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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to simplify denominate numbers. By the end of the module students should be able to convert an unsimplified unit of measure to a simplified unit of measure, be able to add and subtract denominate numbers and be able to multiply and divide a denominate number by a whole number.

Section overview

  • Converting to Multiple Units
  • Adding and Subtracting Denominate Numbers
  • Multiplying a Denominate Number by a Whole Number
  • Dividing a Denominate Number by a Whole Number

Converting to multiple units

Denominate numbers

Numbers that have units of measure associated with them are called denominate numbers . It is often convenient, or even necessary, to simplify a denominate number.

Simplified denominate number

A denominate number is simplified when the number of standard units of measure associated With it does not exceed the next higher type of unit.

The denominate number 55 min is simplified since it is smaller than the next higher type of unit, 1 hr. The denominate number 65 min is not simplified since it is not smaller than the next higher type of unit, 1 hr. The denominate number 65 min can be simplified to 1 hr 5 min. The denominate number 1 hr 5 min is simplified since the next higher type of unit is day, and 1 hr does not exceed 1 day.

Sample set a

Simplify 19 in.

Since 12   in . = 1 ft size 12{"12"" in" "." ="1 ft"} {} , and 19 = 12 + 7 size 12{"19"="12"+7} {} ,

19 in. = 12 in. + 7 in. = 1 ft + 7 in. = 1 ft 7 in.

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Simplify 4 gal 5 qt.

Since 4   qt = 1 gal size 12{4" qt"="1 gal"} {} , and 5 = 4 + 1 size 12{5=4+1} {} ,

4 gal 5 qt = 4 gal + 4 qt + 1qt = 4 gal + 1 gal + 1 qt = 5 gal + 1 qt = 5 gal 1 qt

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Simplify 2 hr 75 min.

Since 60 min = 1 hr size 12{"60 min "="1 hr"} {} , and 75 = 60 + 15 size 12{"75"="60"+"15"} {} ,

2 hr 75 min = 2 hr + 60 min + 15 min = 2 hr + 1 hr + 15 min = 3 hr + 15 min = 3 hr 15 min

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Simplify 43 fl oz.

Since 8 fl oz = 1 c size 12{"8 fl oz"="1 c"} {} (1 cup), and 43 ÷ 8 = 5 R3 size 12{"43" div 8=5" R3"} {} ,

43 fl oz = 40 fl oz + 3 fl oz = 5 8 fl oz + 3 fl oz = 5 1 c + 3 fl oz = 5 c + 3 fl oz

But, 2 c = 1 pt size 12{"2 c"="1 pt"} {} and 5 ÷ 2 = 2 R1 size 12{5 div 2=2" R1"} {} . So,

5 c + 3 fl oz = 2 2 c + 1 c + 3 fl oz = 2 1 pt + 1 c + 3 fl oz = 2 pt + 1 c + 3 fl oz

But, 2 pt = 1 qt size 12{"2 pt"="1 qt"} {} , so

2 pt + 1 c + 3 fl oz = 1 qt 1 c 3 fl oz size 12{"1 pt "+" 1 c "+" 3 fl oz"=" 1 qt 1 c 3 fl oz"} {}

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Practice set a

Simplify each denominate number. Refer to the conversion tables given in [link] , if necessary.

Adding and subtracting denominate numbers

Adding and subtracting denominate numbers

Denominate numbers can be added or subtracted by:
  1. writing the numbers vertically so that the like units appear in the same column.
  2. adding or subtracting the number parts, carrying along the unit.
  3. simplifying the sum or difference.

Sample set b

Add 6 ft 8 in. to 2 ft 9 in.

6 ft  8 in . + 2 ft  9 in . ̲ 8 ft 17 in . Simplify this denominate number. alignr { stack { size 12{"6 ft 8 in" "." } {} #size 12{ {underline {+"2 ft 9 in" "." }} } {} # size 12{"8 ft 17 in" "." } {}} } {}

Since 12 in . = 1 ft size 12{"12 in" "." =" 1 ft"} {} ,

8 ft + 12 in. + 5 in. = 8 ft + 1 ft + 5 in. = 9 ft + 5 in. = 9 ft 5 in.

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Subtract 5 da 3 hr from 8 da 11 hr.

8 da 11 hr - 5 da   3 hr ̲ 3 da   8 hr alignr { stack { size 12{"8 da 11 hr"} {} #size 12{ {underline {"-5 da 3 hr"}} } {} # size 12{"3 da 8 hr"} {}} } {}

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Subtract 3 lb 14 oz from 5 lb 3 oz.

5 lb   3 oz - 3 lb 14 oz ̲ alignr { stack { size 12{"5 lb 3 oz"} {} #size 12{ {underline {"-3 lb 14 oz"}} } {} } } {}

We cannot directly subtract 14 oz from 3 oz, so we must borrow 16 oz from the pounds.

5 lb 3 oz = 5 lb + 3 oz = 4 lb + 1 lb + 3 oz = 4 lb + 16 oz + 3 oz ( Since 1 lb = 16 oz. ) = 4 lb + 19 oz = 4 lb 19 oz

4 lb 19 oz - 3 lb 14 oz ̲ 1 lb   5 oz alignr { stack { size 12{"4 lb 19 oz"} {} #size 12{ {underline {"-3 lb 14 oz"}} } {} # size 12{"1 lb 5 oz"} {}} } {}

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Subtract 4 da 9 hr 21 min from 7 da 10 min.

7 da 0 hr 10 min - 4 da 9 hr 21 min ̲ alignr { stack { size 12{"7 da 0 hr 10 min"} {} #size 12{ {underline {"-4 da 9 hr 21 min"}} } {} } } {} Borrow 1 da from the 7 da.

6 da 24 hr 10 min - 4 da   9 hr 21 min ̲ alignr { stack { size 12{"6 da 24 hr 10 min"} {} #size 12{ {underline {"-4 da 9 hr 21 min"}} } {} } } {} Borrow 1 hr from the 24 hr.

6 da 23 hr 70 min - 4 da   9 hr 21 min ̲ 2 da 14 hr 49 min alignr { stack { size 12{"6 da 23 hr 70 min"} {} #size 12{ {underline {"-4 da 9 hr 21 min"}} } {} # size 12{"2 da 14 hr 49 min"} {}} } {}

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Questions & Answers

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The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
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1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
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Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
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Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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