Fractions for Kids: How to Explain Them Simply

Fractions are often the topic where students first feel lost in math. The easiest way to explain them is with things you can cut into pieces. Below is what a fraction is, how to show it to a child, how to compare, add, multiply and divide fractions and which mistakes come up most often.

What a Fraction Is

The word fraction comes from the Latin fractus, “broken”: a fraction names a part of a whole. In 3/4, the bottom number, the denominator, tells how many equal parts the whole was split into, and the top number, the numerator, tells how many of those parts you take. Three quarters of a cake is a cake cut into four equal slices, three of which you take.

How to Show Fractions to a Child

• Cut an apple, a pizza or a paper circle into equal parts and name each one: a half, a third, a quarter.
• Show that more parts means smaller parts: 1/4 is less than 1/2, even though 4 is more than 2.
• Fold a strip of paper in half, then again, and your child will see for themselves that 2/4 is the same half.

Equal Fractions and Simplifying

Multiplying or dividing the top and bottom by the same nonzero number does not change a fraction: 1/2 = 2/4 = 3/6. Dividing both by a common factor is called simplifying: 6/8 = 3/4.

Comparing, Adding and Subtracting

With the same denominator, it is simple: 2/7 + 3/7 = 5/7, and the fraction with the bigger numerator is larger. With different denominators, first rewrite the fractions over a common denominator: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Multiplying and Dividing

To multiply, multiply the tops together and the bottoms together: 2/3 × 3/5 = 6/15 = 2/5. To divide by a fraction, multiply by its reciprocal, the fraction with the top and bottom swapped: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Improper Fractions and Mixed Numbers

A fraction whose numerator is smaller than its denominator is called proper and is less than 1. If the numerator is equal to or larger than the denominator, the fraction is improper, like 7/4, and it can be written as a mixed number, a whole number plus a proper fraction: 7/4 = 1 3/4. A fraction is also a division: 3/4 = 3 ÷ 4 = 0.75.

Common Mistakes

• Adding the denominators: 1/2 + 1/3 is not 2/5.
• Comparing by the denominator alone: 1/4 has a bigger denominator than 1/2, yet it is the smaller fraction.
• Forgetting to simplify the answer.

Fractions are hard without a solid grasp of times tables, the subject of The Multiplication Table: Its History and How to Learn It.

How to keep a child interested in math is covered in How to Motivate a Child to Learn Math Online.

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