WGU; D771; Objective; Assessment; (Latest; 2025/; 2026; Update); Quantitative; Literacy; Guide|; Q/A; |; Grade; A|; 100%; Correct; (Verified; Answers)
Most; everyday; numbers; involve; units.; A; unit; relates; a; value; to; a; specific; quantity; of; a; thing,; as; in; 90; minutes:; 90; is; a; value,; while; 90; minutes; is; a; specific; quantity; of; a; thing; (minutes).; Units; often; are; objects; like; people; or; cars,; or; ; measurements; like; inches; or; ; pounds.A; ratio; relates; two; amounts,; as; in; 1; adult; per; 4; babies,; written; as; 1/4.; Ex:; California; daycare; ; law; requires; 1; staff; person; for; ; every; 4; babies.; Many; real-; life; problems; involve; maintaining; a; ratio.To; multiply; two; fractions,; you; simply; multiply; the; numerators; (the; top; numbers); together; and; the; denominators; (the; bottom; numbers); together.; For; example,; to; multiply; 2/3; by; 4/5,; you; multiply; 2; by; 4; to; get; 8,; and; 3; by; 5; to; get; 15,; resulting; in; 8/15.; If; the; product; can; be; simplified; by; dividing; both; the; numerator; and; denominator; by; a; common; factor,; do; so; to; get; the; simplest; form.; This; method; works; for; ; multiplying; more; than; two; fractions; as; well;; just; multiply; all; the; numerators; together; and; all; the; denominators; together.; Remember,; multiplying; fractions; is; different; from; adding; or; subtracting; them,; where; you; need; a; common; denominator.
Ratios; and; fractions; are; not; the; same; thing.; A; fraction; is; a; single; quantity; that; expresses; part; of; a; whole,; like; 1/4; of; a; pizza.; A; ratio; compares; two; quantities,; like; 1; adult; per; 4; babies.; The; reason; ratios; and; fractions; use; the; same; notation; 1/4; is; because; in; all; math; procedures,; like; expanding; and; reducing,; ratios; and; fractions; behave; the; same.Ratios; are; spoken; differently; than; fractions,; usually; saying; "one; to; four",; in; contrast; to; "one; fourth"; for; ; a; fraction.; A; person; would; need; to; know; the; context; of; 1/4; to; know; how; to; speak; 1/4:; If; referring; to; staff; per; babies; (a; ratio),; a; person; would; speak; 1/4; as; "one; to; four".; But; if; referring; to; the; amount; of; pizza; remaining; (a; fraction),; a; person; would; speak; 1/4; as; "one; fourth". 1 / 4
The; vision; benchmark; ; is; the; ratio; 20/20,; spoken; simply; as; "twenty; twenty".; Jay; having 20/20; vision; means; ; that; what; Jay; can; see; clearly; from; 20; feet; away,; another; person; with 20/20; vision; also; sees; clearly; from; 20; feet; away.; However,; Nik; having; 20/100; vision; means; that; what; Nik; can; see; clearly; from; 20; feet; away,; a; person; with; 20/20; vision; sees; clearly; from; 100; feet; away.A; rate; is; a; word; sometimes; used; for; ; a; ratio; that; relates; values; with; different; units,; such; as; portable; restrooms; per; person.; Ex:; A; half-day; outdoor; event; requires; about; 9; portable; restrooms; per; 1,000; people,; which; is; written; as; (9; restrooms); /; (1000; people),; spoken; as; "9; restrooms; per; 1,000; people".; Commonly-used; rates; ; are; "miles; per; hour",; "miles; per; gallon",; and; "cost; per; item".
Example:
A; portable; restroom; guideline; says; 9; restrooms; are; needed; per; 1000; people,; written; as;
9/1000.
How; ; many; portable; restrooms; for; ; 3000; people?; The; ratio; should; equal 9/1000.; Expanding; 1000; to; 3000; requires; multiplying; by; 3.Expanding; 9/1000; to; 3000ths; ; requires; multiplying; by; 3/3,; yielding; 27/3000.; The; ratio; is; maintained:; 27/3000; reduces; ; to; 9/1000; (by; dividing; the; top; and; bottom; by; 3).In; practice,; the; distinction; between; ratio; and; rate; can; be; blurry.; A; daycare; center's; staff; to; baby; requirement; is; typically; called; a; ratio; because; staff; and; babies; are; considered; to; be; the; same; units:; humans.; But; a; person; can; view; staff; and; babies; as; different; units.; Conversely,; many; people; use; the; word; ratio; even; when; units; are; different.; Ultimately,; the; concept,; not; the; word,; is; likely; the; most; important; thing.Rates; are; commonly; used; for; ; comparisons,; especially; costs.; Especially; common; is; comparing; prices; for; ; grocery; items.; Unit; price; is; the; price; for one; "unit"; of; an; item,; typically; a; grocery; item,; such; as; one; ounce; of; cereal; or; one; roll; ; of; paper; towels.
Example:
People; often; compare; rates; when; purchasing; items.; A; 2-pack; of; paper; towel; rolls; is; $3,; so; (3; dollars)/(2; rolls).; A; 3-pack; is; $4,; so; (4; dollars)/(3; rolls).; Which; is; a; better; deal?The; rates; ; can; be; reduced; so; the; bottom; of; each; rate; is; 1,; to; enable; easy; comparison.; For; ; (3; dollars)/(2; rolls),; dividing; the; top; and; bottom; by; 2; yields; (1.50; dollars)/(1; roll).
- / 4
For; ; (4; dollars)/(3; rolls),; dividing; the; top; and; bottom; by; 3; yields; (1.33; dollars)/(1; roll),; which; is; less; than; (1.50; dollars)/(1; roll).; So; ; (4; dollars)/(3; rolls); is; a; better; deal.Reducing; so; the; bottom; is; 1; is; the; same; as; just; dividing; the; top; by; the; bottom.; 3/2; =; 1.50,; and; 4/3; =; 1.33.; The; units; remain; as; dollars/roll.; Called:; Unit; price.People; deal; with; rates; when; travelling; to; other; countries; and; exchanging; money,; like; exchanging; dollars; for; ; euros.
Example:
Joe; arrives; in; Europe; and; wants; 200; euros.; TravelEz's; "We; buy"; column; means; ; TravelEz; buys; dollars; at; a; rate; of; (1.8; dollars)/(1; euro).Expanding; is; done; by; multiplying; by; 200/200,; so; 1.8; ×; 200; =; 360; dollars.; When; leaving,; Joe; wants; to; exchange; 50; euros; for; ; dollars.; TravelEz; sells dollars; for; ; (1.4; dollars)/(1; euro).; Expanding; is; done; by; multiplying; by; 50/50, so; 1.4; ×; 50; =; 70; dollars.Rates; are; commonly; used; when; the; bottom; item; involves; time,; as; in; miles; per; hour; or; ; gallons; per; minute.
Example:
This; pool,; costing; a; mere; $60,; requires; almost; no; ; setup; beyond; inflating; the; ring; at; the; top,; then; filling; with; water.; How; ; many; minutes; are; needed; to; fill; the; pool?A; garden; hose; outputs; water; at; a; rate; of; 20; gallons; per; 1; minute,; so; 20/1.; The; pool; specs; say; the; pool; holds; about; 1,000; gallons.So; ; if; 20; gallons; are; filled; in; 1; minute,; 1000; gallons; fill; in; ?; minutes.; 20/1; can; be; expanded; by; multiplying; by; 50/50; to; 1000/50.20; gallons; require; 1; minute,; so; 1000; gallons; require; 50; minutes.; 1000/50; reduces; to; 20/1;; the; rates; are; the; same.People; often; download; movies; to; a; tablet; or; ; laptop; before; a; trip.; Commonly,; time; is; tight,; and; a; person; wonders; if; the; download; will; complete; before; the; person; has; to; leave.; While; some; downloads; estimate; the; time; remaining,; many; just; indicate; the; download; rate; and; percent; completed.; A; person; can; use; the; percent; information; and; time; taken; so; far; to; estimate; the; total; time.
Example:
A; movie; download; started; 10; minutes; ago; and; has; downloaded; 20%.; How; much; longer?A; person; can; estimate; using; rates.; If; 10; minutes; downloaded; 20%,; how; many; minutes; to; download; 100%?; 20; ×; 5; =; 100,; so; 10; ×; 5; =; 50; minutes.50; min; is; the; total; time.; As; 10; min; has; ; already; passed,; the; remaining; time; is 40; min.Alternatively,; a; person; can; set; up; the; rates; for; ; the; remaining; %.; ; If; 10; min; downloaded; 20%,; how; many; more; minutes; to; download; the; remaining; 80%?The; expansion; is; with; 4/4,; so; 10; min; ×; 4; =; 40; min.; Intuitively,; 80%; is; 4 20%'s,; so; 4; more; 10-min; periods; must; pass,; or; ; 40; min. 3 / 4
A; unit; conversion; problem; is; a; problem; that; can; be; solved; by; converting; a; value; from; one; unit; (like; minutes); to; another; unit; (like; hours)
Example:
Lee; needs; to; go; to; bed; in; 2; hours,; so; seeks; a; movie; under; 2; hours.; A; 90; min; movie; is; 1.5; hours; so; is; OK.; A; 180; min; movie; is; 3; hours; so; too; long.Mia; wonders; if; she; must; stop; for; ; gas; if; driving; from; Los; Angeles; to; Phoenix.; Her; car; has; a; 10; gallon; tank; and; gets; 30; mpg,; so; goes; only; 300; miles.; She'll; have; to; stop.Pat; wonders; how; many; pizzas; are; needed; for; ; 8; kids.; If; each; kid; eats; 4; slices,; and; a; pizza; has; 16; slices,; 2; pizzas; are; needed.Each; example; is; a; unit; conversion; problem:; From; min; to; hours,; tanks; to; miles,; and; kids; to; pizzas.
A; unit; conversion; problem; can; be; solved; by; multiplying; by; a; conversion; factor:; A; ratio; that; relates; two; units,; such; as; (60; min)/(1; hour).; Multiplying; by; a; conversion; factor; is; akin; to; multiplying; by; 1,; because; 60; minutes; and; 1 hour; are; the; same; quantity.; Multiplying; by; 1; doesn't; change; a; quantity,; so; the; ending; quantity; equals; the; starting; quantity,; in; different; units.A; unit; appearing; on; the; top; and; bottom; of; an; expression; "cancels".; The; problem; is; solved; by; multiplying; by; unit; conversion; factors; so; the; ending; units; are; the; desired; units.
Example:
A; movie; is; 150; min.; How; ; many; hours; is; the; movie?; The; starting; quantity; is 150; minutes.1; hour; and; 60; minutes; are; the; same; quantity,; so; a; conversion; factor; is; (1; hour)/(60; ; min).; Multiplying; by; that; ; factor; is; like; multiplying; by; 1,; which; doesn't; change; the; quantity.The; minutes; cancel,; so; the; remaining; units; will; be; hours.; 150; min; ×; (1; hour)/(60; min); is; 150; times; 1,; divided; by; 60,; so; 2.5; hours.Sometimes,; several; conversion; factors; must; be; used; until; the; desired; units; are; obtained.
Example:
Starting; quantity; is; 24; hours.; Goal; is; to; convert; to; seconds.A; person; can; multiply; by; a; conversion; factor,; like; (60; min)/(1; hour),; such; that; units; cancel.A; person; can; multiply; by; more; conversion; factors; until; the; desired; units; remain.; Here,; min; can; be; converted; to; sec; via; (60; sec)/(1; min).The; ending; units; are; sec.; The; calculation; yields; 24; ×; 60; ×; 60; =; 86,400; sec.; Again,; the; conversion; factors; need; not; be; universal; factors; that; are; always true,; but; can; be; for; ; a; particular; instance,; like; a; car; that; drives; 25; miles; on; 1 gallon; of; gas,; and; gas; that; costs; 5; dollars; for; ; 1; gallon.; Example: Start; is; 400; miles.; That; quantity; should; be; converted; into; dollars.A; person; can; multiply; by; a; conversion; factor,; like; (1; gal)/(25; miles); for; ; a; car; that; gets; 25; miles-per-gallon,; such; that; units; cancel.
- / 4