Math

Question Find the number that satisfies the inequality 0.625>80.625 > \frac{\square}{8}.

Studdy Solution

STEP 1

Assumptions
1. We are given a decimal number 0.6250.625.
2. We need to find which number out of the given options (3, 4, 5, 6) when placed in the square will make the fraction less than 0.6250.625.
3. The denominator of the fraction is 8.

STEP 2

First, let's convert the decimal number 0.6250.625 into a fraction to make it easier to compare with the other fractions.
0.625=62510000.625 = \frac{625}{1000}

STEP 3

Reduce the fraction 6251000\frac{625}{1000} by dividing both the numerator and the denominator by their greatest common divisor, which is 125.
625÷1251000÷125=58\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}

STEP 4

Now we have the decimal 0.6250.625 expressed as the fraction 58\frac{5}{8}. We can now compare this fraction with the fractions given by the options when the number is placed in the square.

STEP 5

Let's start with option a, which is 3. Place 3 in the square and compare the resulting fraction with 58\frac{5}{8}.
38<58\frac{3}{8} < \frac{5}{8}

STEP 6

Option a (3) makes the statement true because 38\frac{3}{8} is less than 58\frac{5}{8}. However, we should check all options to ensure we find all numbers that make the statement true.

STEP 7

Now let's check option b, which is 4. Place 4 in the square and compare the resulting fraction with 58\frac{5}{8}.
48<58\frac{4}{8} < \frac{5}{8}

STEP 8

Option b (4) also makes the statement true because 48\frac{4}{8} is less than 58\frac{5}{8}. We will continue to check the remaining options.

STEP 9

Next, let's check option c, which is 5. Place 5 in the square and compare the resulting fraction with 58\frac{5}{8}.
58=58\frac{5}{8} = \frac{5}{8}

STEP 10

Option c (5) does not make the statement true because 58\frac{5}{8} is equal to 58\frac{5}{8}, not less than it. We will check the last option.

STEP 11

Finally, let's check option d, which is 6. Place 6 in the square and compare the resulting fraction with 58\frac{5}{8}.
68>58\frac{6}{8} > \frac{5}{8}

STEP 12

Option d (6) does not make the statement true because 68\frac{6}{8} is greater than 58\frac{5}{8}.

STEP 13

After comparing all options, we find that only options a (3) and b (4) make the statement 0.625>80.625 > \frac{\square}{8} true.
The numbers that will make the statement true are 3 and 4.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord