Use the distributive property to calculate each value mentally. 123 5 8 ⋅ 1 1 2 − 23 5 8 ⋅ 1 1 2 123 \frac{5}{8} \cdot 1 \frac{1}{2} - 23 \frac{5}{8} \cdot 1 \frac{1}{2} 123 8 5 ⋅ 1 2 1 − 23 8 5 ⋅ 1 2 1

Hey everyone here we are asked to solve the expression by using the distributive property. So here we are given the expression 256 and 2/5 times two and one half minus 56 2/5 times two and one half. So now our first step here in solving this expression is to use the distributive property but in reverse this means that we need to find a common factor between our two terms here and factor it out. So in this case we see that the left hand side term has a two and one half and this two and one half is on the right hand side as well so we can go ahead and factor out this value. So rewriting our expression, we have two and one half times the quantity of 256 and 2/5 minus 56 2/5. So now from here we just need to continue to simplify by subtracting these two terms in the parentheses. So we have two and one half times the quantity of 200. And now our next step in simplifying is to transform this mixed number here, this two and one half we need to transform it into an improper fraction. So our two and one half becomes 5/2 and again this is multiplied by 200. So now finding our product here five halves times simplifies to just 500 this is our answer here for choice B. Thanks for watching, I hope you found this video helpful and I'll see you again next time

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

1:48 minutes

Problem 139

Textbook Question

Use the distributive property to calculate each value mentally. $123 \frac{5}{8} \cdot 1 \frac{1}{2} - 23 \frac{5}{8} \cdot 1 \frac{1}{2}$

Verified step by step guidance

First, convert the mixed numbers into improper fractions for easier multiplication. For example, convert \$123 \frac{5}{8}$ and $1 \frac{1}{2}$ into improper fractions.

Express the problem as $\left(123 \frac{5}{8}\right) \times \left(1 \frac{1}{2}\right) - \left(23 \frac{5}{8}\right) \times \left(1 \frac{1}{2}\right)$ using the improper fractions.

Notice that both terms share a common factor of \$1 \frac{1}{2}$, so apply the distributive property: factor out $1 \frac{1}{2}$ from both terms.

Rewrite the expression as $\left(123 \frac{5}{8} - 23 \frac{5}{8}\right) \times 1 \frac{1}{2}$, simplifying inside the parentheses first.

Finally, subtract the two mixed numbers inside the parentheses and then multiply the result by \$1 \frac{1}{2}$ to find the answer.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. It is expressed as a(b + c) = ab + ac. This property helps simplify expressions and perform mental calculations efficiently.

Mixed Numbers and Improper Fractions

Mixed numbers combine whole numbers and fractions, such as 1 1/2. Converting mixed numbers to improper fractions (e.g., 1 1/2 = 3/2) simplifies multiplication and subtraction. Understanding this conversion is essential for accurate calculations.

Mental Math Strategies

Mental math involves performing calculations in your head without paper. Using properties like distributive property and converting mixed numbers helps break down complex problems into simpler parts, enabling quicker and more accurate mental computation.

Watch next

Master Introduction to Exponent Rules with a bite sized video explanation from Patrick

Start learning