# Making Unit Conversions in the U.S. System of Measurement

### Learning Outcomes

- Make unit conversions in the U.S. system
- Use mixed units of measurement in the U.S. system

U.S. System Units | |
---|---|

Length |
Volume |

[latex]1[/latex] foot (ft) = [latex]12[/latex] inches (in) [latex]1[/latex] yard (yd) = [latex]3[/latex] feet (ft) [latex]1[/latex] mile (mi) = [latex]5280[/latex] feet (ft) | [latex]3[/latex] teaspoons (t) = [latex]1[/latex] tablespoon (T) [latex]16[/latex] Tablespoons (T) = [latex]1[/latex] cup (C) [latex]1[/latex] cup (C) = [latex]8[/latex] fluid ounces (fl oz) [latex]1[/latex] pint (pt) = [latex]2[/latex] cups (C) [latex]1[/latex] quart (qt) = [latex]2[/latex] pints (pt) [latex]1[/latex] gallon (gal) = [latex]4[/latex] quarts (qt) |

Weight |
Time |

[latex]1[/latex] pound (lb) = [latex]16[/latex] ounces (oz) [latex]1[/latex] ton = [latex]2000[/latex] pounds (lb) | [latex]1[/latex] minute (min) = [latex]60[/latex] seconds (s) [latex]1[/latex] hour (h) = [latex]60[/latex] minutes (min) [latex]1[/latex] day = [latex]24[/latex] hours (h) [latex]1[/latex] week (wk) = [latex]7[/latex] days [latex]1[/latex] year (yr) = [latex]365[/latex] days |

*from*divide out. For example, suppose we wanted to convert [latex]60[/latex] inches to feet. If we choose the fraction that has inches in the denominator, we can eliminate the inches. [latex-display]60\overline{)\text{in}}\cdot\Large\frac{\text{1 ft}}{12\overline{)\text{in}}}\normalsize=\text{5 ft}[/latex-display] On the other hand, if we wanted to convert [latex]5[/latex] feet to inches, we would choose the fraction that has feet in the denominator. [latex-display]\text{5 ft}\cdot\Large\frac{\text{12 in}}{1\overline{)\text{ft}}}\normalsize=\text{60 in}[/latex-display] We treat the unit words like factors and ‘divide out’ common units like we do common factors.

### Make unit conversions.

- Multiply the measurement to be converted by [latex]1[/latex]; write [latex]1[/latex] as a fraction relating the units given and the units needed.
- Multiply.
- Simplify the fraction, performing the indicated operations and removing the common units.

### example

Mary Anne is [latex]66[/latex] inches tall. What is her height in feet? SolutionConvert [latex]66[/latex] inches into feet. | |

Multiply the measurement to be converted by [latex]1[/latex]. | [latex]66[/latex] inches [latex]\cdot 1[/latex] |

Write [latex]1[/latex] as a fraction relating the units given and the units needed. | [latex]\text{66 inches}\cdot \Large\frac{\text{1 foot}}{\text{12 inches}}[/latex] |

Multiply. | [latex]\Large\frac{\text{66 inches}\cdot \text{1 foot}}{\text{12 inches}}[/latex] |

Simplify the fraction. | [latex]\Large\frac{66\overline{)\text{inches}}\cdot \text{1 foot}}{12\overline{)\text{inches}}}[/latex] |

[latex]\Large\frac{\text{66 feet}}{12}[/latex] | |

[latex]\text{5.5 feet}[/latex] |

### try it

[ohm_question]146826[/ohm_question] [ohm_question]146830[/ohm_question]### example

Ndula, an elephant at the San Diego Safari Park, weighs almost [latex]3.2[/latex] tons. Convert her weight to pounds. (credit: Guldo Da Rozze, Flickr)Answer: Solution We will convert [latex]3.2[/latex] tons into pounds, using the equivalencies in the table from earlier. We will use the Identity Property of Multiplication, writing [latex]1[/latex] as the fraction [latex]\Large\frac{\text{2000 pounds}}{\text{1 ton}}[/latex].

[latex]\text{3.2 tons}[/latex] | |

Multiply the measurement to be converted by [latex]1[/latex]. | [latex]\text{3.2 tons}\cdot 1[/latex] |

Write [latex]1[/latex] as a fraction relating tons and pounds. | [latex]\text{3.2 tons}\cdot\Large\frac{\text{2000 lbs}}{\text{1 ton}}[/latex] |

Simplify. | [latex]\Large\frac{3.2\overline{)\text{tons}}\cdot \text{2000 lbs}}{1\overline{)\text{ton}}}[/latex] |

Multiply. | [latex]\text{6400 lbs}[/latex] |

Ndula weighs almost [latex]6,400[/latex] pounds. |

### try it

[ohm_question]146831[/ohm_question] [ohm_question]146833[/ohm_question]### example

Juliet is going with her family to their summer home. She will be away for [latex]9[/latex] weeks. Convert the time to minutes.Answer: Solution To convert weeks into minutes, we will convert weeks to days, days to hours, and then hours to minutes. To do this, we will multiply by conversion factors of [latex]1[/latex].

[latex]\text{9 weeks}[/latex] | |

Write 1 as [latex]\Large\frac{7\text{days}}{1\text{week}}\normalsize ,\Large\frac{24\text{hours}}{1\text{day}}\normalsize ,\Large\frac{60\text{minutes}}{1\text{hour}}[/latex] . | [latex]\Large\frac{9 wk}{1}\normalsize\cdot\Large\frac{7 days}{1 wk}\normalsize\cdot\Large\frac{24 hr}{1 day}\normalsize\cdot\Large\frac{60 min}{1 hr}[/latex] |

Cancel common units. | [latex]\Large\frac{9 wk}{1}\normalsize\cdot\Large\frac{7\color{blue}{days}}{1 wk}\normalsize\cdot\Large\frac{24\color{red}{hr}}{1\color{blue}{day}}\normalsize\cdot\Large\frac{60 min}{1\color{red}{hr}}[/latex] |

Multiply. | [latex]\Large\frac{9\cdot 7\cdot 24\cdot 60\text{min}}{1\cdot 1\cdot 1\cdot 1}\normalsize =90,720\text{min}[/latex] |

Juliet will be away for [latex]90,720[/latex] minutes. |

### try it

The distance between Earth and the moon is about [latex]250,000[/latex] miles. Convert this length to yards.Answer: Solution To convert miles into yards, we will convert miles to feet and then feet to yards. To do this, we will multiply by conversion factors of [latex]1[/latex].

[latex]\text{250,000 miles}[/latex] | |

Write 1 as [latex]\Large\frac{5,280\text{feet}}{1\text{mile}}\normalsize ,\Large\frac{1\text{yard}}{3\text{feet}}\normalsize[/latex]. | [latex]\Large\frac{250,000 mi}{1}\normalsize\cdot\Large\frac{5,280 feet}{1 mi}\normalsize\cdot\Large\frac{1 yard}{3 feet}[/latex] |

Cancel common units. | [latex]\Large\frac{250,000\color{red}{mi}}{1}\normalsize\cdot\Large\frac{5,280\color{blue}{feet}}{1\color{red}{ mi}}\normalsize\cdot\Large\frac{1 yard}{3\color{blue}{feet}}[/latex] |

Multiply. | [latex]\Large\frac{250,000\cdot 5,280\cdot 1\text{yard}}{1\cdot 1\cdot 3}\normalsize =44,000,000\text{yard}[/latex] |

The distance between the earth and the moon is [latex]44,000,000[/latex] yards. |

Answer: Solution To convert weeks into minutes, we will convert weeks to days, days to hours, and then hours to minutes. To do this, we will multiply by conversion factors of [latex]1[/latex].

[latex]\text{15 weeks}[/latex] | |

Write 1 as [latex]\Large\frac{7\text{days}}{1\text{week}}\normalsize ,\Large\frac{24\text{hours}}{1\text{day}}\normalsize ,\Large\frac{60\text{minutes}}{1\text{hour}}[/latex] . | [latex]\Large\frac{15 wk}{1}\normalsize\cdot\Large\frac{7 days}{1 wk}\normalsize\cdot\Large\frac{24 hr}{1 day}\normalsize\cdot\Large\frac{60 min}{1 hr}[/latex] |

Cancel common units. | [latex]\Large\frac{15 \color{green}{wk}}{1}\normalsize\cdot\Large\frac{7\color{blue}{days}}{1 \color{green}{wk}}\normalsize\cdot\Large\frac{24\color{red}{hr}}{1\color{blue}{day}}\normalsize\cdot\Large\frac{60 min}{1\color{red}{hr}}[/latex] |

Multiply. | [latex]\Large\frac{15\cdot 7\cdot 24\cdot 60\text{min}}{1\cdot 1\cdot 1\cdot 1}\normalsize =151,200\text{min}[/latex] |

The astronauts will be in space for [latex]151,200[/latex] minutes. |

### example

How many fluid ounces are in [latex]1[/latex] gallon of milk? (credit: www.bluewaikiki.com, Flickr)Answer: Solution Use conversion factors to get the right units: convert gallons to quarts, quarts to pints, pints to cups, and cups to fluid ounces.

[latex]1[/latex] gallon | |

Multiply the measurement to be converted by 1. | [latex]\Large\frac{\text{1 gal}}{1}\normalsize\cdot\Large\frac{\text{4 qt}}{\text{1 gal}}\normalsize\cdot\Large\frac{\text{2 pt}}{\text{1 qt}}\normalsize\cdot\Large\frac{\text{2 C}}{\text{1 pt}}\normalsize\cdot\Large\frac{\text{8 fl oz}}{\text{1 C}}[/latex] |

Simplify. | [latex]\Large\frac{1\overline{)\text{gal}}}{1}\normalsize\cdot\Large\frac{4\overline{)\text{qt}}}{1\overline{)\text{gal}}}\normalsize\cdot\Large\frac{2\overline{)\text{pt}}}{1\overline{)\text{qt}}}\normalsize\cdot\Large\frac{2\overline{)\text{C}}}{1\overline{)\text{pt}}}\normalsize\cdot\Large\frac{\text{8 fl oz}}{1\overline{)\text{C}}}[/latex] |

Multiply. | [latex]\Large\frac{1\cdot 4\cdot 2\cdot 2\cdot \text{8 fl oz}}{1\cdot 1\cdot 1\cdot 1\cdot 1}[/latex] |

Simplify. | [latex]128[/latex] fluid ounces |

There are [latex]128[/latex] fluid ounces in a gallon. |

### try it

[ohm_question]146837[/ohm_question] How many teaspoons are in [latex]1[/latex] cup? [ohm_question]146838[/ohm_question]### Use Mixed Units of Measurement in the U.S. System

Performing arithmetic operations on measurements with mixed units of measures requires care. Be sure to add or subtract like units.### example

Charlie bought three steaks for a barbecue. Their weights were [latex]14[/latex] ounces, [latex]1[/latex] pound [latex]2[/latex] ounces, and [latex]1[/latex] pound [latex]6[/latex] ounces. How many total pounds of steak did he buy? (credit: Helen Penjam, Flickr)Answer: Solution We will add the weights of the steaks to find the total weight of the steaks.

Add the ounces. Then add the pounds. | |

Convert [latex]22[/latex] ounces to pounds and ounces. | |

Add the pounds. | [latex]2[/latex] pounds [latex]+1[/latex] pound, [latex]6[/latex] ounces [latex]3[/latex] pounds, [latex]6[/latex] ounces |

Charlie bought [latex]3[/latex] pounds [latex]6[/latex] ounces of steak. |

### try it

[ohm_question]146961[/ohm_question] [ohm_question]146962[/ohm_question]### example

Anthony bought four planks of wood that were each [latex]6[/latex] feet [latex]4[/latex] inches long. If the four planks are placed end-to-end, what is the total length of the wood?Answer: Solution We will multiply the length of one plank by [latex]4[/latex] to find the total length.

Multiply the inches and then the feet. | |

Convert [latex]16[/latex] inches to feet. | [latex]24[/latex] feet [latex]+1[/latex] foot [latex]4[/latex] inches |

Add the feet. | [latex]25[/latex] feet [latex]4[/latex] inches |

Anthony bought [latex]25[/latex] feet [latex]4[/latex] inches of wood. |

### try it

[ohm_question]146965[/ohm_question] [ohm_question]146970[/ohm_question]## Contribute!

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- Question ID 146970, 146965.
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### CC licensed content, Shared previously

- Examples: Converting Between Different Units of Lengths Using Standard or American System.
**Authored by:**James Sousa (mathispower4u.com).**License:**CC BY: Attribution. - Examples: Converting Between Different Units of Weight in Standard or American System.
**Authored by:**James Sousa (mathispower4u.com).**License:**CC BY: Attribution.

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- Prealgebra.
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