Select all ratios equivalent to 21:6.

Question image

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

  1. 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 $7:2$.

  1. 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.

  • 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 $21:6$.

  1. 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.
Thank you for voting!
Use Quizgecko on...
Browser
Browser