Introduction to Ordering Fractions

Hello, Year 5! Today, we’re going to learn about ordering fractions. This means putting fractions in the right order, from the smallest to the largest or the largest to the smallest.

What is a Fraction?

A fraction shows a part of a whole. It has two numbers:

  • The top number (numerator) tells us how many parts we have.
  • The bottom number (denominator) tells us how many equal parts the whole is divided into.

For example, in the fraction \frac{3}{4}, 3 is the numerator, and 4 is the denominator.

Why Order Fractions?

Ordering fractions helps us compare them. It’s important because it helps us understand which fraction is larger or smaller.

How to Order Fractions

Here are some simple steps to help you order fractions:

Step 1: Make the Denominators the Same

To compare fractions easily, we often need to make the denominators (the bottom numbers) the same. This way, we can just look at the numerators.

Example:

  • To compare \frac{1}{2} and \frac{1}{3}, we need a common denominator. The smallest common denominator for 2 and 3 is 6.
  • Convert both fractions:
    • \frac{1}{2} = \frac{3}{6} (because 1 \times 3 = 3 and 2 \times 3 = 6)
    • \frac{1}{3} = \frac{2}{6} (because 1 \times 2 = 2 and 3 \times 2 = 6)

Now we compare:

  • \frac{3}{6} is bigger than \frac{2}{6}.
  • So, \frac{1}{2} > \frac{1}{3}.

Step 2: Compare the Numerators

Once the denominators are the same, compare the numerators:

  • The larger numerator means the larger fraction.

Step 3: Order the Fractions

Write the fractions in order from smallest to largest or vice versa based on your comparison.

Key Rules

  1. Same Denominator: If fractions have the same denominator, just compare the numerators.
  2. Different Denominators: Find a common denominator first.
  3. Simplifying: Sometimes, simplifying fractions can make it easier to compare them.

Tips and Tricks

  • Visual Aids: Draw pictures of fractions to see which is bigger.
  • Number Lines: Use number lines to place fractions accurately.
  • Practice: The more you practise, the better you’ll get!

Questions on Ordering Fractions

Easy Level Questions

  1. Order these fractions: \frac{1}{4}, \frac{1}{2}, \frac{3}{4}
  2. Which is greater: \frac{2}{5} or \frac{1}{5}?
  3. Order these fractions: \frac{1}{3}, \frac{2}{3}, \frac{1}{2}
  4. Which is smaller: \frac{3}{8} or \frac{5}{8}?
  5. Order these fractions: \frac{1}{6}, \frac{2}{6}, \frac{3}{6}
  6. Which is greater: \frac{2}{7} or \frac{3}{7}?
  7. Order these fractions: \frac{1}{10}, \frac{1}{5}, \frac{1}{2}
  8. Which is smaller: \frac{4}{5} or \frac{1}{5}?
  9. Order these fractions: \frac{2}{4}, \frac{1}{4}, \frac{3}{4}
  10. Which is greater: \frac{3}{10} or \frac{2}{10}?

Medium Level Questions

  1. Order these fractions: \frac{3}{5}, \frac{1}{2}, \frac{4}{5}
  2. Which is greater: \frac{2}{3} or \frac{3}{4}?
  3. Order these fractions: \frac{5}{6}, \frac{1}{2}, \frac{2}{3}
  4. Which is smaller: \frac{7}{8} or \frac{3}{4}?
  5. Order these fractions: \frac{2}{9}, \frac{5}{9}, \frac{3}{9}
  6. Which is greater: \frac{1}{4} or \frac{2}{5}?
  7. Order these fractions: \frac{2}{3}, \frac{3}{5}, \frac{1}{2}
  8. Which is smaller: \frac{5}{12} or \frac{1}{2}?
  9. Order these fractions: \frac{4}{7}, \frac{3}{7}, \frac{6}{7}
  10. Which is greater: \frac{5}{8} or \frac{1}{2}?

Hard Level Questions

  1. Order these fractions: \frac{1}{6}, \frac{3}{10}, \frac{1}{3}
  2. Which is greater: \frac{5}{12} or \frac{3}{8}?
  3. Order these fractions: \frac{7}{10}, \frac{2}{5}, \frac{4}{5}
  4. Which is smaller: \frac{9}{10} or \frac{7}{8}?
  5. Order these fractions: \frac{1}{2}, \frac{3}{5}, \frac{2}{3}
  6. Which is greater: \frac{3}{4} or \frac{5}{8}?
  7. Order these fractions: \frac{3}{10}, \frac{1}{5}, \frac{3}{5}
  8. Which is smaller: \frac{11}{12} or \frac{5}{6}?
  9. Order these fractions: \frac{5}{6}, \frac{2}{3}, \frac{1}{2}
  10. Which is greater: \frac{4}{5} or \frac{9}{10}?

Answers and Explanations

Easy Level Answers

  1. \frac{1}{4}, \frac{1}{2}, \frac{3}{4}
  2. \frac{2}{5} > \frac{1}{5}
  3. \frac{1}{3}, \frac{1}{2}, \frac{2}{3}
  4. \frac{3}{8} < \frac{5}{8}
  5. \frac{1}{6}, \frac{2}{6}, \frac{3}{6}
  6. \frac{3}{7} > \frac{2}{7}
  7. \frac{1}{10}, \frac{1}{5}, \frac{1}{2}
  8. \frac{4}{5} > \frac{1}{5}
  9. \frac{1}{4}, \frac{2}{4}, \frac{3}{4}
  10. \frac{3}{10} > \frac{2}{10}

Medium Level Answers

  1. \frac{1}{2}, \frac{3}{5}, \frac{4}{5}
  2. \frac{3}{4} > \frac{2}{3}
  3. \frac{1}{2}, \frac{2}{3}, \frac{5}{6}
  4. \frac{3}{4} < \frac{7}{8}
  5. \frac{2}{9}, \frac{3}{9}, \frac{5}{9}
  6. \frac{2}{5} < \frac{1}{4}
  7. \frac{1}{2}, \frac{3}{5}, \frac{2}{3}
  8. \frac{5}{12} < \frac{1}{2}
  9. \frac{3}{7}, \frac{4}{7}, \frac{6}{7}
  10. \frac{5}{8} > \frac{1}{2}

Hard Level Answers

  1. \frac{1}{6}, \frac{3}{10}, \frac{1}{3}
  2. \frac{5}{12} > \frac{3}{8}
  3. \frac{2}{5}, \frac{7}{10}, \frac{4}{5}
  4. \frac{9}{10} < \frac{7}{8}
  5. \frac{1}{2}, \frac{2}{3}, \frac{3}{5}
  6. \frac{3}{4} > \frac{5}{8}
  7. \frac{1}{5}, \frac{3}{10}, \frac{3}{5}
  8. \frac{11}{12} > \frac{5}{6}
  9. \frac{1}{2}, \frac{2}{3}, \frac{5}{6}
  10. \frac{9}{10} > \frac{4}{5}

Congratulations on learning how to order fractions! Keep practicing, and you’ll be a fraction ordering expert in no time!