QuestionConvert the mixed numbers to improper fractions: a. $5 \frac{1}{6}=$ b. $-3 \frac{5}{7}=$

Studdy Solution

STEP 1

Assumptions1. The mixed number is $5 \frac{1}{6}$ . We want to convert this mixed number into an improper fraction

STEP 2

A mixed number consists of a whole number and a proper fraction. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. This becomes the new numerator, while the denominator remains the same.
$\text{Mixed number} = a \frac{b}{c}$ $\text{Improper fraction} = \frac{a \times c + b}{c}$

STEP 3

Now, plug in the given values for $a$ , $b$ , and $c$ to calculate the improper fraction.
$\text{Improper fraction} = \frac{5 \times6 +1}{6}$

STEP 4

Calculate the numerator of the improper fraction.
$\text{Improper fraction} = \frac{30 +1}{6}$

STEP 5

implify the numerator to get the final improper fraction.
$\text{Improper fraction} = \frac{31}{}$ So, $5 \frac{1}{} = \frac{31}{}$ .

STEP 6

Assumptions1. The mixed number is $-3 \frac{5}{}$
2. We want to convert this mixed number into an improper fraction

STEP 7

We use the same formula as in2. However, since the whole number is negative, the resulting improper fraction will also be negative.
$\text{Mixed number} = -a \frac{b}{c}$ $\text{Improper fraction} = -\frac{a \times c + b}{c}$

STEP 8

Now, plug in the given values for $a$ , $b$ , and $c$ to calculate the improper fraction.
$\text{Improper fraction} = -\frac{3 \times7 +5}{7}$

STEP 9

Calculate the numerator of the improper fraction.
$\text{Improper fraction} = -\frac{21 +5}{7}$

STEP 10

implify the numerator to get the final improper fraction.
$\text{Improper fraction} = -\frac{26}{7}$ So, $-3 \frac{5}{7} = -\frac{26}{7}$ .

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