Math

Question Simplify the expression 23482 \frac{3}{4} \cdot 8.

Studdy Solution

STEP 1

Assumptions
1. We are multiplying a mixed number by a whole number.
2. The mixed number is 2342 \frac{3}{4}.
3. The whole number is 88.

STEP 2

First, we need to convert the mixed number to an improper fraction. A mixed number is composed of an integer and a fraction. To convert it to an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator of the fraction.
Improperfraction=Wholenumber×Denominator+NumeratorImproper\, fraction = Whole\, number \times Denominator + Numerator

STEP 3

Now, plug in the given values for the whole number, denominator, and numerator to calculate the improper fraction.
Improperfraction=2×4+3Improper\, fraction = 2 \times 4 + 3

STEP 4

Calculate the improper fraction.
Improperfraction=2×4+3=8+3=11Improper\, fraction = 2 \times 4 + 3 = 8 + 3 = 11

STEP 5

Now we have the improper fraction, which is 114\frac{11}{4}.

STEP 6

Next, we multiply the improper fraction by the whole number.
Product=ImproperfractionWholenumberProduct = Improper\, fraction \cdot Whole\, number

STEP 7

Plug in the values for the improper fraction and the whole number to calculate the product.
Product=1148Product = \frac{11}{4} \cdot 8

STEP 8

To multiply the fraction by the whole number, we multiply the numerator of the fraction by the whole number and keep the denominator the same.
Product=1184Product = \frac{11 \cdot 8}{4}

STEP 9

Calculate the numerator of the product.
Product=884Product = \frac{88}{4}

STEP 10

Now we simplify the fraction by dividing the numerator by the denominator.
SimplifiedProduct=884=22Simplified\, Product = \frac{88}{4} = 22
The product of 2342 \frac{3}{4} and 88 is 2222.

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