Ratio and Proportion

Once you know that a ratio is a comparison of two numbers and their relationship, understanding proportions becomes easy. A proportion means two equal ratios. An example of a proportion is 1:2=2:4.

One way to check if the proportion is correct is by cross multiplying them or multiplying the first one by the reciprocal or reverse of the second one. Cross multiplying ratios is just like cross multiplying fractions. The result should be equal to 1.

First, we convert our ratios into fractions:

### 1:2 = ^{1}/_{2}

### 2:4 = ^{2}/_{4}

Next, multiply the top numbers by the bottom number of the other fraction, like so:

^{1}/_{2} = ^{2}/_{4} -> ^{1x(4)}/_{2 x(2)} = ^{4}/_{4} or 1

If we follow the method of multiplying the first fraction with the reciprocal of the second it would look like this:

^{1}/_{2} = ^{2}/_{4} > ^{1}/_{2} x ^{4}/_{2} = ^{4}/_{4} or 1

One popular application of this is in cooking. For instance, you have a pancake recipe that is good for 4 servings, and you want to make 8 servings. To make 4 servings of pancakes, your recipe says you need 1 cup of all-purpose flour. Now, you want to know how many cups of all-purpose flour you will need for to make 8 servings of pancakes. Here's how we find out:

X cup(s) of all-purpose flour : 8 servings of pancakes = 1 cup of all-purpose flour : 4 servings of pancakes

### X : 8 = 1 : 4

^{X}/_{8} = ^{1}/_{4}

We find the reciprocal of the second fraction and multiply the two fractions:

^{X}/_{8} x ^{4}/_{1} = ^{4X}/_{8}

Here 4X means 4 x X. We move 8 to the other side of the equation, which means it becomes a numerator

^{8}/

_{1} or 8.

### 4X = 8

Then, we move 4 to the other side of the equation so we are only left with X on the left side of the equal sign. Since 4 is a numerator on the left side of the equation, it becomes a denominator on the other side.

### X = ^{8}/_{4} or 2

So, our completed proportion is: 2:8 = 1:4, which means you need 2 cups of all-purpose flour to make 8 servings of pancakes.