What Are Equivalent Fractions?

Hi, Year 6! Today, we’re going to learn about equivalent fractions. Equivalent fractions are different fractions that represent the same part of a whole.

Understanding Fractions

First, let’s remember what a fraction is. A fraction has two parts:

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

For example, in the fraction \frac{1}{2}

, 1 is the numerator, and 2 is the denominator. This means we have 1 part out of 2 equal parts.

Equivalent Fractions Explained

Now, let’s see what equivalent fractions look like.

For example, the fractions \frac{1}{2}

and \frac{2}{4}
are equivalent. They both represent the same amount. If you have one half of a pizza, it is the same as having two quarters of that same pizza.

How to Find Equivalent Fractions

You can find equivalent fractions by either:

  1. Multiplying the numerator and denominator by the same number.
  2. Dividing the numerator and denominator by the same number.

Example 1: Multiplying

  • Start with \frac{1}{2}
    .
  • Multiply both the numerator and denominator by 2:\frac{1 \times 2}{2 \times 2} = \frac{2}{4}
    .

Example 2: Dividing

  • Start with \frac{4}{8}
    .
  • Divide both the numerator and denominator by 4:\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
    .

Key Rules to Remember

  • Same Value: Equivalent fractions have the same value, even if they look different.
  • Multiplication and Division: You can create equivalent fractions by multiplying or dividing the numerator and denominator by the same number.

Tips and Tricks

  • Use visual aids like pie charts or fraction bars to see how fractions are equivalent.
  • Remember to simplify fractions to their smallest form by dividing the numerator and denominator by their greatest common factor (GCF).

Practice Questions

Easy Level Questions

  1. What is \frac{2}{4}
    equivalent to?
  2. Is \frac{3}{6}
    equivalent to \frac{1}{2}
    ?
  3. What fraction is equivalent to \frac{1}{3}
    when multiplied by 2?
  4. What is \frac{4}{8}
    equal to?
  5. Is \frac{5}{10}
    equivalent to \frac{1}{2}
    ?
  6. What is \frac{6}{12}
    equivalent to?
  7. What fraction is equivalent to \frac{2}{5}
    when multiplied by 3?
  8. Is \frac{8}{16}
    equivalent to \frac{1}{2}
    ?
  9. What is \frac{9}{18}
    equal to?
  10. What fraction is equivalent to \frac{3}{9}
    ?

Medium Level Questions

  1. Find a fraction equivalent to \frac{4}{5}
    by multiplying by 3.
  2. Is \frac{10}{15}
    equivalent to \frac{2}{3}
    ?
  3. Find the equivalent fraction for \frac{7}{14}
    .
  4. What is \frac{12}{16}
    equal to?
  5. Convert \frac{5}{25}
    to an equivalent fraction.
  6. Is \frac{15}{20}
    equivalent to \frac{3}{4}
    ?
  7. Find a fraction equivalent to \frac{9}{27}
    .
  8. Simplify \frac{18}{24}
    to its equivalent fraction.
  9. What is \frac{16}{32}
    equal to?
  10. What fraction is equivalent to \frac{6}{15}
    ?

Hard Level Questions

  1. Find an equivalent fraction for \frac{11}{22}
    .
  2. Simplify \frac{45}{60}
    to its equivalent fraction.
  3. Is \frac{14}{21}
    equivalent to \frac{2}{3}
    ?
  4. Find a fraction equivalent to \frac{3}{4}
    by multiplying by 4.
  5. What is the GCF of the numerator and denominator of \frac{36}{48}
    ?
  6. Find an equivalent fraction for \frac{20}{30}
    .
  7. Is \frac{25}{30}
    equivalent to \frac{5}{6}
    ?
  8. Simplify \frac{28}{42}
    to its equivalent fraction.
  9. Find a fraction equivalent to \frac{8}{12}
    by dividing.
  10. Is \frac{36}{54}
    equivalent to \frac{2}{3}
    ?

Answers

Easy Level Answers

  1. \frac{1}{2}
  2. Yes
  3. \frac{2}{6}
  4. \frac{1}{2}
  5. Yes
  6. \frac{1}{2}
  7. \frac{6}{15}
  8. Yes
  9. \frac{1}{2}
  10. \frac{1}{3}

Medium Level Answers

  1. \frac{12}{15}
  2. Yes
  3. \frac{1}{2}
  4. \frac{3}{4}
  5. \frac{1}{5}
  6. Yes
  7. \frac{1}{3}
  8. \frac{3}{4}
  9. \frac{1}{2}
  10. \frac{2}{5}

Hard Level Answers

  1. \frac{1}{2}
  2. \frac{3}{4}
  3. No
  4. \frac{12}{16}
  5. 12
  6. \frac{2}{3}
  7. Yes
  8. \frac{2}{3}
  9. \frac{2}{3}
  10. Yes

I hope this helps you understand equivalent fractions better! Keep practicing, and you’ll become a fraction expert in no time!