# Rates & Ratios

A ratio is a comparison of two numbers. A ratio can be written using a colon, $3:5$ , or as a fraction $\frac{3}{5}$ .

A rate , by contrast, is a comparison of two quantities which can have different units. For example $5$ miles per $3$ hours is a rate, as is $34$ dollars per square foot.

Example 1:

A punch recipe calls for $6$ ounces of lime juice, $21$ ounces of apricot juice, and $21$ ounces of pineapple juice. What is the ratio of lime juice to apricot juice?

Writing the ratio using a colon, we get $6:21$ .

Note that this can be reduced, like a fraction, by dividing both numbers by a common factor -- in this case, $3$ . In simplest form, the ratio is $2:7$ .

Example 2:

In the recipe above, what is the ratio of apricot juice to the total amount of punch?

To find the total amount of punch, add $6+21+21=48$ .

The ratio of apricot juice to the total amount of punch is $21:48$ . But this ratio is probably more clearly written as a fraction, since the apricot juice makes up a fraction of the whole.

$\frac{21}{48}$

To reduce the fraction, divide both the numerator and the denominator by $3$ .

$\frac{7}{16}$

Note that this can be reduced, like a fraction, by dividing both numbers by a common factor -- in this case, $3$ . In simplest form, the ratio is $2:7$ .

Example 3:

An adult scolopendromorph centipede has $46$ legs and $8$ eyes. In a group of $100$ centipedes of the same species, what is the ratio of legs to eyes?

Note that it doesn't matter if there are $100$ or $10,000$ centipedes; the ratio of legs to eyes will remain the same.

Writing the ratio using a colon, we get $46:8$ .

Divide both numbers by $2$ . In simplest form, the ratio of legs to eyes is $23:4$ .

Example 4:

A bat beats its wings $170$ times in $10$ seconds. Write the rate as a fraction in lowest terms.

Write the rate as a fraction.

$\frac{170\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{wingbeats}}{10\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{seconds}}$

Divide both the numerator and the denominator by ten.

$=\frac{17\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{wingbeats}}{1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{second}}$

So, the rate is $17$ beats per second.

Example 5:

A mountain climber is $3200$ meters from the peak. He climbs $50$ meters per hour for $8$ hours per day. How many days will it be before he reaches the peak?

The first job is to figure out the rate per day.

$\frac{50\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{meters}}{1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{hour}}\cdot \frac{8\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{hours}}{1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{day}}=50\left(8\right)\frac{\text{meters}}{\text{day}}$

$=400\frac{\text{meters}}{\text{day}}$

He is climbing at a rate of $400$ meters per day.

Now divide $3200$ by the daily rate to find the number of days it will take him to reach the top.

$\frac{3200\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{meters}}{400\frac{\text{meters}}{\text{day}}}=8\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{days}$

d:T2038,

# Rates & Ratios

A ratio is a comparison of two numbers. A ratio can be written using a colon, $3:5$ , or as a fraction $\frac{3}{5}$ .

A rate , by contrast, is a comparison of two quantities which can have different units. For example $5$ miles per $3$ hours is a rate, as is $34$ dollars per square foot.

Example 1:

A punch recipe calls for $6$ ounces of lime juice, $21$ ounces of apricot juice, and $21$ ounces of pineapple juice. What is the ratio of lime juice to apricot juice?

Writing the ratio using a colon, we get $6:21$ .

Note that this can be reduced, like a fraction, by dividing both numbers by a common factor -- in this case, $3$ . In simplest form, the ratio is $2:7$ .

Example 2:

In the recipe above, what is the ratio of apricot juice to the total amount of punch?

To find the total amount of punch, add $6+21+21=48$ .

The ratio of apricot juice to the total amount of punch is $21:48$ . But this ratio is probably more clearly written as a fraction, since the apricot juice makes up a fraction of the whole.

$\frac{21}{48}$

To reduce the fraction, divide both the numerator and the denominator by $3$ .

$\frac{7}{16}$

Note that this can be reduced, like a fraction, by dividing both numbers by a common factor -- in this case, $3$ . In simplest form, the ratio is $2:7$ .

Example 3:

An adult scolopendromorph centipede has $46$ legs and $8$ eyes. In a group of $100$ centipedes of the same species, what is the ratio of legs to eyes?

Note that it doesn't matter if there are $100$ or $10,000$ centipedes; the ratio of legs to eyes will remain the same.

Writing the ratio using a colon, we get $46:8$ .

Divide both numbers by $2$ . In simplest form, the ratio of legs to eyes is $23:4$ .

Example 4:

A bat beats its wings $170$ times in $10$ seconds. Write the rate as a fraction in lowest terms.

Write the rate as a fraction.

$\frac{170\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{wingbeats}}{10\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{seconds}}$

Divide both the numerator and the denominator by ten.

$=\frac{17\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{wingbeats}}{1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{second}}$

So, the rate is $17$ beats per second.

Example 5:

A mountain climber is $3200$ meters from the peak. He climbs $50$ meters per hour for $8$ hours per day. How many days will it be before he reaches the peak?

The first job is to figure out the rate per day.

$\frac{50\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{meters}}{1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{hour}}\cdot \frac{8\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{hours}}{1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{day}}=50\left(8\right)\frac{\text{meters}}{\text{day}}$

$=400\frac{\text{meters}}{\text{day}}$

He is climbing at a rate of $400$ meters per day.

Now divide $3200$ by the daily rate to find the number of days it will take him to reach the top.

$\frac{3200\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{meters}}{400\frac{\text{meters}}{\text{day}}}=8\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{days}$

2:[["\$","\$L7",null,{"children":["\$","\$L8",null,{"spaced":false,"sticky":true,"theme":{"backgroundColor":{"hex":"#EDEDF9"},"linkColor":{"hex":"#4A48C6"},"primaryColor":{"hex":"#3D3D63"},"secondaryColor":{"hex":"#4A48C6"},"textColor":{"hex":"#0D0C3C"}},"children":["\$","section",null,{"className":"by9ey40","children":[["\$","div",null,{"className":"by9ey43","children":[null,[["\$","p","0",{"children":["Become a math whiz with AI Tutoring, Practice Questions & more."]}]],null]}],["\$","\$L9",null,{"action":"\$undefined","ctaText":"Join for Free","href":"/membership/signup?vtintref=/hotmath/hotmath_help/topics/rates-ratios&subject=","target":"\$undefined"}]]}]}]}],[["\$","div",null,{"className":"hidden dark:xl:block container-xl sticky top-header-height z-[9]","children":["\$","div",null,{"className":"absolute top-0 right-0 text-sm shadow-md","children":[["\$","div",null,{"className":"bg-[#ffd670] py-1 px-12","children":"We’re Open - Call Now!"}],["\$","div",null,{"className":"bg-[#007ac0] text-white py-2 px-12 rounded-b","children":[["\$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","width":24,"height":24,"fill":"#fff","className":"float-left -ml-8 mt-2","children":[["\$","path",null,{"d":"M0 0h24v24H0z","fill":"none"}],["\$","path",null,{"d":"M6.62 10.79c1.44 2.83 3.76 5.14 6.59 6.59l2.2-2.2c.27-.27.67-.36 1.02-.24 1.12.37 2.33.57 3.57.57.55 0 1 .45 1 1V20c0 .55-.45 1-1 1-9.39 0-17-7.61-17-17 0-.55.45-1 1-1h3.5c.55 0 1 .45 1 1 0 1.25.2 2.45.57 3.57.11.35.03.74-.25 1.02l-2.2 2.2z"}]]}],["\$","div",null,{"children":"Call Now to Set Up Tutoring"}],["\$","div",null,{"className":"font-bold","children":"(888) 736-0920"}]]}]]}]}],["\$","div",null,{"className":"bg-slate-200 py-8 md:py-12 xl:py-18 flex dark:bg-[#adaead] dark:text-white","children":["\$","\$La",null,{"className":"mx-auto px-4 text-center","href":"/hotmath","prefetch":false,"children":[["\$","span",null,{"className":"text-4xl font-semibold mb-3 block dark:font-normal dark:text-5xl","children":"Hotmath"}],["\$","span",null,{"className":"text-2xl block","children":"Math Homework. Do It Faster, Learn It Better."}]]}]}]],["\$","\$Lb",null,{"value":{"cache":"hit","hotmathPage":{"indexable":true,"vars":null,"body":[{"_modelApiKey":"html_container","id":"EFNm2TQ_T7GeTQrHdD6BKg","content":"\$c","__typename":"HtmlContainerRecord"}],"seoMetadata":{"title":"Rates & Ratios","description":"Usually, a ratio is a comparison of two numbers as a fraction a/b, whereas a rate is a comparison of two quantities with different units."},"slug":"hotmath_help/topics/rates-ratios"},"navigation":{"showCart":true,"menus":[{"text":"Varsity Tutors","href":"/","items":null,"slug":"logo"},{"text":"Academic","href":"","items":[{"items":[{"text":"K-5 Subjects","href":"/elementary-tutors"},{"text":"English","href":"/english-tutors"},{"text":"Math","href":"/elementary_math-tutors"},{"text":"Phonics","href":"/phonics-tutors"},{"text":"Reading","href":"/reading-tutors"},{"text":"Study Skills","href":"/study_skills-tutors"},{"text":"Writing","href":"/writing-tutors"}],"text":"K-5 Subjects"},{"items":[{"text":"All AP Subjects","href":"/ap-tutors"},{"text":"AP Biology","href":"/ap_biology-tutors"},{"text":"AP Calculus","href":"/ap_calculus-tutors"},{"text":"AP Chemistry","href":"/ap_chemistry-tutors"},{"text":"AP Computer Science","href":"/ap_computer_science-tutors"},{"text":"AP French","href":"/ap_french-tutors"},{"text":"AP History","href":"/ap_history-tutors"},{"text":"AP Human Geography","href":"/ap_human_geography-tutors"},{"text":"AP Macroeconomics","href":"/ap_macroeconomics-tutors"},{"text":"AP Microeconomics","href":"/ap_microeconomics-tutors"},{"text":"AP Physics","href":"/ap_physics-tutors"},{"text":"AP Spanish","href":"/ap_spanish_language-tutors"},{"text":"AP Statistics","href":"/ap_statistics-tutors"},{"text":"AP US History","href":"/ap_us_history-tutors"},{"text":"AP World History","href":"/ap_world_history-tutors"}],"text":"AP Subjects"},{"items":[{"text":"All Business","href":"/business-tutors"},{"text":"Accounting","href":"/accounting-tutors"},{"text":"Business Calculus","href":"/business_calculus-tutors"},{"text":"Economics","href":"/economics-tutors"},{"text":"Finance","href":"/finance-tutors"},{"text":"Marketing","href":"/marketing-tutors"},{"text":"MBA","href":"/mba-tutors"},{"text":"Microsoft Excel","href":"/microsoft_excel-tutors"},{"text":"Supply Chain Management","href":"/supply_chain_management-tutors"}],"text":"Business"},{"items":[{"text":"All Humanities","href":"/humanities-tutors"},{"text":"Essay Editing","href":"/essay_editing-tutors"},{"text":"History","href":"/history-tutors"},{"text":"Law","href":"/law-tutors"},{"text":"Literature","href":"/literature-tutors"},{"text":"Theology","href":"/theology-tutors"}],"text":"Humanities"},{"items":[{"text":"All Languages","href":"/languages-tutors"},{"text":"Arabic","href":"/arabic-tutors"},{"text":"Bengali","href":"/bengali-tutors"},{"text":"French","href":"/french-tutors"},{"text":"German","href":"/german-tutors"},{"text":"Hindi","href":"/hindi-tutors"},{"text":"Italian","href":"/italian-tutors"},{"text":"Japanese","href":"/japanese-tutors"},{"text":"Korean","href":"/korean-tutors"},{"text":"Latin","href":"/latin-tutors"},{"text":"Mandarin Chinese","href":"/mandarin_chinese-tutors"},{"text":"Portuguese Chinese","href":"/portuguese-tutors"},{"text":"Sign Language","href":"/american_sign_language-tutors"},{"text":"Spanish","href":"/spanish-tutors"}],"text":"Languages"},{"items":[{"text":"All Learning Differences","href":"/learning-differences"},{"text":"ADD & ADHD","href":"/learning-differences/adhd"},{"text":"Autism","href":"/learning-differences/autism"},{"text":"Dyslexia","href":"/learning-differences/dyslexia"},{"text":"Learning Disabilities","href":"/learning_disability-tutoring"},{"text":"Sign Language","href":"/american_sign_language-tutors"},{"text":"Special Education","href":"/special_education-tutoring"}],"text":"Learning Differences"},{"items":[{"text":"All Math","href":"/math-tutors"},{"text":"Algebra","href":"/algebra-tutors"},{"text":"Calculus","href":"/calculus-tutors"},{"text":"College Math","href":"/college_math-tutors"},{"text":"Common Core Math","href":"/common_core_math-tutors"},{"text":"Elementary School Math","href":"/elementary_math-tutors"},{"text":"Geometry","href":"/geometry-tutors"},{"text":"High School Math","href":"/high_school_math-tutors"},{"text":"Middle School Math","href":"/middle_school_math-tutors"},{"text":"Pre-Calculus","href":"/pre_calculus-tutors"},{"text":"Statistics","href":"/statistics-tutors"},{"text":"Trigonometry","href":"/trigonometry-tutors"}],"text":"Math"},{"items":[{"text":"All Science","href":"/science-tutors"},{"text":"Anatomy","href":"/anatomy-tutors"},{"text":"Biology","href":"/biology-tutors"},{"text":"Chemistry","href":"/chemistry-tutors"},{"text":"Organic Chemistry","href":"/organic_chemistry-tutors"},{"text":"Physical Chemistry","href":"/physical_chemistry-tutors"},{"text":"Physics","href":"/physics-tutors"},{"text":"Physiology","href":"/physiology-tutors"}],"text":"Science"},{"items":[{"text":"All Engineering","href":"/engineering-tutors"},{"text":"AutoCAD","href":"/autocad-tutors"},{"text":"C++","href":"/c++-tutors"},{"text":"Chemical Engineering","href":"/chemical_engineering-tutors"},{"text":"Civil Engineering","href":"/civil_engineering-tutors"},{"text":"Computer Science","href":"/computer_science-tutors"},{"text":"Electrical Engineering","href":"/electrical_engineering-tutors"},{"text":"HTML & CSS","href":"/html-tutors"},{"text":"Industrial Engineering","href":"/industrial_engineering-tutors"},{"text":"Java","href":"/java-tutors"},{"text":"Materials Science & Engineering","href":"/materials_science-tutors"},{"text":"Mechanical Engineering","href":"/mechanical_engineering-tutors"},{"text":"Python","href":"/python-tutors"},{"text":"Ruby","href":"/ruby-tutors"},{"text":"SQL","href":"/sql-tutors"},{"text":"Thermodynamics","href":"/thermodynamics-tutors"}],"text":"Tech & Engineering"},{"items":[{"text":"Biostatistics","href":"/biostatistics-tutors"},{"text":"Coding","href":"/coding-tutors"},{"text":"College Essays","href":"/college_essays-tutors"},{"text":"Essay Editing","href":"/essay_editing-tutors"},{"text":"Homeschool","href":"/homeschool-tutors"},{"text":"Minecraft","href":"/minecraft-tutors"},{"text":"Preschool","href":"/preschool-tutors"}],"text":"Popular Subjects"},{"divider":true},{"items":[{"text":"Grades K-8","href":"/membership/k-8"},{"text":"High School","href":"/membership/9-12"},{"text":"College & Adult","href":"/membership/college-adult"},{"text":"Languages","href":"/membership/languages"}],"text":"Learning Membership"},{"items":[{"text":"1-on-1 Private Tutoring","href":"/how-we-help"},{"text":"Online Tutoring","href":"/online-tutoring"},{"text":"Instant Tutoring","href":"/instant-tutoring"},{"text":"Pricing Info","href":"/tutoring-prices-rates-cost"}],"text":"About Tutoring"}],"slug":"academic"},{"text":"Test Prep","href":"","items":[{"items":[{"text":"CogAT","href":"/cogat-tutors"},{"text":"ISEE","href":"/isee-tutors"},{"text":"MAP","href":"/map-tutors"},{"text":"SHSAT","href":"/shsat-tutors"},{"text":"SSAT","href":"/ssat-tutors"}],"text":"K-8 Exams"},{"items":[{"text":"ASVAB","href":"/asvab-tutors"},{"items":[{"text":"All AP Exams","href":"/ap-tutors"},{"text":"AP Biology","href":"/ap_biology-tutors"},{"text":"AP Calculus","href":"/ap_calculus-tutors"},{"text":"AP Chemistry","href":"/ap_chemistry-tutors"},{"text":"AP Computer Science","href":"/ap_computer_science-tutors"},{"text":"AP French","href":"/ap_french-tutors"},{"text":"AP History","href":"/ap_history-tutors"},{"text":"AP Human Geography","href":"/ap_human_geography-tutors"},{"text":"AP Macroeconomics","href":"/ap_macroeconomics-tutors"},{"text":"AP Microeconomics","href":"/ap_microeconomics-tutors"},{"text":"AP Physics","href":"/ap_physics-tutors"},{"text":"AP Spanish","href":"/ap_spanish_language-tutors"},{"text":"AP Statistics","href":"/ap_statistics-tutors"},{"text":"AP US History","href":"/ap_us_history-tutors"},{"text":"AP World History","href":"/ap_world_history-tutors"}],"text":"AP"},{"text":"GED","href":"/ged-tutors"},{"text":"HSPT","href":"/hspt-tutors"},{"text":"IB","href":"/ib-tutors"},{"text":"ISEE","href":"/isee-tutors"},{"text":"SHSAT","href":"/shsat-tutors"},{"text":"SSAT","href":"/ssat-tutors"},{"text":"TACHS","href":"/tachs-tutors"}],"text":"High School Exams"},{"items":[{"items":[{"text":"ACT Tutoring","href":"/act-tutors"},{"text":"ACT Math","href":"/act_math-tutors"},{"text":"ACT Reading","href":"/act_reading-tutors"},{"text":"ACT Science","href":"/act_science-tutors"},{"text":"ACT Writing","href":"/act_writing-tutors"}],"text":"ACT"},{"text":"PSAT","href":"/psat-tutors"},{"items":[{"text":"SAT Tutoring","href":"/sat-tutors"},{"text":"SAT Math","href":"/sat_math-tutors"},{"text":"SAT Reading","href":"/sat_reading-tutors"},{"text":"SAT Writing","href":"/sat_writing-tutors"}],"text":"SAT"}],"text":"College Entrance Exams"},{"items":[{"text":"DAT","href":"/dat-tutors"},{"text":"GMAT","href":"/gmat-tutors"},{"items":[{"text":"GRE Tutoring","href":"/gre-tutors"},{"text":"GRE Prep","href":"/gre"}],"text":"GRE"},{"text":"LSAT","href":"/lsat-tutors"},{"text":"MCAT","href":"/mcat-tutors"},{"text":"PCAT","href":"/pcat-tutors"}],"text":"Graduate School Entrance Exams"},{"items":[{"text":"Bar","href":"/bar_exam-tutors"},{"text":"CPA","href":"/cpa-tutors"},{"items":[{"text":"CAIA","href":"/caia-tutors"},{"text":"CFA","href":"/cfa-tutors"},{"text":"CFP","href":"/cfp-tutors"}],"text":"Finance"},{"items":[{"text":"COMLEX","href":"/comlex-tutors"},{"text":"NAPLEX","href":"/naplex-tutors"},{"text":"USMLE","href":"/usmle-tutors"}],"text":"Medical"},{"items":[{"text":"NCLEX Tutoring","href":"/nclex-tutors"},{"text":"NCLEX Prep","href":"/nclex"}],"text":"NCLEX"},{"text":"NMLS","href":"/nmls-tutors"},{"text":"PMP","href":"/pmp-tutors"},{"text":"Praxis","href":"/praxis-tutors"},{"text":"Real Estate License","href":"/real_estate_license-tutors"},{"items":[{"text":"SIE","href":"/sie-tutors"},{"text":"Series 7","href":"/series_7-tutors"},{"text":"Series 65","href":"/series_65_exam-tutors"}],"text":"Securities"},{"text":"And more... ","href":"/certifications-and-licenses"}],"text":"Certifications & Licenses"}],"slug":"test_prep"},{"text":"Enrichment","href":"","items":[{"text":"StarCourses","href":"/classes/search?f_class_size=large-group"},{"divider":true},{"text":"Art","href":"/art-tutors"},{"text":"Chess","href":"/chess-tutors"},{"items":[{"text":"Beginners Coding","href":"/coding-tutors"},{"text":"Minecraft","href":"/minecraft-tutors"},{"text":"Roblox","href":"/roblox-tutors"},{"text":"Unity","href":"/unity-tutors"}],"text":"Coding"},{"text":"Early Childhood","href":"/kindergarten_readiness-tutors"},{"items":[{"text":"All Languages","href":"/languages-tutors"},{"text":"Arabic","href":"/arabic-tutors"},{"text":"Bengali","href":"/bengali-tutors"},{"text":"French","href":"/french-tutors"},{"text":"German","href":"/german-tutors"},{"text":"Hindi","href":"/hindi-tutors"},{"text":"Italian","href":"/italian-tutors"},{"text":"Japanese","href":"/japanese-tutors"},{"text":"Korean","href":"/korean-tutors"},{"text":"Latin","href":"/latin-tutors"},{"text":"Mandarin Chinese","href":"/mandarin_chinese-tutors"},{"text":"Portuguese Chinese","href":"/portuguese-tutors"},{"text":"Sign Language","href":"/american_sign_language-tutors"},{"text":"Spanish","href":"/spanish-tutors"}],"text":"Languages"},{"text":"Music","href":"/music-tutors"},{"text":"STEM","href":"/stem-tutors"}],"slug":"enrichment"},{"text":"For Schools","href":"","items":[{"text":"For Schools Overview","href":"/school-solutions"},{"text":"High-Dosage Tutoring","href":"/school-solutions/what-we-offer"},{"text":"Free 24/7 Tutoring & Classes","href":"/school-solutions/platform-access"},{"text":"Live Learning Platform","href":"/school-solutions/livelearning"},{"text":"Learning Outcomes","href":"/school-solutions/impact"},{"text":"About The Tutors","href":"/school-solutions/tutors"},{"text":"Resources","href":"/school-solutions/resources"},{"text":"Talk with Our Team","href":"/school-solutions/contact"}],"slug":"for_schools"},{"text":"About","href":"","items":[{"text":"Reviews & Testimonials","href":"/reviews"},{"text":"Press & Media Coverage","href":"https://press.varsitytutors.com"},{"text":"Tutor/Instructor Jobs","href":"/tutor-application"},{"text":"Corporate Solutions","href":"/partnerships"},{"text":"Careers","href":"https://careers.varsitytutors.com"},{"text":"Our Team","href":"/aboutus"},{"text":"About Nerdy","href":"https://www.nerdy.com/"}],"slug":"about"},{"text":"Become a Tutor","href":"/tutor-application","items":null,"slug":"become_a_tutor"},{"text":"Sign In","href":"/login","items":null,"slug":"account"}],"slug":"vt_organic_navbar","showSearch":true}},"children":[null,[["\$","div",null,{"className":"py-8 md:py-12 xl:py-18","data-container-key":0,"id":"\$undefined","children":["\$","div",null,{"className":"container-xl","children":["\$","div",null,{"className":"prose max-w-none","dangerouslySetInnerHTML":{"__html":"\$d"}}]}]}]],["\$","\$Le",null,{}]]}],[["\$","div",null,{"className":"container-xl","children":[["\$","div",null,{"className":"text-base font-bold mb-1","children":"Subjects Near Me"}],["\$","ul",null,{"className":" lg:text-sm leading-5 mb-4 flex flex-wrap flex-col md:flex-row -mx-2 [&>li]:relative [&>li]:after:absolute [&>li]:after:block [&>li]:after:top-2 [&>li]:after:right-0 [&>li]:after:bottom-2 [&>li]:after:md:border-r-gray-400 [&>li]:after:md:border-r-[1px] [&>li:last-child]:after:md:border-r-0","children":[["\$","li","0",{"children":["\$","a",null,{"aria-label":"Link to Latin Courses & Classes","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/latin-courses_classes","children":"Latin Courses & Classes"}]}],["\$","li","1",{"children":["\$","a",null,{"aria-label":"Link to Common Core English Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/common_core_english-tutors","children":"Common Core English Tutors"}]}],["\$","li","2",{"children":["\$","a",null,{"aria-label":"Link to ACSM - American College of Sports Medicine Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/acsm-tutors","children":"ACSM - American College of Sports Medicine Tutors"}]}],["\$","li","3",{"children":["\$","a",null,{"aria-label":"Link to Human Biology Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/human_biology-tutors","children":"Human Biology Tutors"}]}],["\$","li","4",{"children":["\$","a",null,{"aria-label":"Link to Reading Intervention Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/reading_intervention-tutors","children":"Reading Intervention Tutors"}]}],["\$","li","5",{"children":["\$","a",null,{"aria-label":"Link to Series 63 Courses & Classes","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/series_63_exam-courses_classes","children":"Series 63 Courses & Classes"}]}],["\$","li","6",{"children":["\$","a",null,{"aria-label":"Link to Microsoft Access Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/microsoft_access-tutors","children":"Microsoft Access Tutors"}]}],["\$","li","7",{"children":["\$","a",null,{"aria-label":"Link to ISEE-Upper Level Verbal Reasoning Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/isee_upper_level_verbal_reasoning-tutors","children":"ISEE-Upper Level Verbal Reasoning Tutors"}]}],["\$","li","8",{"children":["\$","a",null,{"aria-label":"Link to Series 82 Test Prep","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/series_82_exam-prep","children":"Series 82 Test Prep"}]}],["\$","li","9",{"children":["\$","a",null,{"aria-label":"Link to CompTIA Courses & Classes","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/comptia-courses_classes","children":"CompTIA Courses & Classes"}]}],["\$","li","10",{"children":["\$","a",null,{"aria-label":"Link to World Studies Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/world_studies-tutors","children":"World Studies Tutors"}]}],["\$","li","11",{"children":["\$","a",null,{"aria-label":"Link to IB Physics Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/ib_physics-tutors","children":"IB Physics Tutors"}]}],["\$","li","12",{"children":["\$","a",null,{"aria-label":"Link to Series 30 Test Prep","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/series_30_exam-prep","children":"Series 30 Test Prep"}]}],["\$","li","13",{"children":["\$","a",null,{"aria-label":"Link to EAS - Educating All Students (NY Teaching exam) Courses & Classes","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/eas-courses_classes","children":"EAS - Educating All Students (NY Teaching exam) Courses & Classes"}]}],["\$","li","14",{"children":["\$","a",null,{"aria-label":"Link to Series 4 Courses & Classes","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/series_4_exam-courses_classes","children":"Series 4 Courses & Classes"}]}],["\$","li","15",{"children":["\$","a",null,{"aria-label":"Link to South Carolina Bar Exam Courses & Classes","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/south_carolina_bar_exam-courses_classes","children":"South Carolina Bar Exam Courses & Classes"}]}],["\$","li","16",{"children":["\$","a",null,{"aria-label":"Link to CCNA Cloud - Cisco Certified Network Associate-Cloud Courses & Classes","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/ccna_cloud-courses_classes","children":"CCNA Cloud - Cisco Certified Network Associate-Cloud Courses & Classes"}]}],["\$","li","17",{"children":["\$","a",null,{"aria-label":"Link to High School Political Science Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/high_school_political_science-tutors","children":"High School Political Science Tutors"}]}],["\$","li","18",{"children":["\$","a",null,{"aria-label":"Link to Chess Tutors","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/chess-tutors","children":"Chess Tutors"}]}],["\$","li","19",{"children":["\$","a",null,{"aria-label":"Link to CLEP English Literature Test Prep","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/clep_english_literature-prep","children":"CLEP English Literature Test Prep"}]}]]}]]}],["\$","div",null,{"className":"container-xl","children":[["\$","div",null,{"className":"text-base font-bold mb-1","children":"Popular Cities"}],["\$","ul",null,{"className":" lg:text-sm leading-5 mb-4 flex flex-wrap flex-col md:flex-row -mx-2 [&>li]:relative [&>li]:after:absolute [&>li]:after:block [&>li]:after:top-2 [&>li]:after:right-0 [&>li]:after:bottom-2 [&>li]:after:md:border-r-gray-400 [&>li]:after:md:border-r-[1px] [&>li:last-child]:after:md:border-r-0","children":[["\$","li","0",{"children":["\$","a",null,{"aria-label":"Link to Phoenix Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-phoenix","children":"Phoenix Tutoring"}]}],["\$","li","1",{"children":["\$","a",null,{"aria-label":"Link to San Antonio Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-san_antonio","children":"San Antonio Tutoring"}]}],["\$","li","2",{"children":["\$","a",null,{"aria-label":"Link to Buffalo Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-buffalo","children":"Buffalo Tutoring"}]}],["\$","li","3",{"children":["\$","a",null,{"aria-label":"Link to Charlotte Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-charlotte","children":"Charlotte Tutoring"}]}],["\$","li","4",{"children":["\$","a",null,{"aria-label":"Link to Houston Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-houston","children":"Houston Tutoring"}]}],["\$","li","5",{"children":["\$","a",null,{"aria-label":"Link to Portland Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-portland","children":"Portland Tutoring"}]}],["\$","li","6",{"children":["\$","a",null,{"aria-label":"Link to Atlanta Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-atlanta","children":"Atlanta Tutoring"}]}],["\$","li","7",{"children":["\$","a",null,{"aria-label":"Link to Indianapolis Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-indianapolis","children":"Indianapolis Tutoring"}]}],["\$","li","8",{"children":["\$","a",null,{"aria-label":"Link to Sacramento Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-sacramento","children":"Sacramento Tutoring"}]}],["\$","li","9",{"children":["\$","a",null,{"aria-label":"Link to Dallas Fort Worth Tutoring","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/tutoring-dallas_fort_worth","children":"Dallas Fort Worth Tutoring"}]}]]}]]}],["\$","div",null,{"className":"container-xl","children":[["\$","div",null,{"className":"text-base font-bold mb-1","children":"Popular Subjects"}],["\$","ul",null,{"className":" lg:text-sm leading-5 mb-4 flex flex-wrap flex-col md:flex-row -mx-2 [&>li]:relative [&>li]:after:absolute [&>li]:after:block [&>li]:after:top-2 [&>li]:after:right-0 [&>li]:after:bottom-2 [&>li]:after:md:border-r-gray-400 [&>li]:after:md:border-r-[1px] [&>li:last-child]:after:md:border-r-0","children":[["\$","li","0",{"children":["\$","a",null,{"aria-label":"Link to Math Tutors in San Diego","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/math-tutors-san_diego","children":"Math Tutors in San Diego"}]}],["\$","li","1",{"children":["\$","a",null,{"aria-label":"Link to ISEE Tutors in Dallas Fort Worth","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/isee-tutors-dallas_fort_worth","children":"ISEE Tutors in Dallas Fort Worth"}]}],["\$","li","2",{"children":["\$","a",null,{"aria-label":"Link to French Tutors in Washington DC","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/french-tutors-washington_dc","children":"French Tutors in Washington DC"}]}],["\$","li","3",{"children":["\$","a",null,{"aria-label":"Link to Physics Tutors in Miami","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/physics-tutors-miami","children":"Physics Tutors in Miami"}]}],["\$","li","4",{"children":["\$","a",null,{"aria-label":"Link to Calculus Tutors in Seattle","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/calculus-tutors-seattle","children":"Calculus Tutors in Seattle"}]}],["\$","li","5",{"children":["\$","a",null,{"aria-label":"Link to Chemistry Tutors in Washington DC","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/chemistry-tutors-washington_dc","children":"Chemistry Tutors in Washington DC"}]}],["\$","li","6",{"children":["\$","a",null,{"aria-label":"Link to GRE Tutors in San Diego","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/gre-tutors-san_diego","children":"GRE Tutors in San Diego"}]}],["\$","li","7",{"children":["\$","a",null,{"aria-label":"Link to Reading Tutors in Denver","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/reading-tutors-denver","children":"Reading Tutors in Denver"}]}],["\$","li","8",{"children":["\$","a",null,{"aria-label":"Link to English Tutors in San Francisco-Bay Area","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/english-tutors-san_francisco","children":"English Tutors in San Francisco-Bay Area"}]}],["\$","li","9",{"children":["\$","a",null,{"aria-label":"Link to SSAT Tutors in San Francisco-Bay Area","className":"hover:text-primary hover:underline block p-2 md:py-1","href":"/ssat-tutors-san_francisco","children":"SSAT Tutors in San Francisco-Bay Area"}]}]]}]]}]],";"] 6:[["\$","meta","0",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["\$","meta","1",{"charSet":"utf-8"}],["\$","title","2",{"children":"Rates & Ratios"}],["\$","meta","3",{"name":"description","content":"Usually, a ratio is a comparison of two numbers as a fraction a/b, whereas a rate is a comparison of two quantities with different units."}],["\$","meta","4",{"name":"robots","content":"index, follow"}],["\$","meta","5",{"name":"lang","content":"en"}],["\$","link","6",{"rel":"canonical","href":"/hotmath/hotmath_help/topics/rates-ratios"}],["\$","link","7",{"rel":"icon","href":"https://assets2.varsitytutors.com/vt-ecom/images/basics/favicons/varsity-tutors/favicon.ico"}],["\$","link","8",{"rel":"icon","href":"https://assets2.varsitytutors.com/vt-ecom/images/basics/favicons/varsity-tutors/favicon.png"}],["\$","link","9",{"rel":"apple-touch-icon","href":"https://assets2.varsitytutors.com/vt-ecom/images/basics/favicons/varsity-tutors/apple-touch-icon.png"}],["\$","meta","10",{"name":"next-size-adjust"}]] 1:null