Math Background

Fractions, Ratios, Rates, and Percents: When Students Ask

  • What's the difference between a fraction and a ratio?
    A fraction is a number that names part of a whole or part of a group. The denominator represents the total number of equal parts the whole is divided into. A ratio is a comparison of two quantities. For example, in a group of five students in which there are 4 boys and 1 girl, the fraction of the group that is female is one-fifth . The fraction of the group that is male is four-fifths . The denominator will always be five because the whole group consists of five students.

    In the example given above, the ratio of girls to boys is one-fourth and the ratio of boys to girls is four over one . The ratio of girls to students is one-fifth , and the ratio of boys to students is four-fifths . Ratios depend on the numbers that are being compared.When you are describing a part of a whole, a fraction is appropriate. When you are comparing two numbers, a ratio is appropriate.

    If you slice a pizza into 8 equal parts and eat 3 of the slices, what portion of the pizza remains? eight over onethree-eighths = five-eighths ; the fraction five-eighths names the part of the pizza that remains uneaten. If 4 of the remaining slices contain mushrooms and the other slice is plain cheese, the ratio of plain pizza slices to mushroom pizza slices would be 1 to 4; the ratio of mushroom slices to slices that remain is 4 to 5.

    Another example is a juice drink that consists of 1 part juice to 3 parts water. The ratio of juice to water is one-third , but the fraction of the drink that is juice is one-fourth .

  • When will I use rates?
    Rates are important when you are traveling and are comparing speed, distance, and time. Suppose a car trip takes 3 hours, and the distance traveled is 171 miles.
    Rate = distance traveled
                      time
    Rate = 171 miles, or 57 miles per hour
                3 hours
    Rate = distance traveled
    time
    Rate = 171 miles, or 57 miles per hour
    3 hours

    Rates are also important in figuring gas consumption, or the number of miles driven per gallon. Rates of interest are the conditions for repaying borrowed money. The postal service uses rates based on weight and time to charge for sending letters and packages. Baseball pitchers have fastballs clocked in miles per hour.

  • What's the difference between a ratio and a percent?
    A ratio is a comparison of any two numbers by division. A percent is a special ratio that compares any number to 100, with 100 representing one whole. Representing the unit whole by 100 makes comparisons simple. For example, comparing 15% and 40% is easier than comparing the ratios 3 to 20 and 2 to 5. The ratio of outfielders to infielders during a baseball game is 3 to 6 or one-half . Fifty percent of the number of infielders is the number of outfielders. The ratio of outfielders on the team is three-ninths ; the percent of outfielders on a team is 33one-third %.
  • Is there such a number as a million percent?
    Yes. It is written as 1,000,000%. Students can understand percents in terms of an increase in their allowance: If their allowance is $6.00 a week, 50% of that amount is $3.00 ($6.00 x 0.50 = $3.00). 100% of $6.00 equals $6.00. 200% of $6.00 equals $12.00, or twice the allowance ($6.00 x 2.00 = 12.0000 = $12.00). As you increase the percent, you increase the allowance proportionally. 500% would be 5 times the allowance, or $30.00. 1,000% would be 10 times $6.00, or $60.00. 1,000,000% of $6.00 would be 10,000 times the allowance, or $60,000.00 (sixty thousand dollars).

Houghton Mifflin Math Grade 5