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Generate a list of equivalent fractions. All fractions represent the same value with different numbers.
Equivalent fractions are different fractions that represent the same value or proportion. They look different but mean the same thing. For example, 1/2, 2/4, 3/6, and 4/8 are all equivalent because they all equal 0.5 or "one half."
Think of it like pizza: 1/2 of a pizza is the same amount as 2/4 of the same pizza - you're just cutting it into different numbers of pieces.
There are three ways: (1) Simplify both to lowest terms - if they're the same, they're equivalent. (2) Cross-multiply - if a/b and c/d are equivalent, then a×d = b×c. (3) Convert to decimals - if they equal the same decimal, they're equivalent. For example, 2/3 and 4/6: cross-multiply 2×6 = 12 and 3×4 = 12, so they're equivalent.
Simplifying is finding the equivalent fraction with the smallest numbers. When you simplify 6/8 to 3/4, you're finding an equivalent fraction by dividing (instead of multiplying). Both processes maintain the same value - one makes numbers bigger, one makes them smaller.
Yes! You can divide both numerator and denominator by the same number, but only if they're both divisible by it. For example, 10/15 ÷ 5/5 = 2/3. This is actually simplifying - creating an equivalent fraction with smaller numbers. However, multiplying works with any number, while dividing only works with common factors.
Infinitely many! Since you can multiply by any whole number (2, 3, 4, 5, ...), every fraction has unlimited equivalent forms. For example, 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = ... and so on forever.
Because n/n equals 1, and multiplying anything by 1 doesn't change its value. For example, 2/3 × 4/4 = (2×4)/(3×4) = 8/12. Since 4/4 = 1, we're essentially multiplying by 1, so 2/3 and 8/12 have the same value.
Divide the desired denominator by the original denominator to find the multiplier, then multiply both parts. For example, to convert 2/5 to a denominator of 15: 15÷5 = 3, so multiply by 3/3: 2/5 = 6/15. This is useful when adding fractions with different denominators.