A ratio is a comparison of two numbers or measures using division. BACK  The numbers being compared have the same units.

RATIOS  Note: ratios are “unitless” (no units) A ratio can be written three ways: 3:5 3/5 3 to 5

Ratios are often expressed as fractions in simplest form BACK

A ratio is the comparison of two numbers with the same units by division. A ratio may be written in three ways. What ratios can we form from the tiles above? 12 to 8 BACK

Create as many ratios as possible. Write each ratio three different ways. BACK

Butterfly Ratios

Simplest Form  Write the ratio 50 to 300 in simplest form. BACK

Simplest Form  Write the ratio 60¢ per dozen in simplest form. BACK

Look over the ratios you have written. Is there another way that you can write those ratios? The ratio illustrated here is four filled cells to ten total cells. The ratio shown here is two filled cells to five total cells. What do you know about these two ratios? How can you prove your answer? BACK

RATES  A rate is the comparison of two numbers with different units.  A rate is written as a quotient (fraction) in simplest form.  Note: rates have units

Ex: Write the rate of 25 yards to 30 seconds in simplest form. What are we comparing? yards & seconds25 yards to 30 seconds Units can’t simplify since they are different. Simplify The rate is 5 yards/6 seconds.

Ex: Write the rate of 140 miles in 2 hours in simplest form. What are we comparing? miles & hours140 miles to 2 hours Units can’t simplify since they are different. Simplify The rate is 70 miles/1 hour (70 miles per hour, mph). Notice the denominator is 1 after simplifying.

Unit Rate To find the Unit Rate, you would find the cost or amount for 1. Or the rate when the denominator is 1. “How much for just 1?” BACK

UNIT RATES  The 1 in the denominator is dropped and often the word “per” is used to make the comparison. Ex: miles per hour  mph miles per gallon  mpg

Ex: Write as a unit rate 20 patients in 5 rooms What are we comparing? patients & rooms20 patients in 5 rooms Units can’t simplify since they are different. Simplify The rate is 4 patients/1room  Four patients per room

If it costs $78 for 13 sandwiches, What is the unit rate? Unit Rate BACK

The cost of a 12-ounce box of Cheerios is $3.29. Publix brand Cheerios cost $4.89 for an 18-ounce box. Find the unit rate to find the better buy. BACK

Mile per Gallon  M.P.G. stands for miles per gallon and is usually used for gas mileage in cars. BACK

Unit Rate  If it takes 11 gallons to drive 250 miles, What is the unit rate or mpg? BACK

Solving Word Problems BACK

The End BACK