HSPT Math - How to add and subtract fractions

Solve:

$\frac{1}{2}-\frac{3}{7}$

$\frac{1}{14}$

$\frac{3}{5}$

$-\frac{3}{5}$

$-\frac{1}{14}$

$\frac{1}{7}$

Explanation

The lowest common denominator of 2 and 7 is 14.

$\frac{1}{2}=\frac{7}{14}$

$\frac{3}{7}=\frac{6}{14}$

$\frac{7}{14}-\frac{6}{14}=\frac{1}{14}$

Find the sum of the following:

$5\frac{1}{8}+6\frac{3}{16}?$

Explanation

To get the decimal from a fraction, divide the numerator by the denominator

$\frac{1}{8}=0.125$

$5\frac{1}{8}=5.125$

$\frac{3}{16}=0.1875$

$6\frac{3}{16}=6.1875$

Which of the following statements demonstrates the associative property of addition?

None of the examples in the other responses demonstrates the associative property of addition.

Explanation

The associative property of addition states that to add three numbers, any two can be added first, followed by adding the sum to the third. Of the statements given, only

demonstrates this property, so it is the correct choice.

What is $\frac{5}{12}-\frac{3}8{}=?$

$\frac{1}{24}$

$\frac{2}4{}$

$\frac{6}{8}$

$\frac{5}{6}$

Explanation

To subtract fractions we must first ensure that we have the same denominator which is the bottom part of the fraction.

To do this we must find the least common multiple of the denominators.

The least common multiple is the smallest number that multiples of both of the denominators multiply to. For example, for 2 and 6 it would be 6, for 2 and 5 it would be 10, for 3 and 8 it would be 24.

In this case the LCM is .

We then multiply the numerator and denominator of the fractions by the numbers it takes to reach the LCM $\frac{5}{12}*\frac{2}{2}$ and $\frac{3}{8}*\frac{3}{3}$ to get the same denominator because anything divided by itself is one so the fractions maintain their same value as the numbers change into the format we need to determine the answer.

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction.

After doing this we then subtract the first numerator (top part of the fraction) from the second numerator and place the result over the new denominator

$\frac{10}{24}-\frac{9}{24}=\frac{1}{24}$

The final answer is $\frac{1}{24}$

Evaluate if $a = \frac{5}{7}$ and $b = -\frac{2}{5}$ .

$1\frac{4}{35}$

$\frac{-11}{35}$

$\frac{11}{35}$

$-1\frac{4}{35}$

Explanation

Evaluate if $a = \frac{5}{7}$ and $b = -\frac{2}{5}$

$\frac{5}{7} - (-\frac{2}{5}) =$

$\frac{5}{7} +\frac{2}{5}$ The subtraction of a negative changes the operation from subtraction to addition.

Find the Least Common Multiple of 7 and 5.

Multiples of 7 are 7, 14, 21, 28, 35.

Multiples of 5 are 5, 10, 15, 20 ,25, and 35.

You can also just multiply the denominators.

The LCM or the LCD of 7 and 5 is 35.

Create equivalent fractions with 35 as the denominator.

$\frac{5}{7} =\frac{25}{35}$ Both the numerator and denominator were multiplied by 5.

$\frac{2}{5} = \frac{14}{35}$ Both the numerator and denominator were multiplied by 7.

Now that the denominators are the same, just add the numerators.

$\frac{25}{35} +\frac{14}{35} = \frac{25+14}{35} = \frac{39}{35 } = 1\frac{4}{35}$

Evaluate:

Explanation

The sum of two numbers of unlike sign is the difference of their absolute values, with the sign of the "dominant" number (the positive number here) affixed:

Subtract vertically by aligning the decimal points, making sure you append the 3.2 with a placeholder zero:

$\underline{3.20}$

This is the correct choice.

Evaluate: $8 \tfrac{1}{4} - 5 \tfrac{7}{8}$

$2\tfrac{3}{8}$

$3\tfrac{5}{8}$

$3\tfrac{1}{2}$

$3\tfrac{7}{32}$

$3\tfrac{1}{8}$

Explanation

Rewrite as fractions with a common denominator:

$8 \tfrac{1}{4} - 5 \tfrac{7}{8}$

$8 \tfrac{2}{8} - 5 \tfrac{7}{8}$

Now, in the first number, "borrow" eight eighths from the units column:

$7 \tfrac{8+2}{8} - 5 \tfrac{7}{8}$

$7 \tfrac{10}{8} - 5 \tfrac{7}{8}$

Subtract fractions by subtracting denominators, then subtract integers.

$7 \tfrac{10}{8}$

$\underline{5 \tfrac{7}{8}}$

$2 \tfrac{3}{8}$

$\frac{9}{4}-\frac{3}{2}=?$

$\frac{3}{4}$

$\frac{15}{4}$

Explanation

To add or subtract fractions, you need a common denominator.

You can multiple the second fraction by two to get a common denominator of four.

$\frac{3}{2}\times\frac{2}{2}=\frac{6}{4}$

Then you just subtract the numerators to get

$\frac{9}{4}-\frac{6}{4}=\frac{3}{4}$ .

$-\frac{1}{3} - (-\frac{3}{4})$

$\frac{5}{12}$

$-\frac{5}{12}$

$1\frac{1}{12}$

$-1\frac{1}{12}$

Explanation

$-\frac{1}{3} - (-\frac{3}{4}) =$

$-\frac{1}{3} +\frac{3}{4}$ The subtraction of a negative changes the subtraction sign to a positive.

Find the LCD of 3 and 4 and convert to equivalent fractions, with the LCD as the denominator for both fractions.

The LCD is 12.

$-\frac{1}{3} = -\frac{4}{12}$ The numerator and the denominator were multiplied by 4.

$\frac{3}{4} = \frac{9}{12}$ The numerator and the denominator were multiplied by 3.

$-\frac{4}{12} + \frac{9}{12} = \frac{5}{12}$

Because the absolute value of 9 is greater than the absolute value of -4, the answer is positive.

Find the arithmetic mean of the following five numbers.

$\frac{2}{5}, \frac{1}{5},\frac{1}{2},\frac{3}{10}, \frac{2}{5}$

$\frac{9}{25}$

$\frac{7}{25}$

$\frac{2}{5}$

$\frac{6}{25}$

$\frac{3}{5}$

Explanation

Add the numbers, then divide by or, equivalently, multiply by $\frac{1}{5}$ .

$\frac{\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}}{5}$

$\frac{1}{5} \left(\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}\right )$

Find the common denominator of the terms we are adding.

$\frac{1}{5} \left(\frac{4}{10}+ \frac{2}{10}+\frac{5}{10}+\frac{3}{10}+ \frac{4}{10}\right )$

$\frac{1}{5} \left(\frac{4+2+5+3+4}{10} \right)$

Multiply and simplify.

$\frac{1}{5} \left(\frac{18}{10} \right)= \frac{1}{5} \left(\frac{9}{5} \right) = \frac{9}{25}$

How to add and subtract fractions

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