Select all ratios equivalent to 21:6.
Understand the Problem
The question is asking us to identify which of the given ratios are equivalent to the ratio 21:6. To solve this, we will simplify 21:6 and compare it with the other ratios presented.
Answer
The ratios equivalent to $21:6$ are $7:2$ and $14:4$.
Answer for screen readers
The ratios equivalent to $21:6$ are $7:2$ and $14:4$.
Steps to Solve
- Simplify the Ratio 21:6
To simplify the ratio, divide both numbers by their greatest common divisor (GCD). The GCD of 21 and 6 is 3.
[ 21 \div 3 = 7 ] [ 6 \div 3 = 2 ]
So, $21:6$ simplifies to $7:2$.
- Compare with Other Ratios
Now that we know that $21:6$ is equivalent to $7:2$, we can compare this with the other given ratios.
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Check 4:3
This does not simplify to $7:2$, so it is not equivalent. -
Check 7:2
This is the same as the simplified form of $21:6$, so it is equivalent. -
Check 14:4
To check this ratio, simplify it by finding the GCD, which is 2.
[ 14 \div 2 = 7 ] [ 4 \div 2 = 2 ]
Thus, $14:4$ simplifies to $7:2$, making it equivalent to $21:6$.
- List the Equivalent Ratios
The ratios equivalent to $21:6$ are $7:2$ and $14:4$.
The ratios equivalent to $21:6$ are $7:2$ and $14:4$.
More Information
The ratio $21:6$ simplifies to $7:2$, which is a common form that represents the same relationship. Recognizing equivalent ratios is essential for various mathematical applications including proportions and scaling.
Tips
- Confusing the order of the numbers in the ratios. Ratios $a:b$ and $b:a$ are not the same.
- Failing to find the GCD correctly when simplifying ratios.
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