Math / Numbers & Operations

Question $3 \frac{2}{3}-1 \frac{2}{5}=$

Studdy Solution

STEP 1

What is this asking? We're subtracting two mixed numbers, which is like subtracting two whole numbers and two fractions at the same time! Watch out! Don't forget to find a common denominator when subtracting fractions.
Also, we might need to borrow from the whole number part if the first fraction is smaller than the second.

STEP 2

1. Convert to Improper Fractions
2. Find a Common Denominator
3. Subtract the Fractions
4. Subtract the Whole Numbers
5. Simplify

STEP 3

Alright, let's kick things off by turning these mixed numbers into improper fractions.
Remember, a mixed number is just a whole number plus a fraction.
An improper fraction is where the numerator (top number) is bigger than or equal to the denominator (bottom number).

STEP 4

For $3 \frac{2}{3}$ , we multiply the whole number ( $3$ ) by the denominator ( $3$ ), which gives us $3 \cdot 3 = 9$ .
Then, we add the numerator ( $2$ ) to get $9 + 2 = \mathbf{11}$ .
So, $3 \frac{2}{3}$ becomes $\frac{\mathbf{11}}{3}$ .

STEP 5

For $1 \frac{2}{5}$ , we multiply the whole number ( $1$ ) by the denominator ( $5$ ), which gives us $1 \cdot 5 = 5$ .
Then, we add the numerator ( $2$ ) to get $5 + 2 = \mathbf{7}$ .
So, $1 \frac{2}{5}$ becomes $\frac{\mathbf{7}}{5}$ .

STEP 6

Now, to subtract fractions, we need a common denominator.
The smallest number that both $3$ and $5$ divide into is $\mathbf{15}$ .

STEP 7

To turn $\frac{11}{3}$ into a fraction with a denominator of $15$ , we multiply both the top and bottom by $5$ : $\frac{11}{3} \cdot \frac{5}{5} = \frac{\mathbf{55}}{15}$ .

STEP 8

To turn $\frac{7}{5}$ into a fraction with a denominator of $15$ , we multiply both the top and bottom by $3$ : $\frac{7}{5} \cdot \frac{3}{3} = \frac{\mathbf{21}}{15}$ .

STEP 9

With our common denominator, we can subtract the fractions: $\frac{55}{15} - \frac{21}{15} = \frac{55 - 21}{15} = \frac{\mathbf{34}}{15}$ .

STEP 10

$\frac{34}{15}$ is an improper fraction.
Let's convert it back to a mixed number. $15$ goes into $34$ two times ( $2 \cdot 15 = 30$ ) with a remainder of $4$ ( $34 - 30 = 4$ ).
So, $\frac{34}{15}$ becomes $2 \frac{4}{15}$ .

STEP 11

Our final answer is $2 \frac{4}{15}$ !

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Question $3 \frac{2}{3}-1 \frac{2}{5}=$

Studdy Solution

STEP 1

STEP 2

1. Convert to Improper Fractions
2. Find a Common Denominator
3. Subtract the Fractions
4. Subtract the Whole Numbers
5. Simplify

STEP 3

Alright, let's kick things off by turning these mixed numbers into improper fractions.
Remember, a mixed number is just a whole number plus a fraction.
An improper fraction is where the numerator (top number) is bigger than or equal to the denominator (bottom number).

STEP 4

For $3 \frac{2}{3}$ , we multiply the whole number ( $3$ ) by the denominator ( $3$ ), which gives us $3 \cdot 3 = 9$ .
Then, we add the numerator ( $2$ ) to get $9 + 2 = \mathbf{11}$ .
So, $3 \frac{2}{3}$ becomes $\frac{\mathbf{11}}{3}$ .

STEP 5

For $1 \frac{2}{5}$ , we multiply the whole number ( $1$ ) by the denominator ( $5$ ), which gives us $1 \cdot 5 = 5$ .
Then, we add the numerator ( $2$ ) to get $5 + 2 = \mathbf{7}$ .
So, $1 \frac{2}{5}$ becomes $\frac{\mathbf{7}}{5}$ .

STEP 6

Now, to subtract fractions, we need a common denominator.
The smallest number that both $3$ and $5$ divide into is $\mathbf{15}$ .

STEP 7

To turn $\frac{11}{3}$ into a fraction with a denominator of $15$ , we multiply both the top and bottom by $5$ : $\frac{11}{3} \cdot \frac{5}{5} = \frac{\mathbf{55}}{15}$ .

STEP 8

To turn $\frac{7}{5}$ into a fraction with a denominator of $15$ , we multiply both the top and bottom by $3$ : $\frac{7}{5} \cdot \frac{3}{3} = \frac{\mathbf{21}}{15}$ .

STEP 9

With our common denominator, we can subtract the fractions: $\frac{55}{15} - \frac{21}{15} = \frac{55 - 21}{15} = \frac{\mathbf{34}}{15}$ .

STEP 10

$\frac{34}{15}$ is an improper fraction.
Let's convert it back to a mixed number. $15$ goes into $34$ two times ( $2 \cdot 15 = 30$ ) with a remainder of $4$ ( $34 - 30 = 4$ ).
So, $\frac{34}{15}$ becomes $2 \frac{4}{15}$ .

STEP 11

Our final answer is $2 \frac{4}{15}$ !

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Question323−125=3 \frac{2}{3}-1 \frac{2}{5}=332​−152​=

Studdy Solution

STEP 1

STEP 2

1. Convert to Improper Fractions2. Find a Common Denominator3. Subtract the Fractions4. Subtract the Whole Numbers5. Simplify

STEP 3

Alright, let's kick things off by turning these mixed numbers into improper fractions.Remember, a mixed number is just a whole number plus a fraction.An improper fraction is where the numerator (top number) is bigger than or equal to the denominator (bottom number).

STEP 4

For 3233 \frac{2}{3}332​, we multiply the whole number (333) by the denominator (333), which gives us 3⋅3=93 \cdot 3 = 93⋅3=9.Then, we add the numerator (222) to get 9+2=119 + 2 = \mathbf{11}9+2=11.So, 3233 \frac{2}{3}332​ becomes 113\frac{\mathbf{11}}{3}311​.

STEP 5

For 1251 \frac{2}{5}152​, we multiply the whole number (111) by the denominator (555), which gives us 1⋅5=51 \cdot 5 = 51⋅5=5.Then, we add the numerator (222) to get 5+2=75 + 2 = \mathbf{7}5+2=7.So, 1251 \frac{2}{5}152​ becomes 75\frac{\mathbf{7}}{5}57​.

STEP 6

Now, to subtract fractions, we need a common denominator.The smallest number that both 333 and 555 divide into is 15\mathbf{15}15.

STEP 7

To turn 113\frac{11}{3}311​ into a fraction with a denominator of 151515, we multiply both the top and bottom by 555: 113⋅55=5515\frac{11}{3} \cdot \frac{5}{5} = \frac{\mathbf{55}}{15}311​⋅55​=1555​.

STEP 8

To turn 75\frac{7}{5}57​ into a fraction with a denominator of 151515, we multiply both the top and bottom by 333: 75⋅33=2115\frac{7}{5} \cdot \frac{3}{3} = \frac{\mathbf{21}}{15}57​⋅33​=1521​.

STEP 9

With our common denominator, we can subtract the fractions: 5515−2115=55−2115=3415\frac{55}{15} - \frac{21}{15} = \frac{55 - 21}{15} = \frac{\mathbf{34}}{15}1555​−1521​=1555−21​=1534​.

STEP 10

3415\frac{34}{15}1534​ is an improper fraction.Let's convert it back to a mixed number. 151515 goes into 343434 two times (2⋅15=302 \cdot 15 = 302⋅15=30) with a remainder of 444 (34−30=434 - 30 = 434−30=4).So, 3415\frac{34}{15}1534​ becomes 24152 \frac{4}{15}2154​.

STEP 11

Our final answer is 24152 \frac{4}{15}2154​!

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Question $3 \frac{2}{3}-1 \frac{2}{5}=$

1. Convert to Improper Fractions
2. Find a Common Denominator
3. Subtract the Fractions
4. Subtract the Whole Numbers
5. Simplify

Alright, let's kick things off by turning these mixed numbers into improper fractions.
Remember, a mixed number is just a whole number plus a fraction.
An improper fraction is where the numerator (top number) is bigger than or equal to the denominator (bottom number).

For $3 \frac{2}{3}$ , we multiply the whole number ( $3$ ) by the denominator ( $3$ ), which gives us $3 \cdot 3 = 9$ .
Then, we add the numerator ( $2$ ) to get $9 + 2 = \mathbf{11}$ .
So, $3 \frac{2}{3}$ becomes $\frac{\mathbf{11}}{3}$ .

For $1 \frac{2}{5}$ , we multiply the whole number ( $1$ ) by the denominator ( $5$ ), which gives us $1 \cdot 5 = 5$ .
Then, we add the numerator ( $2$ ) to get $5 + 2 = \mathbf{7}$ .
So, $1 \frac{2}{5}$ becomes $\frac{\mathbf{7}}{5}$ .

Now, to subtract fractions, we need a common denominator.
The smallest number that both $3$ and $5$ divide into is $\mathbf{15}$ .

To turn $\frac{11}{3}$ into a fraction with a denominator of $15$ , we multiply both the top and bottom by $5$ : $\frac{11}{3} \cdot \frac{5}{5} = \frac{\mathbf{55}}{15}$ .

To turn $\frac{7}{5}$ into a fraction with a denominator of $15$ , we multiply both the top and bottom by $3$ : $\frac{7}{5} \cdot \frac{3}{3} = \frac{\mathbf{21}}{15}$ .

With our common denominator, we can subtract the fractions: $\frac{55}{15} - \frac{21}{15} = \frac{55 - 21}{15} = \frac{\mathbf{34}}{15}$ .

$\frac{34}{15}$ is an improper fraction.
Let's convert it back to a mixed number. $15$ goes into $34$ two times ( $2 \cdot 15 = 30$ ) with a remainder of $4$ ( $34 - 30 = 4$ ).
So, $\frac{34}{15}$ becomes $2 \frac{4}{15}$ .

Our final answer is $2 \frac{4}{15}$ !