Math / Numbers & Operations

QuestionWhat is the difference? $\frac{7}{8}-\frac{2}{3}$ $\frac{4}{21}$ $\frac{5}{M}$ $\frac{1}{24}$ 1

Studdy Solution

STEP 1

What is this asking? We need to find the difference between two fractions, $\frac{7}{8}$ and $\frac{2}{3}$ . Watch out! We can't subtract fractions unless they have the same denominator!

STEP 2

1. Find a Common Denominator
2. Rewrite the Fractions
3. Subtract the Fractions

STEP 3

Let's find the least common denominator (LCD) of 8 and 3.
The multiples of 8 are 8, 16, 24, 32... and the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24... Looks like 24 is the smallest number they both go into!

STEP 4

Now, let's rewrite our fractions so they both have a denominator of 24.
For $\frac{7}{8}$ , we multiply the top and bottom by 3 (because $8 \cdot 3 = 24$ ).
This gives us $\frac{7 \cdot 3}{8 \cdot 3} = \frac{21}{24}$ .
We're multiplying by $\frac{3}{3}$ which is equal to one, so we're not changing the value of the fraction, just how it looks!

STEP 5

For $\frac{2}{3}$ , we multiply the top and bottom by 8 (because $3 \cdot 8 = 24$ ).
This gives us $\frac{2 \cdot 8}{3 \cdot 8} = \frac{16}{24}$ .
Again, we multiplied by $\frac{8}{8}$ which is equal to one, so the value stays the same.

STEP 6

Now that our fractions have the same denominator, we can subtract them! $\frac{21}{24} - \frac{16}{24} = \frac{21 - 16}{24} = \frac{5}{24}$ We subtract the numerators and keep the denominator the same.

STEP 7

The difference between $\frac{7}{8}$ and $\frac{2}{3}$ is $\frac{5}{24}$ .

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QuestionWhat is the difference? $\frac{7}{8}-\frac{2}{3}$ $\frac{4}{21}$ $\frac{5}{M}$ $\frac{1}{24}$ 1

Studdy Solution

STEP 1

What is this asking? We need to find the difference between two fractions, $\frac{7}{8}$ and $\frac{2}{3}$ . Watch out! We can't subtract fractions unless they have the same denominator!

STEP 2

1. Find a Common Denominator
2. Rewrite the Fractions
3. Subtract the Fractions

STEP 3

Let's find the least common denominator (LCD) of 8 and 3.
The multiples of 8 are 8, 16, 24, 32... and the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24... Looks like 24 is the smallest number they both go into!

STEP 4

STEP 5

For $\frac{2}{3}$ , we multiply the top and bottom by 8 (because $3 \cdot 8 = 24$ ).
This gives us $\frac{2 \cdot 8}{3 \cdot 8} = \frac{16}{24}$ .
Again, we multiplied by $\frac{8}{8}$ which is equal to one, so the value stays the same.

STEP 6

Now that our fractions have the same denominator, we can subtract them! $\frac{21}{24} - \frac{16}{24} = \frac{21 - 16}{24} = \frac{5}{24}$ We subtract the numerators and keep the denominator the same.

STEP 7

The difference between $\frac{7}{8}$ and $\frac{2}{3}$ is $\frac{5}{24}$ .

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QuestionWhat is the difference? 78−23\frac{7}{8}-\frac{2}{3}87​−32​ 421\frac{4}{21}214​ 5M\frac{5}{M}M5​ 124\frac{1}{24}241​ 1

Studdy Solution

STEP 1

What is this asking? We need to find the difference between two fractions, 78\frac{7}{8}87​ and 23\frac{2}{3}32​. Watch out! We can't subtract fractions unless they have the **same denominator**!

STEP 2

1. Find a Common Denominator2. Rewrite the Fractions3. Subtract the Fractions

STEP 3

Let's find the **least common denominator (LCD)** of 8 and 3.The multiples of 8 are 8, 16, 24, 32... and the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24... Looks like **24** is the smallest number they both go into!

STEP 4

STEP 5

For 23\frac{2}{3}32​, we multiply the top and bottom by **8** (because 3⋅8=243 \cdot 8 = 243⋅8=24).This gives us 2⋅83⋅8=1624\frac{2 \cdot 8}{3 \cdot 8} = \frac{16}{24}3⋅82⋅8​=2416​.Again, we multiplied by 88\frac{8}{8}88​ which is equal to one, so the value stays the same.

STEP 6

Now that our fractions have the **same denominator**, we can subtract them! 2124−1624=21−1624=524 \frac{21}{24} - \frac{16}{24} = \frac{21 - 16}{24} = \frac{5}{24} 2421​−2416​=2421−16​=245​ We subtract the numerators and keep the denominator the same.

STEP 7

The difference between 78\frac{7}{8}87​ and 23\frac{2}{3}32​ is 524\frac{5}{24}245​.

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QuestionWhat is the difference? $\frac{7}{8}-\frac{2}{3}$ $\frac{4}{21}$ $\frac{5}{M}$ $\frac{1}{24}$ 1

What is this asking? We need to find the difference between two fractions, $\frac{7}{8}$ and $\frac{2}{3}$ . Watch out! We can't subtract fractions unless they have the same denominator!

1. Find a Common Denominator
2. Rewrite the Fractions
3. Subtract the Fractions

Let's find the least common denominator (LCD) of 8 and 3.
The multiples of 8 are 8, 16, 24, 32... and the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24... Looks like 24 is the smallest number they both go into!

For $\frac{2}{3}$ , we multiply the top and bottom by 8 (because $3 \cdot 8 = 24$ ).
This gives us $\frac{2 \cdot 8}{3 \cdot 8} = \frac{16}{24}$ .
Again, we multiplied by $\frac{8}{8}$ which is equal to one, so the value stays the same.

Now that our fractions have the same denominator, we can subtract them! $\frac{21}{24} - \frac{16}{24} = \frac{21 - 16}{24} = \frac{5}{24}$ We subtract the numerators and keep the denominator the same.

The difference between $\frac{7}{8}$ and $\frac{2}{3}$ is $\frac{5}{24}$ .