Question

remember
for problems 13–16, multiply.

1. \\(\frac{2}{3} \times 15\\)
2. \\(\frac{3}{5} \times 40\\)
3. \\(\frac{7}{8} \times 6\\)
4. \\(\frac{5}{9} \times 50\\)

for problems 17 and 18, combine like terms to write an equivalent expression.

1. \\(10y - y\\)
2. \\(5w + 12x + 20 + 10w + 9x\\)
3. write a word problem that can be solved by using \\(\frac{1}{2} \times \frac{3}{4}\\). then solve the problem.

Explanation:

Step1: Multiply fraction by integer

$\frac{2}{3} \times 15 = \frac{2 \times 15}{3} = 2 \times 5 = 10$

Step2: Multiply fraction by integer

$\frac{3}{5} \times 40 = \frac{3 \times 40}{5} = 3 \times 8 = 24$

Step3: Multiply fraction by integer

$\frac{7}{8} \times 6 = \frac{7 \times 6}{8} = \frac{42}{8} = \frac{21}{4}$

Step4: Multiply fraction by integer

$\frac{5}{9} \times 50 = \frac{5 \times 50}{9} = \frac{250}{9}$

Step5: Combine like terms (y terms)

$10y - y = (10-1)y = 9y$

Step6: Group and combine like terms

$5w + 12x + 20 + 10w + 9x = (5w+10w)+(12x+9x)+20 = 15w + 21x + 20$

Step7: Create & solve word problem

Word problem: Mia has $\frac{1}{2}$ of a pizza. She gives $\frac{3}{4}$ of her portion to her little brother. What fraction of the whole pizza does the brother get?
Calculation: $\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}$

Answer:

1. $10$
2. $24$
3. $\frac{21}{4}$
4. $\frac{250}{9}$
5. $9y$
6. $15w + 21x + 20$
7. Word problem: Mia has $\frac{1}{2}$ of a pizza. She gives $\frac{3}{4}$ of her portion to her little brother. What fraction of the whole pizza does the brother get?; Solution: $\frac{3}{8}$