Question Solve $4 \frac{5}{8} \cdot\left(-1 \frac{3}{5}\right)$ . Choices: $1 \frac{1}{2}$ , $-4 \frac{3}{8}$ , $-\frac{296}{40}$ , $\frac{296}{40}$ .

Studdy Solution

STEP 1

Assumptions1. We are multiplying two mixed numbers $4 \frac{5}{8}$ and $-1 \frac{3}{5}$ . . We know that multiplication of two numbers with different signs (one positive and one negative) results in a negative number.

STEP 2

First, we need to convert the mixed numbers into improper fractions. The formula to convert a mixed number into an improper fraction is $\text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{umerator}$

STEP 3

Convert $\frac{5}{8}$ into an improper fraction.
$\text{Improper Fraction} = \times8 +5$

STEP 4

Calculate the improper fraction for $4 \frac{}{8}$ .
$\text{Improper Fraction} =4 \times8 + =37/8$

STEP 5

Convert $-1 \frac{3}{5}$ into an improper fraction.
$\text{Improper Fraction} = -1 \times5 +3$

STEP 6

Calculate the improper fraction for $-1 \frac{3}{5}$ .
$\text{Improper Fraction} = -1 \times5 +3 = -8/5$

STEP 7

Now we multiply the two improper fractions.
$\text{Product} = \frac{37}{} \times \frac{-}{5}$

STEP 8

Multiply the numerators together and the denominators together.
$\text{Product} = \frac{37 \times -8}{8 \times5}$

STEP 9

Calculate the product.
$\text{Product} = \frac{-296}{40}$

STEP 10

Now we simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD). The GCD of296 and40 is8.
$\text{implified Product} = \frac{-296/8}{40/8}$

STEP 11

Calculate the simplified product.
$\text{implified Product} = \frac{-37}{5}$

STEP 12

Convert the improper fraction back to a mixed number. The whole number is the quotient of the division, and the remainder is the numerator of the fraction.
$\text{Mixed Number} = -7 \frac{2}{5}$ So, the solution to $4 \frac{5}{8} \cdot\left(- \frac{}{5}\right)$ is $-7 \frac{2}{5}$ . However, this option is not available in the multiple choice answers. The closest option is $-\frac{296}{40}$ , which is the unsimplified version of our answer. Therefore, the correct choice is $-\frac{296}{40}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms