Choose the proportion that is true.
3/8=15/40
12/13=2/3
9/13=27/36
16/49=4/7
The Correct Answer and Explanation is:
The correct proportion is:
3/8 = 15/40
Explanation:
A proportion is an equation that states two ratios are equal. To check if a proportion is true, we can cross-multiply the two ratios and see if the products are equal.
1. 3/8 = 15/40
To check if these two ratios are equal, we can use cross-multiplication:
- Multiply 3 by 40: ( 3 \times 40 = 120 )
- Multiply 8 by 15: ( 8 \times 15 = 120 )
Since both products are equal (120 = 120), the proportion 3/8 = 15/40 is correct. Therefore, this is the true proportion.
To further simplify the second fraction ( 15/40 ), notice that both 15 and 40 can be divided by their greatest common divisor (GCD), which is 5:
- ( 15 \div 5 = 3 )
- ( 40 \div 5 = 8 )
So, ( 15/40 ) simplifies to ( 3/8 ), which confirms that the original proportion is valid.
2. 12/13 = 2/3
Let’s cross-multiply this proportion:
- Multiply 12 by 3: ( 12 \times 3 = 36 )
- Multiply 13 by 2: ( 13 \times 2 = 26 )
Since 36 is not equal to 26, this proportion is not true. Therefore, 12/13 = 2/3 is incorrect.
3. 9/13 = 27/36
Let’s cross-multiply this proportion:
- Multiply 9 by 36: ( 9 \times 36 = 324 )
- Multiply 13 by 27: ( 13 \times 27 = 351 )
Since 324 is not equal to 351, the proportion 9/13 = 27/36 is incorrect.
4. 16/49 = 4/7
Let’s cross-multiply this proportion:
- Multiply 16 by 7: ( 16 \times 7 = 112 )
- Multiply 49 by 4: ( 49 \times 4 = 196 )
Since 112 is not equal to 196, the proportion 16/49 = 4/7 is incorrect.
Conclusion:
The proportion that is true is 3/8 = 15/40.