Rates and ratios

The ratio is the relationship of two numbers. For example you have 2 flashlights and 5 batteries. To compare the ratio between the flashlights and the batteries we divide the set of flashlights with the set of batteries.

The ratio is 2 to 5 or 2:5 or 2/5. All these describe the ratio in different forms of fractions. The ratio can consequently be expressed as fractions or as a decimal. 2:5 in decimals is 0.4.

A rate is a little bit different than the ratio, it is a special ratio. It is a comparison of measurements that have different units, like cents and grams. A unit rate is a rate with a denominator of 1.


Sarah is buying jellybeans for her best friend's birthday party. She buys a bag of 10 lb of jellybeans that costs $45. Sarah is wondering how much 1 lb of jellybeans cost.

$$\$ 45=4500 \, cents$$

$$\frac{4500 \: cents}{10\: lb}=\frac{4500 \: cents{\color{green} {\, \div\, 10}}}{10\: lb{\color{green} {\, \div\, 10}}}=\frac{450 \: cents}{1\: lb}$$

$$1\: lb=450\: cents=\$ 4.50$$

Video lesson

Express the ratio as a fraction in simplest form and as a decimal