Grade 4 Mathematics
Equivalent fractions are different fractions that represent the same amount.
To find an equivalent fraction, multiply or divide BOTH the numerator AND denominator by the SAME number.
This works because you're really multiplying by 1 (like 2/2 = 1 or 3/3 = 1)!
1/2 and 2/4 show the SAME amount!
Pick a number to multiply by. Let's use 2.
Multiply BOTH numerator and denominator by 2:
Remember: 2/2 = 1, so we're just multiplying by 1!
6/8 simplifies to 3/4
Find a common factor of 6 and 8. Both can be divided by 2.
Divide BOTH numerator and denominator by 2:
3/4 is in simplest form (3 and 4 share no common factors except 1)!
WRONG: To find an equivalent fraction for 1/3, some students add 2 to both: 1+2=3 and 3+2=5, so they write 3/5. This is INCORRECT!
RIGHT: MULTIPLY both by 2: 1x2=2 and 3x2=6, so 1/3 = 2/6. Always multiply (or divide), never add or subtract!
Memorize these benchmarks to quickly compare fractions:
Ask yourself: "Is this fraction less than, equal to, or greater than 1/2?"
Example: 5/8 is greater than 1/2 (because 4/8 = 1/2, and 5/8 > 4/8)
1. Find an equivalent fraction for 2/3 with a denominator of 9.
What did you multiply by?
2. Simplify 8/12 to its lowest terms.
What did you divide by?
3. Are these fractions equivalent? Circle YES or NO, then explain.
YES / NO
How do you know? ___________________________________
4. Compare using benchmarks. Write < , > , or =
Hint: How does each compare to 1/2?