Math / Algebra

QuestionSelect the equation that has $a=1 \frac{1}{2}$ as its solution. $a-1 \frac{1}{4}=\frac{3}{5}$ $a+3 \frac{5}{8}=4 \frac{3}{4}$ $4 \frac{1}{6}+a=5 \frac{2}{3}$ $a \times \frac{3}{8}=2 \frac{1}{4}$

Studdy Solution

STEP 1

What is this asking? Which of these equations is true when $a$ is one and a half? Watch out! Don't get tricked by the mixed numbers!
Convert everything to a single fraction to make calculations easier.

STEP 2

1. Convert the value of $a$ to an improper fraction.
2. Check each equation.

STEP 3

We're given $a = 1 \frac{1}{2}$ , which is a mixed number.
Let's turn it into an improper fraction!
Remember, $1 \frac{1}{2}$ means $1 + \frac{1}{2}$ .

STEP 4

To add the whole number 1 to the fraction $\frac{1}{2}$ , we need to give 1 the same denominator.
We can rewrite 1 as $\frac{2}{2}$ since any number divided by itself is 1.

STEP 5

Now, we have $\frac{2}{2} + \frac{1}{2}$ .
Since the denominators are the same, we can add the numerators directly: $2 + 1 = 3$ .
So, $1 \frac{1}{2}$ is the same as $\frac{3}{2}$ .
We'll use this value for $a$ as we check the equations.

STEP 6

Substitute $a = \frac{3}{2}$ : $\frac{3}{2} - 1\frac{1}{4} = \frac{3}{2} - \frac{5}{4}$ .
To subtract, we need a common denominator, which is 4.
Multiply the first fraction by $\frac{2}{2}$ to get $\frac{6}{4} - \frac{5}{4} = \frac{1}{4}$ .
Is $\frac{1}{4}$ equal to $\frac{3}{5}$ ?
Nope!

STEP 7

Substitute $a = \frac{3}{2}$ : $\frac{3}{2} + 3\frac{5}{8} = \frac{3}{2} + \frac{29}{8}$ .
Common denominator is 8: $\frac{12}{8} + \frac{29}{8} = \frac{41}{8}$ .
Convert $4\frac{3}{4}$ to an improper fraction: $4\frac{3}{4} = \frac{19}{4} = \frac{38}{8}$ .
Is $\frac{41}{8}$ equal to $\frac{38}{8}$ ?
No way!

STEP 8

Substitute $a = \frac{3}{2}$ : $4\frac{1}{6} + \frac{3}{2} = \frac{25}{6} + \frac{3}{2}$ .
Common denominator is 6: $\frac{25}{6} + \frac{9}{6} = \frac{34}{6} = \frac{17}{3}$ .
Now convert $5\frac{2}{3}$ to an improper fraction: $5\frac{2}{3} = \frac{17}{3}$ .
Is $\frac{17}{3}$ equal to $\frac{17}{3}$ ?
Yes! This is our answer.

STEP 9

Substitute $a = \frac{3}{2}$ : $\frac{3}{2} \cdot \frac{3}{8} = \frac{3 \cdot 3}{2 \cdot 8} = \frac{9}{16}$ .
Convert $2\frac{1}{4}$ to an improper fraction: $2\frac{1}{4} = \frac{9}{4}$ .
Is $\frac{9}{16}$ equal to $\frac{9}{4}$ ?
Nope!

STEP 10

The equation $4 \frac{1}{6} + a = 5 \frac{2}{3}$ has $a = 1 \frac{1}{2}$ as its solution.

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QuestionSelect the equation that has $a=1 \frac{1}{2}$ as its solution. $a-1 \frac{1}{4}=\frac{3}{5}$ $a+3 \frac{5}{8}=4 \frac{3}{4}$ $4 \frac{1}{6}+a=5 \frac{2}{3}$ $a \times \frac{3}{8}=2 \frac{1}{4}$

Studdy Solution

STEP 1

What is this asking? Which of these equations is true when $a$ is one and a half? Watch out! Don't get tricked by the mixed numbers!
Convert everything to a single fraction to make calculations easier.

STEP 2

1. Convert the value of $a$ to an improper fraction.
2. Check each equation.

STEP 3

We're given $a = 1 \frac{1}{2}$ , which is a mixed number.
Let's turn it into an improper fraction!
Remember, $1 \frac{1}{2}$ means $1 + \frac{1}{2}$ .

STEP 4

To add the whole number 1 to the fraction $\frac{1}{2}$ , we need to give 1 the same denominator.
We can rewrite 1 as $\frac{2}{2}$ since any number divided by itself is 1.

STEP 5

Now, we have $\frac{2}{2} + \frac{1}{2}$ .
Since the denominators are the same, we can add the numerators directly: $2 + 1 = 3$ .
So, $1 \frac{1}{2}$ is the same as $\frac{3}{2}$ .
We'll use this value for $a$ as we check the equations.

STEP 6

Substitute $a = \frac{3}{2}$ : $\frac{3}{2} - 1\frac{1}{4} = \frac{3}{2} - \frac{5}{4}$ .
To subtract, we need a common denominator, which is 4.
Multiply the first fraction by $\frac{2}{2}$ to get $\frac{6}{4} - \frac{5}{4} = \frac{1}{4}$ .
Is $\frac{1}{4}$ equal to $\frac{3}{5}$ ?
Nope!

STEP 7

STEP 8

STEP 9

Substitute $a = \frac{3}{2}$ : $\frac{3}{2} \cdot \frac{3}{8} = \frac{3 \cdot 3}{2 \cdot 8} = \frac{9}{16}$ .
Convert $2\frac{1}{4}$ to an improper fraction: $2\frac{1}{4} = \frac{9}{4}$ .
Is $\frac{9}{16}$ equal to $\frac{9}{4}$ ?
Nope!

STEP 10

The equation $4 \frac{1}{6} + a = 5 \frac{2}{3}$ has $a = 1 \frac{1}{2}$ as its solution.

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Studdy Solution

STEP 1

What is this asking? Which of these equations is true when aaa is one and a half? Watch out! Don't get tricked by the mixed numbers!Convert everything to a single fraction to make calculations easier.

STEP 2

1. Convert the value of aaa to an improper fraction.2. Check each equation.

STEP 3

We're given a=112a = 1 \frac{1}{2}a=121​, which is a mixed number.Let's turn it into an improper fraction!Remember, 1121 \frac{1}{2}121​ means 1+121 + \frac{1}{2}1+21​.

STEP 4

To add the whole number 1 to the fraction 12\frac{1}{2}21​, we need to give 1 the same denominator.We can rewrite 1 as 22\frac{2}{2}22​ since any number divided by itself is 1.

STEP 5

Now, we have 22+12\frac{2}{2} + \frac{1}{2}22​+21​.Since the denominators are the same, we can add the numerators directly: 2+1=32 + 1 = 32+1=3.So, 1121 \frac{1}{2}121​ is the same as 32\frac{3}{2}23​.We'll use this value for aaa as we check the equations.

STEP 6

STEP 7

STEP 8

STEP 9

STEP 10

The equation 416+a=5234 \frac{1}{6} + a = 5 \frac{2}{3}461​+a=532​ has a=112a = 1 \frac{1}{2}a=121​ as its solution.

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Studdy solves anything!

Start learning now

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

What is this asking? Which of these equations is true when $a$ is one and a half? Watch out! Don't get tricked by the mixed numbers!
Convert everything to a single fraction to make calculations easier.

1. Convert the value of $a$ to an improper fraction.
2. Check each equation.

We're given $a = 1 \frac{1}{2}$ , which is a mixed number.
Let's turn it into an improper fraction!
Remember, $1 \frac{1}{2}$ means $1 + \frac{1}{2}$ .

To add the whole number 1 to the fraction $\frac{1}{2}$ , we need to give 1 the same denominator.
We can rewrite 1 as $\frac{2}{2}$ since any number divided by itself is 1.

Now, we have $\frac{2}{2} + \frac{1}{2}$ .
Since the denominators are the same, we can add the numerators directly: $2 + 1 = 3$ .
So, $1 \frac{1}{2}$ is the same as $\frac{3}{2}$ .
We'll use this value for $a$ as we check the equations.

The equation $4 \frac{1}{6} + a = 5 \frac{2}{3}$ has $a = 1 \frac{1}{2}$ as its solution.