Explain what equivalent fractions are and why they are equal in value
Find equivalent fractions by multiplying or dividing numerator and denominator by the same number
Fill in a missing numerator or denominator in an equivalent fraction pair
Use equivalent fractions to compare and order fractions
Real-World Applications
Recipes: A recipe for 4 people uses \(\frac{1}{2}\) cup of rice. Scaling up to 8 people means you need \(\frac{2}{4}\) = \(\frac{1}{2}\) doubled — understanding equivalence makes scaling easy.
Comparing prices: Is \(\frac{3}{8}\) of a litre for £1 better value than \(\frac{5}{12}\) of a litre for £1? Convert to equivalent fractions with the same denominator to compare.
Adding fractions: You cannot add \(\frac{1}{3} + \frac{1}{4}\) directly. First make equivalent fractions: \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12}\).
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Equivalent fractions have the same value but look different because they have different numerators and denominators. Think of cutting a pizza — whether you cut it into 2 and take 1 piece, or cut it into 4 and take 2 pieces, you have the same amount.
Key rule: You must multiply (or divide) BOTH the numerator AND the denominator by the same number. Doing it to just one changes the value of the fraction.
Example 1 — Find two fractions equivalent to \(\frac{2}{3}\)
Step 1
Multiply top and bottom by 2: \(\frac{2 \times 2}{3 \times 2} = \frac{4}{6}\)
Step 2
Multiply top and bottom by 5: \(\frac{2 \times 5}{3 \times 5} = \frac{10}{15}\)
Step 3
So \(\frac{2}{3} = \frac{4}{6} = \frac{10}{15}\). All three are equivalent.
Example 2 — Are \(\frac{3}{5}\) and \(\frac{9}{15}\) equivalent?
Step 1
Check: is the numerator multiplied by the same factor as the denominator? \(3 \times 3 = 9\) and \(5 \times 3 = 15\). Yes — factor is 3.
Step 2
\(\frac{3}{5} = \frac{9}{15}\) — they are equivalent.
✓ Quick Check 1 — What equivalent fractions are
Question 1 of 10
Finding Equivalent Fractions — Fill in the Missing Number
To find a missing numerator or denominator, work out the multiplying factor between the two denominators (or numerators), then apply the same factor to the other number.
Using Equivalent Fractions — Comparing and Real-Life
Equivalent fractions let us compare fractions (by giving them the same denominator) and help with adding fractions with different denominators. They also appear in scaled recipes.
Example 5 — Compare \(\frac{3}{4}\) and \(\frac{5}{6}\): which is larger?
Step 1
Find a common denominator. Smallest common multiple of 4 and 6 = 12.
Step 2
\(\frac{3}{4} = \frac{9}{12}\) (×3 on top and bottom)
Step 3
\(\frac{5}{6} = \frac{10}{12}\) (×2 on top and bottom)
Step 4
\(\frac{10}{12} > \frac{9}{12}\), so \(\frac{5}{6} > \frac{3}{4}\)
Example 6 — Recipe scaling
Step 1
A cake for 6 needs \(\frac{2}{3}\) cup of sugar. Scaling to 12 people (double) means doubling the fraction.
Step 2
\(\frac{2}{3} \times 2 = \frac{4}{3}\) cups. Or find equivalent fraction with denominator 3 for 12 portions.
Step 3
Answer: \(\frac{4}{3} = 1\frac{1}{3}\) cups of sugar for 12 people.
Tip for comparing: Always convert to the same denominator first, then compare numerators. The fraction with the bigger numerator is the larger fraction.
✓ Quick Check 3 — Using equivalent fractions
Question 1 of 10
Practice
Find the missing number or simplified fraction. Type just the number or fraction (e.g. 5 or 3/4).
#
Question
Your answer
Result
1
1/2 = ?/10 — what is the missing number?
2
3/4 = ?/20 — what is the missing number?
3
2/5 = ?/15 — what is the missing number?
4
Simplify 6/8 — give your answer as a fraction.
5
1/3 = ?/12 — what is the missing number?
6
5/6 = ?/18 — what is the missing number?
7
Simplify 10/15 — give your answer as a fraction.
⚠ Things to Watch Out For
Multiplying only the top or bottom: To make equivalent fractions, you MUST multiply (or divide) BOTH numerator and denominator by the same number. Changing only one part changes the fraction's value.
Using different operations on top and bottom: You cannot multiply the numerator by 3 and add 2 to the denominator. Both must undergo the same operation.
Confusing equivalent with equal in appearance: ½, 2/4, 3/6, 4/8 all look different but are equal in value. Always simplify to check if two fractions are equivalent.
Saying fractions are equivalent because numerators match: 2/3 and 2/5 are NOT equivalent — the denominators differ. Only fractions that represent the same proportion are equivalent.
Finding equivalent fractions for comparison: To compare ¾ and ⅔, find a common denominator (12): 9/12 and 8/12. Now you can compare directly.