((7)/(4)×(5)/(8))+((7)/(4)×(1)/(2))

Simplify First Multiplication: We will first simplify the multiplication within each fraction separately. The first multiplication is (7/4) × (5/8). To multiply fractions, we multiply the numerators together and the denominators together. So, (7 × 5) / (4 × 8) = 35 / 32.Simplify Second Multiplication: Now we will simplify the second multiplication, which is (7/4) × (1/2). Again, we multiply the numerators together and the denominators together. So, (7 × 1) / (4 × 2) = 7 / 8.Add Fractions: Next, we will add the two results together. We have 35/32 from the first multiplication and 7/8 from the second multiplication. To add fractions, we need a common denominator. The common denominator for 32 and 8 is 32.Convert to Common Denominator: We will convert 7/8 to have the common denominator of 32. To do this, we multiply both the numerator and the denominator by 4. So, 7/8 becomes (7 × 4) / (8 × 4) = 28/32.Add Fractions with Common Denominator: Now we can add the two fractions with the common denominator. So, 35/32 + 28/32 = (35 + 28) / 32.Add Numerators: We add the numerators together. 35 + 28 = 63. So, the combined fraction is 63/32.Check for Simplest Form: The fraction 63/32 is already in its simplest form because 63 and 32 have no common factors other than 1. Therefore, the simplified result of the expression is 63/32.

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$\left(\frac{7}{4} \times \frac{5}{8}\right)+\left(\frac{7}{4} \times \frac{1}{2}\right)$

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Algebra 1

Multiplication with rational exponents

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\left(\frac{7}{4} \times \frac{5}{8}\right)+\left(\frac{7}{4} \times \frac{1}{2}\right)

Simplify First Multiplication: We will first simplify the multiplication within each fractions" target="_blank" class="backlink">fraction separately. $\newline$ The first multiplication is $(\frac{7}{4}) \times (\frac{5}{8})$ . $\newline$ To multiply fractions, we multiply the numerators together and the denominators together. $\newline$ So, $(7 \times 5) / (4 \times 8) = \frac{35}{32}$ .
Simplify Second Multiplication: Now we will simplify the second multiplication, which is $(\frac{7}{4}) \times (\frac{1}{2})$ . Again, we multiply the numerators together and the denominators together. So, $(7 \times 1) / (4 \times 2) = \frac{7}{8}$ .
Add Fractions: Next, we will add the two results together. $\newline$ We have $\frac{35}{32}$ from the first multiplication and $\frac{7}{8}$ from the second multiplication. $\newline$ To add fractions, we need a common denominator. $\newline$ The common denominator for $32$ and $8$ is $32$ .
Convert to Common Denominator: We will convert $\frac{7}{8}$ to have the common denominator of $32$ . To do this, we multiply both the numerator and the denominator by $4$ . So, $\frac{7}{8}$ becomes $\left(\frac{7 \times 4}{8 \times 4}\right) = \frac{28}{32}$ .
Add Fractions with Common Denominator: Now we can add the two fractions with the common denominator. $\newline$ So, $\frac{35}{32} + \frac{28}{32} = \frac{(35 + 28)}{32}$ .
Add Numerators: We add the numerators together. $35 + 28 = 63$ . So, the combined fraction is $\frac{63}{32}$ .
Check for Simplest Form: The fraction $\frac{63}{32}$ is already in its simplest form because $63$ and $32$ have no common factors other than $1$ . $\newline$ Therefore, the simplified result of the expression is $\frac{63}{32}$ .