Which of the following fractions is equivalent to 10/12? 40/48 20/30 4/5 12/14
The correct answer and explanation is:
The fraction equivalent to 10/12 from the options given is 40/48.
Here is the explanation:
Two fractions are equivalent if they represent the same value when simplified or expressed in lowest terms. To check if a fraction is equivalent to 10/12, simplify both fractions or cross-multiply to compare.
First, simplify 10/12:
- Both numerator and denominator can be divided by 2.
- 10 ÷ 2 = 5
- 12 ÷ 2 = 6
- So, 10/12 simplifies to 5/6.
Now check each option to see if it also simplifies to 5/6 or has the same value:
- 40/48
- Divide numerator and denominator by 8.
- 40 ÷ 8 = 5
- 48 ÷ 8 = 6
- So, 40/48 simplifies to 5/6, which matches 10/12 simplified.
- 20/30
- Divide numerator and denominator by 10.
- 20 ÷ 10 = 2
- 30 ÷ 10 = 3
- So, 20/30 simplifies to 2/3, which is not equal to 5/6.
- 4/5
- This fraction cannot be simplified further.
- 4/5 is not equal to 5/6.
- 12/14
- Divide numerator and denominator by 2.
- 12 ÷ 2 = 6
- 14 ÷ 2 = 7
- So, 12/14 simplifies to 6/7, which is not equal to 5/6.
Since only 40/48 simplifies to 5/6, it is equivalent to 10/12.
This process of checking equivalence through simplification or cross multiplication ensures accuracy. It helps identify fractions representing the same portion or value, even if they look different initially. This skill is fundamental in mathematics, especially when working with ratios, proportions, or fractions in various problems.