Math / Numbers & Operations

QuestionPut these numbers in order from greatest to least. $-88 \frac{3}{15}$ $88 \frac{9}{10}$ 88.6 $88 \frac{32}{40}$ $-\frac{18}{30}$ Submit

Studdy Solution

STEP 1

What is this asking? We need to arrange a mix of negative and positive numbers, some of which are fractions and some decimals, from largest to smallest. Watch out! Don't forget that negative numbers get smaller as their absolute value increases!
Also, be careful when comparing fractions and decimals – it's easy to make mistakes if we don't convert them to a common format.

STEP 2

1. Simplify the fractions
2. Convert to decimals
3. Order the numbers

STEP 3

Let's simplify those fractions to make them easier to work with!
We've got $-88 \frac{3}{15}$ , and we can simplify $\frac{3}{15}$ by dividing both the numerator and denominator by their greatest common divisor, which is 3.
So, $\frac{3}{15} = \frac{3 \div 3}{15 \div 3} = \frac{1}{5}$ .
This gives us $-88 \frac{1}{5}$ .

STEP 4

Next up is $88 \frac{9}{10}$ .
This one's already pretty simple, but we'll keep it in mind.

STEP 5

Now, we have $88 \frac{32}{40}$ .
We can simplify $\frac{32}{40}$ by dividing both the numerator and denominator by their greatest common divisor, which is 8.
So, $\frac{32}{40} = \frac{32 \div 8}{40 \div 8} = \frac{4}{5}$ .
This gives us $88 \frac{4}{5}$ .

STEP 6

Lastly, we have $-\frac{18}{30}$ .
We can simplify this by dividing both the numerator and denominator by their greatest common divisor, which is 6.
So, $-\frac{18}{30} = -\frac{18 \div 6}{30 \div 6} = -\frac{3}{5}$ .

STEP 7

To compare these numbers easily, let's convert them all to decimals.
We already have 88.6.

STEP 8

We have $-88 \frac{1}{5}$ .
Since $\frac{1}{5} = 0.2$ , we have $-88.2$ .

STEP 9

We have $88 \frac{9}{10}$ .
Since $\frac{9}{10} = 0.9$ , we have 88.9.

STEP 10

We have $88 \frac{4}{5}$ .
Since $\frac{4}{5} = 0.8$ , we have 88.8.

STEP 11

Finally, we have $-\frac{3}{5}$ .
Since $\frac{3}{5} = 0.6$ , we have -0.6.

STEP 12

Now that everything is in decimal form, we can order them from greatest to least.
Remember, larger positive numbers are greater than smaller positive numbers, and all positive numbers are greater than all negative numbers.
Also, negative numbers get smaller as their absolute value increases.

STEP 13

So, our numbers from greatest to least are: $88.9 > 88.8 > 88.6 > -0.6 > -88.2$ .

STEP 14

From greatest to least, the numbers are $88 \frac{9}{10}$ , $88 \frac{32}{40}$ , $88.6$ , $-\frac{18}{30}$ , and $-88 \frac{3}{15}$ .

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