Reduce to simplest form. -(3)/(7)+(5)/(2)=

Identify Common Denominator: Identify a common denominator for the fractions $ \frac{3}{7} $ and $ \frac{5}{2} $. The common denominator for 7 and 2 is 14, as it is the least common multiple of these two numbers.Convert to Equivalent Fractions: Convert each fraction to an equivalent fraction with the common denominator of 14. For $ \frac{3}{7} $, multiply the numerator and denominator by 2 to get $ \frac{6}{14} $. For $ \frac{5}{2} $, multiply the numerator and denominator by 7 to get $ \frac{35}{14} $.Rewrite Expression: Rewrite the original expression with the new fractions. The new expression is -$ \frac{6}{14} $ + $ \frac{35}{14} $.Add Fractions: Add the fractions now that they have a common denominator. - $ \frac{6}{14} $ + $ \frac{35}{14} $ = $ \frac{35}{14} - \frac{6}{14} $ = $ \frac{29}{14} $.Simplify Fraction: Simplify the fraction, if possible. The fraction $ \frac{29}{14} $ is already in its simplest form because 29 and 14 have no common factors other than 1.

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Math Problems

Grade 6

Multiply using the distributive property

Full solution

Q. Reduce to simplest form.

\newline

-\frac{3}{7}+\frac{5}{2}=

Identify Common Denominator: Identify a common denominator for the fractions $\frac{3}{7}$ and $\frac{5}{2}$ . $\newline$ The common denominator for $7$ and $2$ is $14$ , as it is the least common multiple of these two numbers.
Convert to Equivalent Fractions: Convert each fraction to an equivalent fraction with the common denominator of $14$ . $\newline$ For $\frac{3}{7}$ , multiply the numerator and denominator by $2$ to get $\frac{6}{14}$ . $\newline$ For $\frac{5}{2}$ , multiply the numerator and denominator by $7$ to get $\frac{35}{14}$ .
Rewrite Expression: Rewrite the original expression with the new fractions. $\newline$ The new expression is - $\frac{6}{14}$ + $\frac{35}{14}$ .
Add Fractions: Add the fractions now that they have a common denominator. $\newline$ - $\frac{6}{14}$ + $\frac{35}{14}$ = $\frac{35}{14} - \frac{6}{14}$ = $\frac{29}{14}$ .
Simplify Fraction: Simplify the fraction, if possible. $\newline$ The fraction $\frac{29}{14}$ is already in its simplest form because $29$ and $14$ have no common factors other than $1$ .