Ctrl+k

Generate equivalent ratios

Equivalent ratios describe the same multiplicative relationship between two quantities: multiplying or dividing both terms by the same positive scale factor produces a new ratio with the same value, as in 3:53:5 and 12:2012:20. The understanding includes generating and checking equivalent ratios with whole-number or rational quantities using ratio tables, pairs, or double-number lines, while distinguishing multiplicative scaling from adding the same amount; more advanced abstract or algebraic generalizations are outside this scope.

Detailed Explanation: Generate equivalent ratios

Equivalent ratios are made by multiplying or dividing both parts of a ratio by the same positive number.

For example, suppose you need to find a ratio equivalent to 3:53:5 with a first term of 1818.

  1. Find the scale factor:
3×6=183 \times 6=18

So, the scale factor is 66.

  1. Multiply the second term by the same factor:
5×6=305 \times 6=30
  1. Write the new ratio:
3:5=18:303:5=18:30
  1. Check by comparing the scale factors:
18÷3=6and30÷5=618\div 3=6 \qquad\text{and}\qquad 30\div 5=6

Since both terms were multiplied by 66, the ratios are equivalent.

Remember, you must multiply or divide both terms by the same number. Adding the same amount does not usually make an equivalent ratio. For example, 3:53:5 and 4:64:6 are not equivalent because the parts were changed by adding 11, not by using the same multiplicative scale factor.

Learn by doing: Generate equivalent ratios

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Ratios - Equivalent, Expanding Recipes with Non-Integer Multiples - Decimals


    ?