Math / Geometry

Question(3) The perimater of a triangle is 10 inches. One side is $3 \frac{9}{16}$ inches long. Another side is $4 \frac{5}{8}$ inches long. About how many inches long is the third side? Explain how you estimated. $\qquad$ $\qquad$ $\qquad$

Studdy Solution

STEP 1

What is this asking? We need to find the length of the third side of a triangle when we know the total length around the triangle is 10 inches and the lengths of the other two sides. Watch out! Don't forget to convert those mixed numbers into something we can easily add and subtract!

STEP 2

1. Convert mixed numbers to improper fractions
2. Add the two known sides
3. Subtract from the total perimeter

STEP 3

Alright, let's rewrite those mixed numbers as improper fractions!
Remember, a mixed number is just a whole number plus a fraction.
We multiply the whole number by the denominator and add it to the numerator.
It's like saying we have that many pieces of that size!

STEP 4

So, for $3 \frac{9}{16}$ , we multiply $3 \cdot 16 = 48$ and then add 9 to get $48 + 9 = 57$ .
This gives us $\frac{57}{16}$ inches.

STEP 5

For $4 \frac{5}{8}$ , we do the same thing. $4 \cdot 8 = 32$ , and then $32 + 5 = 37$ , giving us $\frac{37}{8}$ inches.

STEP 6

Now, we want to add the two sides we know.
But wait!
We can't add fractions with different denominators.
Think of it like trying to add apples and oranges - we need a common "fruit" to add them together!

STEP 7

Let's convert $\frac{37}{8}$ to have a denominator of 16.
We multiply both the numerator and the denominator by 2 (because $8 \cdot 2 = 16$ ).
So, $\frac{37}{8} \cdot \frac{2}{2} = \frac{74}{16}$ .
Remember, multiplying by $\frac{2}{2}$ is the same as multiplying by 1, so we're not changing the value of the fraction, just how it looks.

STEP 8

Now, we can add the two sides: $\frac{57}{16} + \frac{74}{16} = \frac{57 + 74}{16} = \frac{131}{16}$ .
So, the combined length of the two known sides is $\frac{131}{16}$ inches.

STEP 9

We know the total perimeter is 10 inches.
To find the length of the third side, we subtract the combined length of the other two sides from the total perimeter.

STEP 10

First, let's convert 10 inches into a fraction with a denominator of 16.
We can do this by multiplying 10 by $\frac{16}{16}$ , which is just 1: $10 \cdot \frac{16}{16} = \frac{160}{16}$ .

STEP 11

Now we subtract: $\frac{160}{16} - \frac{131}{16} = \frac{160 - 131}{16} = \frac{29}{16}$ inches.

STEP 12

Let's convert that back to a mixed number.
16 goes into 29 once with a remainder of 13.
So, the third side is $1 \frac{13}{16}$ inches long.

STEP 13

The third side of the triangle is $1 \frac{13}{16}$ inches long.

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Question(3) The perimater of a triangle is 10 inches. One side is $3 \frac{9}{16}$ inches long. Another side is $4 \frac{5}{8}$ inches long. About how many inches long is the third side? Explain how you estimated. $\qquad$ $\qquad$ $\qquad$

Studdy Solution

STEP 1

What is this asking? We need to find the length of the third side of a triangle when we know the total length around the triangle is 10 inches and the lengths of the other two sides. Watch out! Don't forget to convert those mixed numbers into something we can easily add and subtract!

STEP 2

1. Convert mixed numbers to improper fractions
2. Add the two known sides
3. Subtract from the total perimeter

STEP 3

Alright, let's rewrite those mixed numbers as improper fractions!
Remember, a mixed number is just a whole number plus a fraction.
We multiply the whole number by the denominator and add it to the numerator.
It's like saying we have that many pieces of that size!

STEP 4

So, for $3 \frac{9}{16}$ , we multiply $3 \cdot 16 = 48$ and then add 9 to get $48 + 9 = 57$ .
This gives us $\frac{57}{16}$ inches.

STEP 5

For $4 \frac{5}{8}$ , we do the same thing. $4 \cdot 8 = 32$ , and then $32 + 5 = 37$ , giving us $\frac{37}{8}$ inches.

STEP 6

Now, we want to add the two sides we know.
But wait!
We can't add fractions with different denominators.
Think of it like trying to add apples and oranges - we need a common "fruit" to add them together!

STEP 7

STEP 8

Now, we can add the two sides: $\frac{57}{16} + \frac{74}{16} = \frac{57 + 74}{16} = \frac{131}{16}$ .
So, the combined length of the two known sides is $\frac{131}{16}$ inches.

STEP 9

We know the total perimeter is 10 inches.
To find the length of the third side, we subtract the combined length of the other two sides from the total perimeter.

STEP 10

First, let's convert 10 inches into a fraction with a denominator of 16.
We can do this by multiplying 10 by $\frac{16}{16}$ , which is just 1: $10 \cdot \frac{16}{16} = \frac{160}{16}$ .

STEP 11

Now we subtract: $\frac{160}{16} - \frac{131}{16} = \frac{160 - 131}{16} = \frac{29}{16}$ inches.

STEP 12

Let's convert that back to a mixed number.
16 goes into 29 once with a remainder of 13.
So, the third side is $1 \frac{13}{16}$ inches long.

STEP 13

The third side of the triangle is $1 \frac{13}{16}$ inches long.

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Question(3) The perimater of a triangle is 10 inches. One side is 39163 \frac{9}{16}3169​ inches long. Another side is 4584 \frac{5}{8}485​ inches long. About how many inches long is the third side? Explain how you estimated. \qquad \qquad \qquad

Studdy Solution

STEP 1

What is this asking? We need to find the length of the third side of a triangle when we know the total length around the triangle is 10 inches and the lengths of the other two sides. Watch out! Don't forget to convert those mixed numbers into something we can easily add and subtract!

STEP 2

1. Convert mixed numbers to improper fractions2. Add the two known sides3. Subtract from the total perimeter

STEP 3

Alright, let's **rewrite** those mixed numbers as improper fractions!Remember, a mixed number is just a whole number plus a fraction.We **multiply** the whole number by the denominator and **add** it to the numerator.It's like saying we have that many pieces of that size!

STEP 4

So, for 39163 \frac{9}{16}3169​, we **multiply** 3⋅16=483 \cdot 16 = 483⋅16=48 and then **add** 9 to get 48+9=5748 + 9 = 5748+9=57.This gives us 5716\frac{57}{16}1657​ inches.

STEP 5

For 4584 \frac{5}{8}485​, we do the same thing. 4⋅8=324 \cdot 8 = 324⋅8=32, and then 32+5=3732 + 5 = 3732+5=37, giving us 378\frac{37}{8}837​ inches.

STEP 6

Now, we want to **add** the two sides we know.But wait!We can't add fractions with different denominators.Think of it like trying to add apples and oranges - we need a common "fruit" to add them together!

STEP 7

STEP 8

Now, we can **add** the two sides: 5716+7416=57+7416=13116\frac{57}{16} + \frac{74}{16} = \frac{57 + 74}{16} = \frac{131}{16}1657​+1674​=1657+74​=16131​.So, the combined length of the two known sides is 13116\frac{131}{16}16131​ inches.

STEP 9

We know the total perimeter is 10 inches.To find the length of the third side, we **subtract** the combined length of the other two sides from the total perimeter.

STEP 10

First, let's **convert** 10 inches into a fraction with a denominator of 16.We can do this by multiplying 10 by 1616\frac{16}{16}1616​, which is just 1: 10⋅1616=1601610 \cdot \frac{16}{16} = \frac{160}{16}10⋅1616​=16160​.

STEP 11

Now we **subtract**: 16016−13116=160−13116=2916\frac{160}{16} - \frac{131}{16} = \frac{160 - 131}{16} = \frac{29}{16}16160​−16131​=16160−131​=1629​ inches.

STEP 12

Let's **convert** that back to a mixed number.16 goes into 29 once with a remainder of 13.So, the third side is 113161 \frac{13}{16}11613​ inches long.

STEP 13

The third side of the triangle is 113161 \frac{13}{16}11613​ inches long.

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Question(3) The perimater of a triangle is 10 inches. One side is $3 \frac{9}{16}$ inches long. Another side is $4 \frac{5}{8}$ inches long. About how many inches long is the third side? Explain how you estimated. $\qquad$ $\qquad$ $\qquad$

1. Convert mixed numbers to improper fractions
2. Add the two known sides
3. Subtract from the total perimeter

Alright, let's rewrite those mixed numbers as improper fractions!
Remember, a mixed number is just a whole number plus a fraction.
We multiply the whole number by the denominator and add it to the numerator.
It's like saying we have that many pieces of that size!

So, for $3 \frac{9}{16}$ , we multiply $3 \cdot 16 = 48$ and then add 9 to get $48 + 9 = 57$ .
This gives us $\frac{57}{16}$ inches.

For $4 \frac{5}{8}$ , we do the same thing. $4 \cdot 8 = 32$ , and then $32 + 5 = 37$ , giving us $\frac{37}{8}$ inches.

Now, we want to add the two sides we know.
But wait!
We can't add fractions with different denominators.
Think of it like trying to add apples and oranges - we need a common "fruit" to add them together!

Now, we can add the two sides: $\frac{57}{16} + \frac{74}{16} = \frac{57 + 74}{16} = \frac{131}{16}$ .
So, the combined length of the two known sides is $\frac{131}{16}$ inches.

We know the total perimeter is 10 inches.
To find the length of the third side, we subtract the combined length of the other two sides from the total perimeter.

First, let's convert 10 inches into a fraction with a denominator of 16.
We can do this by multiplying 10 by $\frac{16}{16}$ , which is just 1: $10 \cdot \frac{16}{16} = \frac{160}{16}$ .

Now we subtract: $\frac{160}{16} - \frac{131}{16} = \frac{160 - 131}{16} = \frac{29}{16}$ inches.

Let's convert that back to a mixed number.
16 goes into 29 once with a remainder of 13.
So, the third side is $1 \frac{13}{16}$ inches long.

The third side of the triangle is $1 \frac{13}{16}$ inches long.