Fractions: learn and practice

Who this lesson is for

This fractions lesson is for grades 3–5. Grade 3 names equal parts and equivalent fractions, grade 4 adds fractions with the same denominator, and grade 5 adds fractions whose denominators are related. The practice link opens grade 4 addition. The same lesson is linked from each of those grade hubs.

A fraction names equal parts

A fraction names part of one whole, or part of one group. The bottom number is the denominator. It tells how many equal parts the whole is split into. The top number is the numerator. It tells how many of those parts you have. In 3/4 the whole is split into 4 equal parts and 3 of them are counted. One half, written 1/2, means 1 of 2 equal parts. The parts have to be the same size. Four unequal pieces of a bar are not fourths, even if there are four of them.

Equivalent fractions name the same amount

Two fractions can look different and still name the same amount. One half of a bar is the same amount as two quarters of that bar, so 1/2 = 2/4. These are equivalent fractions. You make another equivalent fraction by multiplying the numerator and the denominator by the same whole number. Multiply 1/2 by 2/2 and you get 2/4. Multiply by 3/3 and you get 3/6. You are multiplying by 1, written as a fraction, so the amount does not change. Only the size of the pieces changes.

Worked example 1: shade one half

A bar is already split into 4 equal parts. Shade 1/2 of the bar. The drawing is in fourths, so the answer should be written in fourths too. One half of 4 parts is 2 parts, because 4 ÷ 2 = 2. Shade 2 of the 4 parts. The shaded fraction is 2/4. Check the equivalence: 2/4 = 1/2, since dividing both numbers by 2 gives 1/2. If the same bar had been split into sixths, one half would be 3/6. The picture uses more lines, and the shaded amount is still half of the bar.

Worked example 2: add fifths

Add 1/5 + 2/5. The denominators already match, so the pieces are the same size and you may add the numerators. 1 + 2 = 3. The denominator stays 5, because you still have fifths. The sum is 3/5. Do not add the denominators. 1/5 + 2/5 is not 3/10. That mistake treats the fraction as two separate whole numbers. On a number line, start at the first fifth and move two more fifths. You land on 3/5, which is less than 1. Three fifths cannot be simplified, because 3 and 5 share no factor other than 1.

Worked example 3: a fraction of a group

A bag has 20 apples. What is 3/4 of 20? The word of means multiply. Find one fourth of 20 first: 20 ÷ 4 = 5. Then take three of those parts: 3 × 5 = 15. So 3/4 of 20 apples is 15 apples. The same product written as one multiplication is (3/4) × 20 = 60/4 = 15. Both paths agree, which is a useful check. You did not need a common denominator here, because you were taking a part of a whole number rather than adding two fractions.

Checks before you leave the problem

Before you finish, ask three questions. Are the parts equal? Did you add numerators only when the denominators match? If the problem asks for simplest form, divide by a common factor until you cannot. Then practice the same addition on the board.

Common questions about fractions

Can a fraction be greater than 1?

Yes. 5/4 means five quarter-pieces, which is more than one whole. You can write the same amount as the mixed number 1 1/4. Both names are correct. Use the form the problem requests.

Should every answer be simplified?

Simplify when the problem says simplest form, or when you are checking two answers against each other. 2/4 and 1/2 are equal. Simplest form uses the smallest whole numbers, so 1/2.

What if the denominators are different?

Do not add the numerators until the parts are the same size. Rename one fraction so the denominators match, then add. Grade 4 practice on this page starts with a shared denominator.