What ratios are equivalent to 26:14
The Correct Answer and Explanation is :
To find ratios equivalent to 26:14, we can simplify the ratio first and then find multiples of the simplified ratio.
Step 1: Simplifying the Ratio
To simplify the ratio 26:14, we divide both numbers by their greatest common divisor (GCD).
- The GCD of 26 and 14 is 2.
So, we divide both terms:
[
\frac{26}{2} : \frac{14}{2} = 13:7
]
Thus, the simplified form of 26:14 is 13:7.
Step 2: Finding Equivalent Ratios
To find equivalent ratios, we can multiply both sides of the simplified ratio (13:7) by the same non-zero integer. Here are a few examples:
- Multiply by 1:
- ( 13 \times 1 : 7 \times 1 = 13:7 ) (This is the original simplified ratio.)
- Multiply by 2:
- ( 13 \times 2 : 7 \times 2 = 26:14 ) (This is the original ratio.)
- Multiply by 3:
- ( 13 \times 3 : 7 \times 3 = 39:21 )
- Multiply by 4:
- ( 13 \times 4 : 7 \times 4 = 52:28 )
- Multiply by 5:
- ( 13 \times 5 : 7 \times 5 = 65:35 )
Conclusion
Thus, some equivalent ratios to 26:14 include:
- 13:7 (simplified ratio)
- 39:21 (obtained by multiplying both sides by 3)
- 52:28 (obtained by multiplying both sides by 4)
- 65:35 (obtained by multiplying both sides by 5)
Equivalent ratios maintain the same relationship between the two quantities, which can be useful in various mathematical contexts such as scaling recipes, comparing quantities, or solving problems involving proportions. Understanding equivalent ratios helps in recognizing that while the numbers can change, the fundamental relationship they represent remains constant.