Math / Numbers & Operations

Question1 is what percent of $20 ?$

Studdy Solution

STEP 1

What is this asking? We need to figure out what percentage 1 is out of 20.
Imagine we have 20 cookies, and we only eat 1.
What percentage of the cookies did we eat? Watch out! Don't mix up the part and the whole.
Remember, we're looking at 1 out of 20, not 20 out of 1!

STEP 2

1. Set up a proportion
2. Solve for the percentage

STEP 3

We can represent the unknown percentage as a fraction: $\frac{x}{100}$ .
Here, $x$ is the percentage we're trying to find.
Think of this as " $x$ out of 100".

STEP 4

We can set up a proportion to relate the percentage to the given numbers.
We know that 1 is to 20 as $x$ is to 100.
This gives us the proportion: $\frac{1}{20} = \frac{x}{100}$

STEP 5

To isolate $x$ , we can multiply both sides of the equation by 100.
We're doing this to divide the right-hand side by one, so $x$ is by itself. $\frac{1}{20} \cdot 100 = \frac{x}{100} \cdot 100$

STEP 6

Now, we can simplify the left side.
We can think of 100 as $\frac{100}{1}$ .
So, we have: $\frac{1}{20} \cdot \frac{100}{1} = \frac{1 \cdot 100}{20 \cdot 1} = \frac{100}{20}$ We can divide both the numerator and the denominator by 20: $\frac{100}{20} = \frac{100 \div 20}{20 \div 20} = \frac{5}{1} = 5$ And on the right side, we have: $\frac{x}{100} \cdot \frac{100}{1} = \frac{x \cdot 100}{100 \cdot 1} = \frac{100x}{100}$ We can divide both the numerator and the denominator by 100: $\frac{100x}{100} = \frac{100x \div 100}{100 \div 100} = \frac{x}{1} = x$ So, we have $x = \textbf{5}$ .

STEP 7

1 is 5% of 20!

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