- 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
Inside Collection (Textbook): Fundamentals of Mathematics
Summary: 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.
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.
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.
Simplify 19 in.
Since
Simplify 4 gal 5 qt.
Since
Simplify 2 hr 75 min.
Since
Simplify 43 fl oz.
Since
But,
But,
Simplify each denominate number. Refer to the conversion tables given in (Reference), if necessary.
18 in.
1 ft 6 in.
8 gal 9 qt
10 gal 1 qt
5 hr 80 min
6 hr 20 min
8 wk 11 da
9 wk 4 da
86 da
12 wk 2 da
Denominate numbers can be added or subtracted by:
Add 6 ft 8 in. to 2 ft 9 in.
Since
Subtract 5 da 3 hr from 8 da 11 hr.
Subtract 3 lb 14 oz from 5 lb 3 oz.
We cannot directly subtract 14 oz from 3 oz, so we must borrow 16 oz from the pounds.
Subtract 4 da 9 hr 21 min from 7 da 10 min.
Perform each operation. Simplify when possible.
Add 4 gal 3 qt to 1 gal 2 qt.
6 gal 1 qt
Add 9 hr 48 min to 4 hr 26 min.
14 hr 14 min
Subtract 2 ft 5 in. from 8 ft 7 in.
6 ft 2in.
Subtract 15 km 460 m from 27 km 800 m.
12 km 340 m
Subtract 8 min 35 sec from 12 min 10 sec.
3 min 35 sec
Add 4 yd 2 ft 7 in. to 9 yd 2 ft 8 in.
14 yd 2 ft 3 in
Subtract 11 min 55 sec from 25 min 8 sec.
13 min 13 sec
Let's examine the repeated sum
Recalling that multiplication is a description of repeated addition, by the distributive property we have
From these observations, we can suggest the following rule.
To multiply a denominate number by a whole number, multiply the number part of each unit by the whole number and affix the unit to this product.
Perform the following multiplications. Simplify if necessary.
Since
Perform the following multiplications. Simplify.
20 min
To divide a denominate number by a whole number, divide the number part of each unit by the whole number beginning with the largest unit. Affix the unit to this quotient. Carry any remainder to the next unit.
Perform the following divisions. Simplify if necessary.
Thus
Thus
Perform the following divisions. Simplify if necessary.
2 hr 4 min
4 hr 16 min
2 yd 1 ft 11 in
15 gal 3 qt 1 pt
For the following 15 problems, simplify the denominate numbers.
16 in.
1 foot 4 inches
19 ft
85 min
1 hour 25 minutes
90 min
17 da
2 weeks 3 days
25 oz
240 oz
15 pounds
3,500 lb
26 qt
6 gallons 2 quarts
300 sec
135 oz
8 pounds 7 ounces
14 tsp
18 pt
2 gallons 1 quart
3,500 m
16,300 mL
16 liters 300 milliliters (or 1daL 6 L 3dL)
For the following 15 problems, perform the indicated operations and simplify the answers if possible.
Add 6 min 12 sec to 5 min 15 sec.
Add 14 da 6 hr to 1 da 5 hr.
15 days 11 hours
Add 9 gal 3 qt to 2 gal 3 qt.
Add 16 lb 10 oz to 42 lb 15 oz.
59 pounds 9 ounces
Subtract 3 gal 1 qt from 8 gal 3 qt.
Subtract 3 ft 10 in. from 5 ft 8 in.
1 foot 10 inches
Subtract 5 lb 9 oz from 12 lb 5 oz.
Subtract 10 hr 10 min from 11 hr 28 min.
1 hour 18 minutes
Add 3 fl oz 1 tbsp 2 tsp to 5 fl oz 1 tbsp 2 tsp.
Add 4 da 7 hr 12 min to 1 da 8 hr 53 min.
5 days 16 hours 5 minutes
Subtract 5 hr 21 sec from 11 hr 2 min 14 sec.
Subtract 6 T 1,300 lb 10 oz from 8 T 400 lb 10 oz.
1 ton 1,100 pounds (or 1T 1,100 lb)
Subtract 15 mi 10 in. from 27 mi 800 ft 7 in.
Subtract 3 wk 5 da 50 min 12 sec from 5 wk 6 da 20 min 5 sec.
2 weeks 23 hours 29 minutes 53 seconds
Subtract 3 gal 3 qt 1 pt 1 oz from 10 gal 2 qt 2 oz.
((Reference)) Find the value:
1
((Reference)) Find the sum:
((Reference)) Convert
((Reference)) An acid solution is composed of 3 parts acid to 7 parts water. How many parts of acid are there in a solution that contains 126 parts water?
((Reference)) Convert 126 kg to grams.
126,000 g
"Used as supplemental materials for developmental math courses."