ACT Math - Operations and Fractions

Simplfiy the following expression;

$\frac{2}{3}\times\frac{6}{8}\times\frac{4}{12}$

$\frac{1}{6}$

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{5}{6}$

Explanation

Multiply the numerators 2 x 6 x 4 = 48. Then multiply the denominators 3 x 8 x 12 = 288. The answer is 48/288. To simplify, divide both numerator and denominator by 48 to get 1/6.

What common number can you add to the numerator and denominator of $\frac{7}{19}$ to get $\frac{1}{2}$ ?

Explanation

Set up an equation where you add the same unknown number (x) to both the numerator and the denominator of the original fraction, and set the equation equal to $\frac{1}{2}$ .

$ewline \frac{7+x}{19+x}=\frac{1}{2}$

Cross-multiply the fractions to simplify.

$(7+x)\cdot (2)=(19+x)\cdot (1)$

Now, solve for x.

Simplfiy the following expression;

$\frac{2}{3}\times\frac{6}{8}\times\frac{4}{12}$

$\frac{1}{6}$

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{5}{6}$

Explanation

Multiply the numerators 2 x 6 x 4 = 48. Then multiply the denominators 3 x 8 x 12 = 288. The answer is 48/288. To simplify, divide both numerator and denominator by 48 to get 1/6.

What common number can you add to the numerator and denominator of $\frac{7}{19}$ to get $\frac{1}{2}$ ?

Explanation

Set up an equation where you add the same unknown number (x) to both the numerator and the denominator of the original fraction, and set the equation equal to $\frac{1}{2}$ .

$ewline \frac{7+x}{19+x}=\frac{1}{2}$

Cross-multiply the fractions to simplify.

$(7+x)\cdot (2)=(19+x)\cdot (1)$

Now, solve for x.

Solve for x where

$4\frac{1}{3}=x+1\frac{1}{2}$

$2\frac{5}{6}$

$3\frac{1}{5}$

$3\frac{5}{6}$

$5\frac{2}{5}$

$5\frac{2}{3}$

Explanation

To solve this, subtract 1 1/2 from both sides. Convert to common denominators.

4 1/3 – 1 1/2 = 4 2/6 – 1 3/6.

In order to subtract, you'll want to "borrow" from the 4 2/6. Rewrite 4 2/6 as 3 8/6 and then subtract 1 3/6 from this. Your solution is 2 5/6. Most calculators will also do these calculations for you.

Solve for x where

$4\frac{1}{3}=x+1\frac{1}{2}$

$2\frac{5}{6}$

$3\frac{1}{5}$

$3\frac{5}{6}$

$5\frac{2}{5}$

$5\frac{2}{3}$

Explanation

To solve this, subtract 1 1/2 from both sides. Convert to common denominators.

4 1/3 – 1 1/2 = 4 2/6 – 1 3/6.

Simplify the following into one fraction

$\frac{2}{7}\cdot\frac{12}{5}\cdot\frac{25}{6}$

$\frac{20}{7}$

$\frac{15}{35}$

$\frac{2}{5}$

$\frac{5}{6}$

$\frac{50}{42}$

Explanation

To multiply fractions you multiply the entire numerator and the entire denominator together. However, before we do that we can cancel anything from the denominator with anything in the numerator.

Six cancels with 12

$\frac{2}{7}\cdot\frac{\textbf{12}}{5}\cdot\frac{25}{\textbf{6}}=\frac{2}{7}\cdot\frac{2}{5}\cdot25$

5 cancels with 25

$\frac{2}{7}\cdot\frac{2}{\textbf5}\cdot\textbf{25}=\frac{2}{7}\cdot2\cdot5$

multiply it all out and get

$\frac{20}{7}$

Simplify the following into one fraction

$\frac{2}{7}\cdot\frac{12}{5}\cdot\frac{25}{6}$

$\frac{20}{7}$

$\frac{15}{35}$

$\frac{2}{5}$

$\frac{5}{6}$

$\frac{50}{42}$

Explanation

To multiply fractions you multiply the entire numerator and the entire denominator together. However, before we do that we can cancel anything from the denominator with anything in the numerator.

Six cancels with 12

$\frac{2}{7}\cdot\frac{\textbf{12}}{5}\cdot\frac{25}{\textbf{6}}=\frac{2}{7}\cdot\frac{2}{5}\cdot25$

5 cancels with 25

$\frac{2}{7}\cdot\frac{2}{\textbf5}\cdot\textbf{25}=\frac{2}{7}\cdot2\cdot5$

multiply it all out and get

$\frac{20}{7}$

Add the following fractions

$\frac{2}{5}+\frac{3}{4}+\frac{1}{12}$

$\frac{37}{30}$

$\frac{321}{240}$

$\frac{79}{60}$

$\frac{6}{240}$

$\frac{22}{60}$

Explanation

To add fractions you first must find the lowest common denominator. For these fractions it is 60. Then you must multiply the numerator and denominator by the number such that the denominator is equal to the LCD. For example $\frac{2}{5}$ gets multiplied by 12 (on both the numerator and denominator) because 5 times 12 is 60. When you do that you get the expression

$\frac{24}{60}+\frac{45}{60}+\frac{5}{60}$

then you just add the numerators and get

$\frac{74}{60}$

2 goes into both of those numbers so you get

$\frac{37}{30}$

Add the following fractions

$\frac{2}{5}+\frac{3}{4}+\frac{1}{12}$

$\frac{37}{30}$

$\frac{321}{240}$

$\frac{79}{60}$

$\frac{6}{240}$

$\frac{22}{60}$

Explanation

$\frac{24}{60}+\frac{45}{60}+\frac{5}{60}$

then you just add the numerators and get

$\frac{74}{60}$

2 goes into both of those numbers so you get

$\frac{37}{30}$

Operations and Fractions

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