English | Español

Try our Free Online Math Solver!

Online Math Solver












Please use this form if you would like
to have this math solver on your website,
free of charge.

Fractions II


• Are whole numbers fractions ?

• If Annie got 1/8 of a pie and Manny got 1/13 of a pie, who ate more pie?

▪ If Annie got 2/3 of a pie and Manny got 3/4 of a pie, who ate more pie?

▪ How can we compare fractions ? Are there some that are easier to compare?

Comparing fractions

▪ Convert fractions into equivalent ones that are easier to compare.

▪ OR

▪ Use your fraction sense.

But, I could also think about how far each of these is from 1!


▪ Arrange these fractions from smallest to largest without converting to equivalent fractions, decimals, drawing pictures . Use your fraction sense and reasoning tools:

▪ Is it possible to put a fraction between any two fractions on a number line?

▪ Why or why not?

▪ We say that the set of fractions is dense.

Addition of fractions

▪ Can you come up with a way of adding two fractions with equal denominators ? Give an example and show on a model why your method works .

▪ What about adding fractions with different denominators ?


▪ Let be any two fractions. Then


▪ Some students initially view the addition of fractions as adding the numerators and denominators as follows :

Using this example discuss why such method for addition is unreasonable.



▪ What properties of whole number addition do you think fraction addition has?

▪ Closure?

▪ Commutativity?

▪ Associativity?

▪ Additive identity?



▪ Let be any two fractions. Then

Mental math and properties of addition

Multiplication: a whole number times a fraction

▪ Use the repeated addition approach:

Multiplication: a fraction times a whole number

▪ Repeated addition doesn’t make sense for

▪ We can think of taking one third of 6.

Multiplication: a fraction times a fraction

▪ Use the new approach!

is one fifth of


Take one fifth:


▪ For any two fractions we define


▪ Is Why or why not?

Properties of multiplication

▪ All the properties of whole number multiplication and

▪ Multiplicative inverse property:

▪ For every nonzero fraction  there is a unique fraction such that


▪ During one evening Kathleen devoted 2/5 of her time to mathematics , 3/20 of her time to Spanish, 1/3 of her time to biology and the remaining 35 minutes to English. How much time did she spend studying her Spanish?

Prev Next