Find equivalent fractions using multiplication and division
Fractions can wear disguises! 🥸 Fractions that look different but have the same value are 'equivalent'. The secret to finding them is a simple rule: whatever you do to the top, you do to the bottom!
Do this: Read the concept below, then try the quiz or activity.
Concept
The most powerful way to find equivalent fractions is by using multiplication and division. This is faster than drawing models every time.
The Golden Rule: To create an equivalent fraction, you must multiply OR divide the numerator and the denominator by the same non-zero number.
1. Finding Equivalent Fractions using Multiplication (Building Up) This makes the numbers in the fraction bigger, but the value stays the same.
* Example: Find a fraction equivalent to 2/3.
* Let's multiply by 4/4 (which is the same as 1).
* (2 x 4) / (3 x 4) = 8/12
* So, 2/3 and 8/12 are equivalent.* Example: 3/5 = ?/20
* Think: "What did I do to the 5 to get 20?" (5 x 4 = 20).
* Do the same to the top: 3 x 4 = 12.
* So, 3/5 = 12/20.2. Finding Equivalent Fractions using Division (Simplifying) This makes the numbers in the fraction smaller. This is also called "simplifying" or "reducing" a fraction.
* Example: Simplify the fraction 9/12.
* Think: "What number can divide both 9 and 12?" The number is 3 (their greatest common factor).
* Divide both by 3:
* (9 ÷ 3) / (12 ÷ 3) = 3/4
* So, 9/12 simplifies to 3/4. They are equivalent.* A fraction is in its simplest form when you can't divide the top and bottom by any common number other than 1.
Key Idea: Multiplying or dividing a fraction by a version of 1 (like 2/2, 3/3, 4/4...) doesn't change its value, it just changes what it looks like. It's like trading a $1 bill for four quarters – different look, same value.
Try it
Practice finding equivalent fractions!
Using Multiplication: 1. 2/5 = ?/10 2. 3/4 = 9/? 3. 5/6 = ?/18 4. Find two fractions equivalent to 1/3.
Using Division (Simplifying): 5. 6/8 = ?/4 6. 10/15 = 2/? 7. Write 8/12 in simplest form. 8. Write 15/20 in simplest form.
Mixed Practice: 9. Are 4/5 and 12/15 equivalent? (Yes/No) 10. Are 3/7 and 6/12 equivalent? (Yes/No) 11. Find the missing number: 4/9 = 16/? 12. Simplify: 20/25
Word Problems: 13. John ate 4/8 of a pizza. What is this fraction in simplest form? 14. A recipe calls for 3/4 cup of sugar. You only have a measuring cup for 12ths of a cup. How many 12ths do you need? (3/4 = ?/12)
Challenge Problems: 15. Find a fraction with a denominator of 100 that is equivalent to 7/10. 16. Simplify the fraction 36/48 completely.