Question

ratio and proportion​

Answer 1

Answer:

Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers.

Step-by-step explanation:

Hope this answer helps you!

Answer 2

• ᴀɴꜱᴡᴇʀ :

• ᴅᴇꜰɪɴɪᴛɪᴏɴ ᴏꜰ ʀᴀᴛɪᴏ :

ɪɴ ᴄᴇʀᴛᴀɪɴ ꜱɪᴛᴜᴀᴛɪᴏɴꜱ, ᴛʜᴇ ᴄᴏᴍᴘᴀʀɪꜱᴏɴ ᴏꜰ ᴛᴡᴏ Qᴜᴀɴᴛɪᴛɪᴇꜱ ʙʏ ᴛʜᴇ ᴍᴇᴛʜᴏᴅ ᴏꜰ ᴅɪᴠɪꜱɪᴏɴ ɪꜱ ᴠᴇʀʏ ᴇꜰꜰɪᴄɪᴇɴᴛ. ᴡᴇ ᴄᴀɴ ꜱᴀʏ ᴛʜᴀᴛ ᴛʜᴇ ᴄᴏᴍᴘᴀʀɪꜱᴏɴ ᴏʀ ꜱɪᴍᴘʟɪꜰɪᴇᴅ ꜰᴏʀᴍ ᴏꜰ ᴛᴡᴏ Qᴜᴀɴᴛɪᴛɪᴇꜱ ᴏꜰ ᴛʜᴇ ꜱᴀᴍᴇ ᴋɪɴᴅ ɪꜱ ʀᴇꜰᴇʀʀᴇᴅ ᴛᴏ ᴀꜱ ʀᴀᴛɪᴏ. ᴛʜɪꜱ ʀᴇʟᴀᴛɪᴏɴ ɢɪᴠᴇꜱ ᴜꜱ ʜᴏᴡ ᴍᴀɴʏ ᴛɪᴍᴇꜱ ᴏɴᴇ Qᴜᴀɴᴛɪᴛʏ ɪꜱ ᴇQᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴛʜᴇʀ Qᴜᴀɴᴛɪᴛʏ. ɪɴ ꜱɪᴍᴘʟᴇ ᴡᴏʀᴅꜱ, ᴛʜᴇ ʀᴀᴛɪᴏ ɪꜱ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴡʜɪᴄʜ ᴄᴀɴ ʙᴇ ᴜꜱᴇᴅ ᴛᴏ ᴇxᴘʀᴇꜱꜱ ᴏɴᴇ Qᴜᴀɴᴛɪᴛʏ ᴀꜱ ᴀ ꜰʀᴀᴄᴛɪᴏɴ ᴏꜰ ᴛʜᴇ ᴏᴛʜᴇʀ ᴏɴᴇꜱ.

ᴛʜᴇ ᴛᴡᴏ ɴᴜᴍʙᴇʀꜱ ɪɴ ᴀ ʀᴀᴛɪᴏ ᴄᴀɴ ᴏɴʟʏ ʙᴇ ᴄᴏᴍᴘᴀʀᴇᴅ ᴡʜᴇɴ ᴛʜᴇʏ ʜᴀᴠᴇ ᴛʜᴇ ꜱᴀᴍᴇ ᴜɴɪᴛ. ᴡᴇ ᴍᴀᴋᴇ ᴜꜱᴇ ᴏꜰ ʀᴀᴛɪᴏꜱ ᴛᴏ ᴄᴏᴍᴘᴀʀᴇ ᴛᴡᴏ ᴛʜɪɴɢꜱ. ᴛʜᴇ ꜱɪɢɴ ᴜꜱᴇᴅ ᴛᴏ ᴅᴇɴᴏᴛᴇ ᴀ ʀᴀᴛɪᴏ ɪꜱ ‘:’.

ᴀ ʀᴀᴛɪᴏ ᴄᴀɴ ʙᴇ ᴡʀɪᴛᴛᴇɴ ᴀꜱ ᴀ ꜰʀᴀᴄᴛɪᴏɴ, ꜱᴀʏ 2/5. ᴡᴇ ʜᴀᴘᴘᴇɴ ᴛᴏ ꜱᴇᴇ ᴠᴀʀɪᴏᴜꜱ ᴄᴏᴍᴘᴀʀɪꜱᴏɴꜱ ᴏʀ ꜱᴀʏ ʀᴀᴛɪᴏꜱ ɪɴ ᴏᴜʀ ᴅᴀɪʟʏ ʟɪꜰᴇ.

ᴋᴇʏ ᴘᴏɪɴᴛꜱ ᴛᴏ ʀᴇᴍᴇᴍʙᴇʀ:

ᴛʜᴇ ʀᴀᴛɪᴏ ꜱʜᴏᴜʟᴅ ᴇxɪꜱᴛ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ Qᴜᴀɴᴛɪᴛɪᴇꜱ ᴏꜰ ᴛʜᴇ ꜱᴀᴍᴇ ᴋɪɴᴅ

ᴡʜɪʟᴇ ᴄᴏᴍᴘᴀʀɪɴɢ ᴛᴡᴏ ᴛʜɪɴɢꜱ, ᴛʜᴇ ᴜɴɪᴛꜱ ꜱʜᴏᴜʟᴅ ʙᴇ ꜱɪᴍɪʟᴀʀ

ᴛʜᴇʀᴇ ꜱʜᴏᴜʟᴅ ʙᴇ ꜱɪɢɴɪꜰɪᴄᴀɴᴛ ᴏʀᴅᴇʀ ᴏꜰ ᴛᴇʀᴍꜱ

ᴛʜᴇ ᴄᴏᴍᴘᴀʀɪꜱᴏɴ ᴏꜰ ᴛᴡᴏ ʀᴀᴛɪᴏꜱ ᴄᴀɴ ʙᴇ ᴘᴇʀꜰᴏʀᴍᴇᴅ, ɪꜰ ᴛʜᴇ ʀᴀᴛɪᴏꜱ ᴀʀᴇ ᴇQᴜɪᴠᴀʟᴇɴᴛ ʟɪᴋᴇ ᴛʜᴇ ꜰʀᴀᴄᴛɪᴏɴꜱ

• ᴅᴇꜰɪɴɪᴛɪᴏɴ ᴏꜰ ᴘʀᴏᴘᴏʀᴛɪᴏɴ :

ᴘʀᴏᴘᴏʀᴛɪᴏɴ ɪꜱ ᴀɴ ᴇQᴜᴀᴛɪᴏɴ ᴡʜɪᴄʜ ᴅᴇꜰɪɴᴇꜱ ᴛʜᴀᴛ ᴛʜᴇ ᴛᴡᴏ ɢɪᴠᴇɴ ʀᴀᴛɪᴏꜱ ᴀʀᴇ ᴇQᴜɪᴠᴀʟᴇɴᴛ ᴛᴏ ᴇᴀᴄʜ ᴏᴛʜᴇʀ. ɪɴ ᴏᴛʜᴇʀ ᴡᴏʀᴅꜱ, ᴛʜᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ꜱᴛᴀᴛᴇꜱ ᴛʜᴇ ᴇQᴜᴀʟɪᴛʏ ᴏꜰ ᴛʜᴇ ᴛᴡᴏ ꜰʀᴀᴄᴛɪᴏɴꜱ ᴏʀ ᴛʜᴇ ʀᴀᴛɪᴏꜱ. ɪɴ ᴘʀᴏᴘᴏʀᴛɪᴏɴ, ɪꜰ ᴛᴡᴏ ꜱᴇᴛꜱ ᴏꜰ ɢɪᴠᴇɴ ɴᴜᴍʙᴇʀꜱ ᴀʀᴇ ɪɴᴄʀᴇᴀꜱɪɴɢ ᴏʀ ᴅᴇᴄʀᴇᴀꜱɪɴɢ ɪɴ ᴛʜᴇ ꜱᴀᴍᴇ ʀᴀᴛɪᴏ, ᴛʜᴇɴ ᴛʜᴇ ʀᴀᴛɪᴏꜱ ᴀʀᴇ ꜱᴀɪᴅ ᴛᴏ ʙᴇ ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴇᴀᴄʜ ᴏᴛʜᴇʀ.

ꜰᴏʀ ᴇxᴀᴍᴘʟᴇ, ᴛʜᴇ ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ʙʏ ᴛʀᴀɪɴ ᴛᴏ ᴄᴏᴠᴇʀ 100ᴋᴍ ᴘᴇʀ ʜᴏᴜʀ ɪꜱ ᴇQᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ʙʏ ɪᴛ ᴛᴏ ᴄᴏᴠᴇʀ ᴛʜᴇ ᴅɪꜱᴛᴀɴᴄᴇ ᴏꜰ 500ᴋᴍ ꜰᴏʀ 5 ʜᴏᴜʀꜱ. ꜱᴜᴄʜ ᴀꜱ 100ᴋᴍ/ʜʀ = 500ᴋᴍ/5ʜʀꜱ.

ʀᴀᴛɪᴏ ᴀɴᴅ ᴘʀᴏᴘᴏʀᴛɪᴏɴꜱ ᴀʀᴇ ꜱᴀɪᴅ ᴛᴏ ʙᴇ ꜰᴀᴄᴇꜱ ᴏꜰ ᴛʜᴇ ꜱᴀᴍᴇ ᴄᴏɪɴ. ᴡʜᴇɴ ᴛᴡᴏ ʀᴀᴛɪᴏꜱ ᴀʀᴇ ᴇQᴜᴀʟ ɪɴ ᴠᴀʟᴜᴇ, ᴛʜᴇɴ ᴛʜᴇʏ ᴀʀᴇ ꜱᴀɪᴅ ᴛᴏ ʙᴇ ɪɴ ᴘʀᴏᴘᴏʀᴛɪᴏɴ. ɪɴ ꜱɪᴍᴘʟᴇ ᴡᴏʀᴅꜱ, ɪᴛ ᴄᴏᴍᴘᴀʀᴇꜱ ᴛᴡᴏ ʀᴀᴛɪᴏꜱ. ᴘʀᴏᴘᴏʀᴛɪᴏɴꜱ ᴀʀᴇ ᴅᴇɴᴏᴛᴇᴅ ʙʏ ᴛʜᴇ ꜱʏᴍʙᴏʟ ‘::’ ᴏʀ ‘=’.

• ʀᴀᴛɪᴏ ꜰᴏʀᴍᴜʟᴀ :

ᴀꜱꜱᴜᴍᴇ ᴛʜᴀᴛ, ᴡᴇ ʜᴀᴠᴇ ᴛᴡᴏ Qᴜᴀɴᴛɪᴛɪᴇꜱ (ᴏʀ ᴛᴡᴏ ɴᴜᴍʙᴇʀꜱ ᴏʀ ᴛᴡᴏ ᴇɴᴛɪᴛɪᴇꜱ) ᴀɴᴅ ᴡᴇ ʜᴀᴠᴇ ᴛᴏ ꜰɪɴᴅ ᴛʜᴇ ʀᴀᴛɪᴏ ᴏꜰ ᴛʜᴇꜱᴇ ᴛᴡᴏ, ᴛʜᴇɴ ᴛʜᴇ ꜰᴏʀᴍᴜʟᴀ ꜰᴏʀ ʀᴀᴛɪᴏ ɪꜱ ᴅᴇꜰɪɴᴇᴅ ᴀꜱ;

ᴀ: ʙ ⇒ ᴀ/ʙ

ᴡʜᴇʀᴇ ᴀ ᴀɴᴅ ʙ ᴄᴏᴜʟᴅ ʙᴇ ᴀɴʏ ᴛᴡᴏ Qᴜᴀɴᴛɪᴛɪᴇꜱ.

ʜᴇʀᴇ, “ᴀ” ɪꜱ ᴄᴀʟʟᴇᴅ ᴛʜᴇ ꜰɪʀꜱᴛ ᴛᴇʀᴍ ᴏʀ ᴀɴᴛᴇᴄᴇᴅᴇɴᴛ, ᴀɴᴅ “ʙ” ɪꜱ ᴄᴀʟʟᴇᴅ ᴛʜᴇ ꜱᴇᴄᴏɴᴅ ᴛᴇʀᴍ ᴏʀ ᴄᴏɴꜱᴇQᴜᴇɴᴛ.

ᴇxᴀᴍᴘʟᴇ: ɪɴ ʀᴀᴛɪᴏ 4:9, ɪꜱ ʀᴇᴘʀᴇꜱᴇɴᴛᴇᴅ ʙʏ 4/9, ᴡʜᴇʀᴇ 4 ɪꜱ ᴀɴᴛᴇᴄᴇᴅᴇɴᴛ ᴀɴᴅ 9 ɪꜱ ᴄᴏɴꜱᴇQᴜᴇɴᴛ.

ɪꜰ ᴡᴇ ᴍᴜʟᴛɪᴘʟʏ ᴀɴᴅ ᴅɪᴠɪᴅᴇ ᴇᴀᴄʜ ᴛᴇʀᴍ ᴏꜰ ʀᴀᴛɪᴏ ʙʏ ᴛʜᴇ ꜱᴀᴍᴇ ɴᴜᴍʙᴇʀ (ɴᴏɴ-ᴢᴇʀᴏ), ɪᴛ ᴅᴏᴇꜱɴ’ᴛ ᴀꜰꜰᴇᴄᴛ ᴛʜᴇ ʀᴀᴛɪᴏ.

ᴇxᴀᴍᴘʟᴇ: 4:9 = 8:18 = 12:27

• ᴘʀᴏᴘᴏʀᴛɪᴏɴ ꜰᴏʀᴍᴜʟᴀ :

ɴᴏᴡ, ʟᴇᴛ ᴜꜱ ᴀꜱꜱᴜᴍᴇ ᴛʜᴀᴛ, ɪɴ ᴘʀᴏᴘᴏʀᴛɪᴏɴ, ᴛʜᴇ ᴛᴡᴏ ʀᴀᴛɪᴏꜱ ᴀʀᴇ ᴀ:ʙ & ᴄ:ᴅ. ᴛʜᴇ ᴛᴡᴏ ᴛᴇʀᴍꜱ ‘ʙ’ ᴀɴᴅ ‘ᴄ’ ᴀʀᴇ ᴄᴀʟʟᴇᴅ ‘ᴍᴇᴀɴꜱ ᴏʀ ᴍᴇᴀɴ ᴛᴇʀᴍ,’ ᴡʜᴇʀᴇᴀꜱ ᴛʜᴇ ᴛᴇʀᴍꜱ ‘ᴀ’ ᴀɴᴅ ‘ᴅ’ ᴀʀᴇ ᴋɴᴏᴡɴ ᴀꜱ ‘ᴇxᴛʀᴇᴍᴇꜱ ᴏʀ ᴇxᴛʀᴇᴍᴇ ᴛᴇʀᴍꜱ.’

ᴀ/ʙ = ᴄ/ᴅ ᴏʀ ᴀ : ʙ :: ᴄ : ᴅ

ᴇxᴀᴍᴘʟᴇ: ʟᴇᴛ ᴜꜱ ᴄᴏɴꜱɪᴅᴇʀ ᴏɴᴇ ᴍᴏʀᴇ ᴇxᴀᴍᴘʟᴇ ᴏꜰ ᴀ ɴᴜᴍʙᴇʀ ᴏꜰ ꜱᴛᴜᴅᴇɴᴛꜱ ɪɴ ᴀ ᴄʟᴀꜱꜱʀᴏᴏᴍ. ᴏᴜʀ ꜰɪʀꜱᴛ ʀᴀᴛɪᴏ ᴏꜰ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏꜰ ɢɪʀʟꜱ ᴛᴏ ʙᴏʏꜱ ɪꜱ 3:5 ᴀɴᴅ ᴛʜᴀᴛ ᴏꜰ ᴛʜᴇ ᴏᴛʜᴇʀ ɪꜱ 4:8, ᴛʜᴇɴ ᴛʜᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ᴄᴀɴ ʙᴇ ᴡʀɪᴛᴛᴇɴ ᴀꜱ:

3 : 5 :: 4 : 8 ᴏʀ 3/5 = 4/8

ʜᴇʀᴇ, 3 & 8 ᴀʀᴇ ᴛʜᴇ ᴇxᴛʀᴇᴍᴇꜱ, ᴡʜɪʟᴇ 5 & 4 ᴀʀᴇ ᴛʜᴇ ᴍᴇᴀɴꜱ.

ɴᴏᴛᴇ: ᴛʜᴇ ʀᴀᴛɪᴏ ᴠᴀʟᴜᴇ ᴅᴏᴇꜱ ɴᴏᴛ ᴀꜰꜰᴇᴄᴛ ᴡʜᴇɴ ᴛʜᴇ ꜱᴀᴍᴇ ɴᴏɴ-ᴢᴇʀᴏ ɴᴜᴍʙᴇʀ ɪꜱ ᴍᴜʟᴛɪᴘʟɪᴇᴅ ᴏʀ ᴅɪᴠɪᴅᴇᴅ ᴏɴ ᴇᴀᴄʜ ᴛᴇʀᴍ.

• ꜱᴛᴇᴘ-ʙʏ-ꜱᴛᴇᴘ-ᴇxᴘʟᴀɴᴀᴛɪᴏɴ

• ʀᴀᴛɪᴏꜱ ᴀɴᴅ ᴘʀᴏᴘᴏʀᴛɪᴏɴ :

ʀᴀᴛɪᴏ ᴀɴᴅ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ᴀʀᴇ ᴇxᴘʟᴀɪɴᴇᴅ ᴍᴀᴊᴏʀʟʏ ʙᴀꜱᴇᴅ ᴏɴ ꜰʀᴀᴄᴛɪᴏɴꜱ. ᴡʜᴇɴ ᴀ ꜰʀᴀᴄᴛɪᴏɴ ɪꜱ ʀᴇᴘʀᴇꜱᴇɴᴛᴇᴅ ɪɴ ᴛʜᴇ ꜰᴏʀᴍ ᴏꜰ ᴀ:ʙ, ᴛʜᴇɴ ɪᴛ ɪꜱ ᴀ ʀᴀᴛɪᴏ ᴡʜᴇʀᴇᴀꜱ ᴀ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ꜱᴛᴀᴛᴇꜱ ᴛʜᴀᴛ ᴛᴡᴏ ʀᴀᴛɪᴏꜱ ᴀʀᴇ ᴇQᴜᴀʟ. ʜᴇʀᴇ, ᴀ ᴀɴᴅ ʙ ᴀʀᴇ ᴀɴʏ ᴛᴡᴏ ɪɴᴛᴇɢᴇʀꜱ. ᴛʜᴇ ʀᴀᴛɪᴏ ᴀɴᴅ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ᴀʀᴇ ᴛʜᴇ ᴛᴡᴏ ɪᴍᴘᴏʀᴛᴀɴᴛ ᴄᴏɴᴄᴇᴘᴛꜱ, ᴀɴᴅ ɪᴛ ɪꜱ ᴛʜᴇ ꜰᴏᴜɴᴅᴀᴛɪᴏɴ ᴛᴏ ᴜɴᴅᴇʀꜱᴛᴀɴᴅ ᴛʜᴇ ᴠᴀʀɪᴏᴜꜱ ᴄᴏɴᴄᴇᴘᴛꜱ ɪɴ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄꜱ ᴀꜱ ᴡᴇʟʟ ᴀꜱ ɪɴ ꜱᴄɪᴇɴᴄᴇ.

ɪɴ ᴏᴜʀ ᴅᴀɪʟʏ ʟɪꜰᴇ, ᴡᴇ ᴜꜱᴇ ᴛʜᴇ ᴄᴏɴᴄᴇᴘᴛ ᴏꜰ ʀᴀᴛɪᴏ ᴀɴᴅ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ꜱᴜᴄʜ ᴀꜱ ɪɴ ʙᴜꜱɪɴᴇꜱꜱ ᴡʜɪʟᴇ ᴅᴇᴀʟɪɴɢ ᴡɪᴛʜ ᴍᴏɴᴇʏ ᴏʀ ᴡʜɪʟᴇ ᴄᴏᴏᴋɪɴɢ ᴀɴʏ ᴅɪꜱʜ, ᴇᴛᴄ. ꜱᴏᴍᴇᴛɪᴍᴇꜱ, ꜱᴛᴜᴅᴇɴᴛꜱ ɢᴇᴛ ᴄᴏɴꜰᴜꜱᴇᴅ ᴡɪᴛʜ ᴛʜᴇ ᴄᴏɴᴄᴇᴘᴛ ᴏꜰ ʀᴀᴛɪᴏ ᴀɴᴅ ᴘʀᴏᴘᴏʀᴛɪᴏɴ. ɪɴ ᴛʜɪꜱ ᴀʀᴛɪᴄʟᴇ, ᴛʜᴇ ꜱᴛᴜᴅᴇɴᴛꜱ ɢᴇᴛ ᴀ ᴄʟᴇᴀʀ ᴠɪꜱɪᴏɴ ᴏꜰ ᴛʜᴇꜱᴇ ᴛᴡᴏ ᴄᴏɴᴄᴇᴘᴛꜱ ᴡɪᴛʜ ᴍᴏʀᴇ ꜱᴏʟᴠᴇᴅ ᴇxᴀᴍᴘʟᴇꜱ ᴀɴᴅ ᴘʀᴏʙʟᴇᴍꜱ.

ꜰᴏʀ ᴇxᴀᴍᴘʟᴇ, ⅘ ɪꜱ ᴀ ʀᴀᴛɪᴏ ᴀɴᴅ ᴛʜᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ꜱᴛᴀᴛᴇᴍᴇɴᴛ ɪꜱ 20/25 = ⅘. ɪꜰ ᴡᴇ ꜱᴏʟᴠᴇ ᴛʜɪꜱ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ꜱᴛᴀᴛᴇᴍᴇɴᴛ, ᴡᴇ ɢᴇᴛ:

20/25 = ⅘

20 x 5 = 25 x 4

100 = 100

ᴛʜᴇʀᴇꜰᴏʀᴇ, ᴛʜᴇ ʀᴀᴛɪᴏ ᴅᴇꜰɪɴᴇꜱ ᴛʜᴇ ʀᴇʟᴀᴛɪᴏɴ ʙᴇᴛᴡᴇᴇɴ ᴛᴡᴏ Qᴜᴀɴᴛɪᴛɪᴇꜱ ꜱᴜᴄʜ ᴀꜱ ᴀ:ʙ, ᴡʜᴇʀᴇ ʙ ɪꜱ ɴᴏᴛ ᴇQᴜᴀʟ ᴛᴏ 0. ᴇxᴀᴍᴘʟᴇ: ᴛʜᴇ ʀᴀᴛɪᴏ ᴏꜰ 2 ᴛᴏ 4 ɪꜱ ʀᴇᴘʀᴇꜱᴇɴᴛᴇᴅ ᴀꜱ 2:4 = 1:2. ᴀɴᴅ ᴛʜᴇ ꜱᴛᴀᴛᴇᴍᴇɴᴛ ɪꜱ ꜱᴀɪᴅ ᴛᴏ ʙᴇ ɪɴ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ʜᴇʀᴇ. ᴛʜᴇ ᴀᴘᴘʟɪᴄᴀᴛɪᴏɴ ᴏꜰ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ᴄᴀɴ ʙᴇ ꜱᴇᴇɴ ɪɴ ᴅɪʀᴇᴄᴛ ᴘʀᴏᴘᴏʀᴛɪᴏɴ.

• ᴡʜᴀᴛ ɪꜱ ʀᴀᴛɪᴏ ᴀɴᴅ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ɪɴ ᴍᴀᴛʜꜱ?

ᴛʜᴇ ᴅᴇꜰɪɴɪᴛɪᴏɴ ᴏꜰ ʀᴀᴛɪᴏ ᴀɴᴅ ᴘʀᴏᴘᴏʀᴛɪᴏɴ ɪꜱ ᴅᴇꜱᴄʀɪʙᴇᴅ ʜᴇʀᴇ ɪɴ ᴛʜɪꜱ ꜱᴇᴄᴛɪᴏɴ. ʙᴏᴛʜ ᴄᴏɴᴄᴇᴘᴛꜱ ᴀʀᴇ ᴀɴ ɪᴍᴘᴏʀᴛᴀɴᴛ ᴘᴀʀᴛ ᴏꜰ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄꜱ. ɪɴ ʀᴇᴀʟ ʟɪꜰᴇ ᴀʟꜱᴏ, ʏᴏᴜ ᴍᴀʏ ꜰɪɴᴅ ᴀ ʟᴏᴛ ᴏꜰ ᴇxᴀᴍᴘʟᴇꜱ ꜱᴜᴄʜ ᴀꜱ ᴛʜᴇ ʀᴀᴛᴇ ᴏꜰ ꜱᴘᴇᴇᴅ (ᴅɪꜱᴛᴀɴᴄᴇ/ᴛɪᴍᴇ) ᴏʀ ᴘʀɪᴄᴇ (ʀᴜᴘᴇᴇꜱ/ᴍᴇᴛᴇʀ) ᴏꜰ ᴀ ᴍᴀᴛᴇʀɪᴀʟ, ᴇᴛᴄ, ᴡʜᴇʀᴇ ᴛʜᴇ ᴄᴏɴᴄᴇᴘᴛ ᴏꜰ ᴛʜᴇ ʀᴀᴛɪᴏ ɪꜱ ʜɪɢʜʟɪɢʜᴛᴇᴅ.

ᴘʀᴏᴘᴏʀᴛɪᴏɴ ɪꜱ ᴀɴ ᴇQᴜᴀᴛɪᴏɴ ᴡʜɪᴄʜ ᴅᴇꜰɪɴᴇꜱ ᴛʜᴀᴛ ᴛʜᴇ ᴛᴡᴏ ɢɪᴠᴇɴ ʀᴀᴛɪᴏꜱ ᴀʀᴇ ᴇQᴜɪᴠᴀʟᴇɴᴛ ᴛᴏ ᴇᴀᴄʜ ᴏᴛʜᴇʀ. ꜰᴏʀ ᴇxᴀᴍᴘʟᴇ, ᴛʜᴇ ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ʙʏ ᴛʀᴀɪɴ ᴛᴏ ᴄᴏᴠᴇʀ 100ᴋᴍ ᴘᴇʀ ʜᴏᴜʀ ɪꜱ ᴇQᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ʙʏ ɪᴛ ᴛᴏ ᴄᴏᴠᴇʀ ᴛʜᴇ ᴅɪꜱᴛᴀɴᴄᴇ ᴏꜰ 500ᴋᴍ ꜰᴏʀ 5 ʜᴏᴜʀꜱ. ꜱᴜᴄʜ ᴀꜱ 100ᴋᴍ/ʜʀ = 500ᴋᴍ/5ʜʀꜱ.