Determine if the 3/8 and 375/1000 pairs are equal by writing each in their simplest form
The correct answer and explanation is:
To determine if the fractions 3/8 and 375/1000 are equal, first simplify both to their lowest terms.
Step 1: Simplify 3/8
The fraction 3/8 is already in its simplest form. The numerator (3) and the denominator (8) have no common factor other than 1.
So:
3/8 = 3/8
Step 2: Simplify 375/1000
To simplify this, find the greatest common factor (GCF) of 375 and 1000.
- Factors of 375: 1, 3, 5, 15, 25, 75, 125, 375
- Factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
- The greatest common factor is 125
Now divide both numerator and denominator by 125:
375 ÷ 125 = 3
1000 ÷ 125 = 8
So:
375/1000 = 3/8
Conclusion:
Since both 3/8 and 375/1000 simplify to the same value (3/8), they are equal.
Explanation:
Two fractions are considered equal if they reduce to the same simplest form. Simplifying a fraction means dividing both the numerator and the denominator by their greatest common factor. The fraction 3/8 is already in lowest terms, and 375/1000 reduces to 3/8 when both parts are divided by 125. This shows that both represent the same part of a whole. Simplifying fractions is a crucial step in comparing them, especially when the numerators and denominators differ. In practical situations, such as measurements, simplifying helps clarify equivalencies between values expressed in different forms. Therefore, 3/8 and 375/1000 are indeed equal.