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Question Add two mixed fractions, then express the result in simplest form: 423+3124 \frac{2}{3} + 3 \frac{1}{2}

Studdy Solution

STEP 1

Assumptions1. The numbers are mixed numbers, which means they consist of a whole number and a fraction. . We need to add these mixed numbers.
3. The result should be in simplest form.

STEP 2

First, we need to convert each mixed number into an improper fraction. An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). We can do this by multiplying the whole number by the denominator of the fraction and then adding the numerator.
For the first mixed number42=4×+24 \frac{2}{} = \frac{4 \times +2}{}

STEP 3

Now, calculate the numerator for the first fraction.
23=×3+23=143 \frac{2}{3} = \frac{ \times3 +2}{3} = \frac{14}{3}

STEP 4

Repeat the same process for the second mixed number312=3×2+123 \frac{1}{2} = \frac{3 \times2 +1}{2}

STEP 5

Calculate the numerator for the second fraction.
312=3×2+12=723 \frac{1}{2} = \frac{3 \times2 +1}{2} = \frac{7}{2}

STEP 6

Now that we have both fractions in improper form, we can add them together.
143+2\frac{14}{3} + \frac{}{2}

STEP 7

To add fractions, we need a common denominator. The least common denominator (LCD) of3 and2 is6. Multiply each fraction by the necessary value to achieve the LCD.
143×22+72×33=286+216\frac{14}{3} \times \frac{2}{2} + \frac{7}{2} \times \frac{3}{3} = \frac{28}{6} + \frac{21}{6}

STEP 8

Now that the fractions have the same denominator, add the numerators.
286+216=496\frac{28}{6} + \frac{21}{6} = \frac{49}{6}

STEP 9

The result is an improper fraction. Convert it back to a mixed number by dividing the numerator by the denominator.
496=86\frac{49}{6} =8 \frac{}{6}So, 423+32=864 \frac{2}{3} +3 \frac{}{2} =8 \frac{}{6}.

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