What are Equivalent Fractions?

Hello, Year 4! Today, we’re going to learn about equivalent fractions. But first, let’s understand what a fraction is. A fraction represents a part of a whole. For example, if you have a pizza and you cut it into 4 equal slices, each slice is a fraction of the whole pizza, represented as $$\frac{1}{4}$$.

Now, equivalent fractions are fractions that look different but actually represent the same amount. For example, $$\frac{1}{2}$$ and $$\frac{2}{4}$$ are equivalent fractions because if you have a whole pizza, both fractions show you have the same amount of pizza.

How to Find Equivalent Fractions

Key Rules

  1. Multiplying: You can create an equivalent fraction by multiplying both the top (numerator) and the bottom (denominator) of a fraction by the same number. For example:
    • If we take $$\frac{1}{2}$$ and multiply both the numerator and the denominator by 2, we get:
    $$\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$$.
  2. Dividing: You can also create equivalent fractions by dividing both the numerator and the denominator by the same number. For example:
    • If we take $$\frac{4}{8}$$ and divide both by 4, we get:
    $$\frac{4 \div 4}{8 \div 4} = \frac{1}{2}$$.

Tips and Tricks

  • Visual Aids: Sometimes it helps to draw pictures or use shapes to see the fractions. For example, if you shade in half of a square, you can see that shading in two out of four equal parts looks the same!
  • Multiples: Remember that equivalent fractions are just different ways of saying the same amount. Look for patterns in numbers. For instance, the fraction $$\frac{1}{3}$$ is equivalent to $$\frac{2}{6}$$ and $$\frac{3}{9}$$ because:
    • $$1 \times 2 = 2$$ and $$3 \times 2 = 6$$
    • $$1 \times 3 = 3$$ and $$3 \times 3 = 9$$
  • Fraction Wall: You can create a fraction wall where you list fractions that are equivalent. This can be a fun visual tool to see how fractions relate to one another.

Practice Questions

Now it’s time to practice what we’ve learned! Here are some questions for you.

Easy Level Questions

  1. What is $$\frac{2}{4}$$ equivalent to?
  2. Is $$\frac{1}{3}$$ equivalent to $$\frac{2}{6}$$?
  3. Write an equivalent fraction for $$\frac{3}{5}$$ by multiplying both by 2.
  4. What is $$\frac{4}{8}$$ equivalent to?
  5. Is $$\frac{2}{3}$$ equivalent to $$\frac{4}{6}$$?
  6. Write an equivalent fraction for $$\frac{1}{2}$$ by multiplying both by 3.
  7. What is $$\frac{6}{12}$$ equivalent to?
  8. Is $$\frac{3}{4}$$ equivalent to $$\frac{6}{8}$$?
  9. Write an equivalent fraction for $$\frac{5}{10}$$ by dividing both by 5.
  10. What is $$\frac{1}{4}$$ equivalent to?

Medium Level Questions

  1. Write an equivalent fraction for $$\frac{3}{7}$$ by multiplying both by 4.
  2. Are $$\frac{2}{5}$$ and $$\frac{4}{10}$$ equivalent?
  3. Write an equivalent fraction for $$\frac{5}{8}$$ by dividing both by 1.
  4. What is $$\frac{2}{6}$$ equivalent to?
  5. Are $$\frac{1}{6}$$ and $$\frac{2}{12}$$ equivalent?
  6. Write an equivalent fraction for $$\frac{4}{9}$$ by multiplying both by 3.
  7. What is $$\frac{8}{16}$$ equivalent to?
  8. Are $$\frac{3}{5}$$ and $$\frac{6}{10}$$ equivalent?
  9. Write an equivalent fraction for $$\frac{7}{14}$$ by dividing both by 7.
  10. What is $$\frac{9}{18}$$ equivalent to?

Hard Level Questions

  1. Write an equivalent fraction for $$\frac{5}{12}$$ by multiplying both by 5.
  2. Are $$\frac{4}{10}$$ and $$\frac{2}{5}$$ equivalent?
  3. Write an equivalent fraction for $$\frac{6}{15}$$ by dividing both by 3.
  4. What is $$\frac{1}{10}$$ equivalent to when the numerator is multiplied by 2?
  5. Are $$\frac{8}{12}$$ and $$\frac{2}{3}$$ equivalent?
  6. Write an equivalent fraction for $$\frac{7}{21}$$ by dividing both by 7.
  7. What is $$\frac{12}{16}$$ equivalent to?
  8. Are $$\frac{2}{8}$$ and $$\frac{1}{4}$$ equivalent?
  9. Write an equivalent fraction for $$\frac{9}{27}$$ by dividing both by 9.
  10. What is $$\frac{5}{25}$$ equivalent to when the numerator is multiplied by 3?

Answers

Easy Level Answers

  1. $$\frac{1}{2}$$
  2. Yes
  3. $$\frac{6}{10}$$
  4. $$\frac{1}{2}$$
  5. Yes
  6. $$\frac{3}{6}$$
  7. $$\frac{1}{2}$$
  8. Yes
  9. $$\frac{1}{2}$$
  10. $$\frac{2}{8}$$

Medium Level Answers

  1. $$\frac{12}{28}$$
  2. Yes
  3. $$\frac{5}{8}$$
  4. $$\frac{1}{3}$$
  5. Yes
  6. $$\frac{12}{27}$$
  7. $$\frac{1}{2}$$
  8. Yes
  9. $$\frac{1}{2}$$
  10. $$\frac{1}{2}$$

Hard Level Answers

  1. $$\frac{25}{60}$$
  2. Yes
  3. $$\frac{2}{5}$$
  4. $$\frac{2}{20}$$
  5. Yes
  6. $$\frac{1}{3}$$
  7. $$\frac{3}{4}$$
  8. Yes
  9. $$\frac{1}{3}$$
  10. $$\frac{15}{75}$$

Great job, Year 4! Keep practicing those equivalent fractions, and soon you’ll be a fraction expert!