835

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Simplify expressions using the order of operations

The order of operations introduced in Use the Language of Algebra also applies to decimals. Do you remember what the phrase “Please excuse my dear Aunt Sally” stands for?

Simplify the expressions:

7 ( 18.3 21.7 )

2 3 ( 8.3 3.8 )

Solution

7 ( 18.3 21.7 )
Simplify inside parentheses. 7 ( −3.4 )
Multiply. −23.8
2 3 ( 8.3 3.8 )
Simplify inside parentheses. 2 3 ( 4.5 )
Write 4.5 as a fraction. 2 3 ( 4.5 1 )
Multiply. 9 3
Simplify. 3
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Simplify: 8 ( 14.6 37.5 ) 3 5 ( 9.6 2.1 ) .

  1. −183.2
  2. 4.5

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Simplify: 25 ( 25.69 56.74 ) 2 7 ( 11.9 4.2 ) .

  1. −776.25
  2. 2.2

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Simplify each expression:

6 ÷ 0.6 + ( 0.2 ) 4 ( 0.1 ) 2

( 1 10 ) 2 + ( 3.5 ) ( 0.9 )

Solution

6 ÷ 0.6 + ( 0.2 ) 4 ( 0.1 ) 2
Simplify exponents. 6 ÷ 0.6 + ( 0.2 ) 4 0.01
Divide. 10 + ( 0.2 ) 4 0.01
Multiply. 10 + 0.8 0.01
Add. 10.8 0.01
Subtract. 10.79
( 1 10 ) 2 + ( 3.5 ) ( 0.9 )
Simplify exponents. 1 100 + ( 3.5 ) ( 0.9 )
Multiply. 1 100 + 3.15
Convert 1 100 to a decimal. 0.01 + 3.15
Add. 3.16
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Simplify: 9 ÷ 0.9 + ( 0.4 ) 3 ( 0.2 ) 2 .

11.16

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Simplify: ( 1 2 ) 2 + ( 0.3 ) ( 4.2 ) .

1.51

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Find the circumference and area of circles

The properties of circles have been studied for over 2,000 years. All circles have exactly the same shape, but their sizes are affected by the length of the radius , a line segment from the center to any point on the circle. A line segment that passes through a circle’s center connecting two points on the circle is called a diameter . The diameter is twice as long as the radius. See [link] .

The size of a circle can be measured in two ways. The distance around a circle is called its circumference .

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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