find four equivalent fractions of each of the following fractions 3/4
The Correct Answer and Explanation is:
To find four equivalent fractions of 3/4, we multiply both the numerator (top number) and the denominator (bottom number) by the same nonzero number. This method keeps the value of the fraction the same.
Here are four equivalent fractions of 3/4:
- Multiply by 2:
(3×2)/(4×2)=6/8(3 × 2)/(4 × 2) = 6/8(3×2)/(4×2)=6/8 - Multiply by 3:
(3×3)/(4×3)=9/12(3 × 3)/(4 × 3) = 9/12(3×3)/(4×3)=9/12 - Multiply by 4:
(3×4)/(4×4)=12/16(3 × 4)/(4 × 4) = 12/16(3×4)/(4×4)=12/16 - Multiply by 5:
(3×5)/(4×5)=15/20(3 × 5)/(4 × 5) = 15/20(3×5)/(4×5)=15/20
So, four equivalent fractions of 3/4 are:
6/8, 9/12, 12/16, and 15/20
Explanation
A fraction represents a part of a whole. The fraction 3/4 means 3 parts out of 4 equal parts. To find equivalent fractions, we create new fractions that have different numerators and denominators but still represent the same value or portion.
The key to finding equivalent fractions is multiplying or dividing both the numerator and denominator by the same number. This is because when you multiply both parts of the fraction by the same number, you are simply increasing the number of parts and their size equally, so the overall value does not change.
For example, if you multiply both 3 and 4 by 2, you get 6 and 8. The new fraction becomes 6/8. Even though the numbers are different, if you simplify 6/8 by dividing both numbers by 2, you get back to 3/4, showing that the value is the same.
Similarly, multiplying by 3 gives 9/12, by 4 gives 12/16, and by 5 gives 15/20. All these are equal in value to 3/4. If you were to simplify any of them, you would return to the original fraction.
This process helps compare, add, or subtract fractions with different denominators and is useful in daily life situations such as cooking, dividing items, or measuring.
In summary, equivalent fractions represent the same quantity, and you can find them by multiplying or dividing both the numerator and denominator by the same number.
